yield curve

Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues
by Alain Ruttiens
Published 24 Apr 2013

Contents Cover Series Title Page Copyright Dedication Foreword Main Notations Introduction Part I: The Deterministic Environment Chapter 1: Prior to the yield curve: spot and forward rates 1.1 INTEREST RATES, PRESENT AND FUTURE VALUES, INTEREST COMPOUNDING 1.2 DISCOUNT FACTORS 1.3 CONTINUOUS COMPOUNDING AND CONTINUOUS RATES 1.4 FORWARD RATES 1.5 THE NO ARBITRAGE CONDITION FURTHER READING Chapter 2: The term structure or yield curve 2.1 INTRODUCTION TO THE YIELD CURVE 2.2 THE YIELD CURVE COMPONENTS 2.3 BUILDING A YIELD CURVE: METHODOLOGY 2.4 AN EXAMPLE OF YIELD CURVE POINTS DETERMINATION 2.5 INTERPOLATIONS ON A YIELD CURVE FURTHER READING Chapter 3: Spot instruments 3.1 SHORT-TERM RATES 3.2 BONDS 3.3 CURRENCIES FURTHER READING Chapter 4: Equities and stock indexes 4.1 STOCKS VALUATION 4.2 STOCK INDEXES 4.3 THE PORTFOLIO THEORY FURTHER READING Chapter 5: Forward instruments 5.1 THE FORWARD FOREIGN EXCHANGE 5.2 FRAs 5.3 OTHER FORWARD CONTRACTS 5.4 CONTRACTS FOR DIFFERENCE (CFD) FURTHER READING Chapter 6: Swaps 6.1 DEFINITIONS AND FIRST EXAMPLES 6.2 PRIOR TO AN IRS SWAP PRICING METHOD 6.3 PRICING OF AN IRS SWAP 6.4 (RE)VALUATION OF AN IRS SWAP 6.5 THE SWAP (RATES) MARKET 6.6 PRICING OF A CRS SWAP 6.7 PRICING OF SECOND-GENERATION SWAPS FURTHER READING Chapter 7: Futures 7.1 INTRODUCTION TO FUTURES 7.2 FUTURES PRICING 7.3 FUTURES ON EQUITIES AND STOCK INDEXES 7.4 FUTURES ON SHORT-TERM INTEREST RATES 7.5 FUTURES ON BONDS 7.6 FUTURES ON CURRENCIES 7.7 FUTURES ON (NON-FINANCIAL) COMMODITIES FURTHER READING Part II: The Probabilistic Environment Chapter 8: The basis of stochastic calculus 8.1 STOCHASTIC PROCESSES 8.2 THE STANDARD WIENER PROCESS, OR BROWNIAN MOTION 8.3 THE GENERAL WIENER PROCESS 8.4 THE ITÔ PROCESS 8.5 APPLICATION OF THE GENERAL WIENER PROCESS 8.6 THE ITÔ LEMMA 8.7 APPLICATION OF THE ITô LEMMA 8.8 NOTION OF RISK NEUTRAL PROBABILITY 8.9 NOTION OF MARTINGALE ANNEX 8.1: PROOFS OF THE PROPERTIES OF dZ(t) ANNEX 8.2: PROOF OF THE ITÔ LEMMA FURTHER READING Chapter 9: Other financial models: from ARMA to the GARCH family 9.1 THE AUTOREGRESSIVE (AR) PROCESS 9.2 THE MOVING AVERAGE (MA) PROCESS 9.3 THE AUTOREGRESSION MOVING AVERAGE (ARMA) PROCESS 9.4 THE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) PROCESS 9.5 THE ARCH PROCESS 9.6 THE GARCH PROCESS 9.7 VARIANTS OF (G)ARCH PROCESSES 9.8 THE MIDAS PROCESS FURTHER READING Chapter 10: Option pricing in general 10.1 INTRODUCTION TO OPTION PRICING 10.2 THE BLACK–SCHOLES FORMULA 10.3 FINITE DIFFERENCE METHODS: THE COX–ROSS–RUBINSTEIN (CRR) OPTION PRICING MODEL 10.4 MONTE CARLO SIMULATIONS 10.5 OPTION PRICING SENSITIVITIES FURTHER READING Chapter 11: Options on specific underlyings and exotic options 11.1 CURRENCY OPTIONS 11.2 OPTIONS ON BONDS 11.3 OPTIONS ON INTEREST RATES 11.4 EXCHANGE OPTIONS 11.5 BASKET OPTIONS 11.6 BERMUDAN OPTIONS 11.7 OPTIONS ON NON-FINANCIAL UNDERLYINGS 11.8 SECOND-GENERATION OPTIONS, OR EXOTICS FURTHER READING Chapter 12: Volatility and volatility derivatives 12.1 PRACTICAL ISSUES ABOUT THE VOLATILITY 12.2 MODELING THE VOLATILITY 12.3 REALIZED VOLATILITY MODELS 12.4 MODELING THE CORRELATION 12.5 VOLATILITY AND VARIANCE SWAPS FURTHER READING Chapter 13: Credit derivatives 13.1 INTRODUCTION TO CREDIT DERIVATIVES 13.2 VALUATION OF CREDIT DERIVATIVES 13.3 CONCLUSION FURTHER READING Chapter 14: Market performance and risk measures 14.1 RETURN AND RISK MEASURES 14.2 VaR OR VALUE-AT-RISK FURTHER READING Chapter 15: Beyond the Gaussian hypothesis: potential troubles with derivatives valuation 15.1 ALTERNATIVES TO THE GAUSSIAN HYPOTHESIS 15.2 POTENTIAL TROUBLES WITH DERIVATIVES VALUATION FURTHER READING Bibliography Index For other titles in the Wiley Finance series please see www.wiley.com/finance This edition first published 2013 Copyright © 2013 Alain Ruttiens Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

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Since most of the time interest rates are higher with longer maturities, one talks of a “normal” yield curve if it is going upwards, and of an “inverse” yield curve if and when longer rates are lower than shorter rates. Alternatively, the term structure can be built on discount factors, as functions of the zero rates, but this way is less used in practice. Yield curves can be built with mid rates – the most usual way – or with borrowing or lending rates. The two main uses of a yield curve are: to determine the corresponding interest rate for a given maturity, by interpolation on the yield curve; to serve as the “spinal column” for the pricing of any kind of financial instruments involving future cash flows, such as bonds, stocks, and all kinds of derivative products.

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Hence, Cox, Ingersoll, and Ross proposed a similar model, but with a stochastic term in σ r1/2: (11.1bis) However, by modeling a single interest rate process, one forgets that interest rates are belonging to a set of rates, that is, the market yield curve. Inevitably, the output of the previous models applied to interest rates of different maturities will produce independent results, not fitting the observed yield curve! Hence, the need for a second generation of more ambitious processes for yield curve modeling: 11.3.2 Modeling the yield curve In a first approach, this was done through modeling a set of zero-coupon bonds, representing the yield curve. The simplest is the Ho and Lee model, which does not, however, incorporate the mean reversion feature.

Stigum's Money Market, 4E
by Marcia Stigum and Anthony Crescenzi
Published 9 Feb 2007

This strategy was deployed by many portfolio managers when the yield curve became steeper following the interest-rate cuts of the early 2000s. The main threats to the success of such a strategy are (1) that short-term rates might rise across the board and (2) that the yield curve might invert at the short end. These threats came to bear on the bond market in 2004 when the yield curve began to flatten and eventually FIGURE 11.1 Yield curve in an example of riding the yield curve inverted in response to the Fed’s interest-rate hikes, which began in June 2004. This eliminated the allure of riding the yield curve. Assume that an investor has funds to invest for three months.

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Before we go on, let us tell you a little bit about what the yield curve is. For simplicity’s sake, assume that when we say “yield curve,” we are talking about the yield curve for U.S. Treasuries. The yield curve is a chart that plots the yield on bonds against their maturities. The shape of the yield curve is generally upward-sloping, with yields increasing in ascending order as the maturities lengthen. In other words, a “normal” yield curve is one in which the yields on long-term maturities are higher than the yields on short-term maturities. The maturities generally included in yield curve graphs usually range from 12 In bond-land, “100 [cash] bonds” is understood to be $100 million face value.

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The few examples shown above clearly suggest that the yield curve truly is the bond market’s equivalent of a crystal ball. And it’s a tool that’s so simple to use that just about anyone can use it. Why the Treasury Yield Curve? The Treasury yield curve is by far the most closely followed yield curve. It is the first yield curve that market participants and forecasters look to for signals about the economy and the financial markets. There are two main reasons for this. First, because Treasuries are not at risk of default, the Treasury yield curve provides a “clean” look at where market participants believe interest rates should be along the various maturities.

Expected Returns: An Investor's Guide to Harvesting Market Rewards
by Antti Ilmanen
Published 4 Apr 2011

Implied spot yield curve one year forward Current spot yield curve Roll or slide is another nuanced aspect of carry. The random walk hypothesis assumes that the current yield curve is the best predictor of the future yield curve. If an upward-sloping yield curve remains unchanged over the next year, a long-term bond’s yield income advantage over the one-year bond will be augmented by capital gains through a “rolldown” effect. For example, if the current 4-year rate is 20 bp lower than the current 5-year rate, the assumption of an unexpected yield curve implies that the bond’s yield will fall by 20 bp simply as a result of aging and rolling down the yield curve.

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And perhaps they went too far, given the reappearance of extreme safe haven premia during the 2007–2008 systemic financial crisis. 9.3 ALTERNATIVE EX ANTE MEASURES OF THE BRP I discuss four ex ante measures: curve steepness and three smarter measures of the bond risk premium (BRP). Yield curve steepness (YC) Yield curve steepness is the simplest and most popular proxy for the ex ante BRP, but it has its flaws. Since the shape of the yield curve reflects the market’s expectations of future rate changes as well as the required BRP, some alternative measures (see below) try to isolate the BRP component by purging the rate expectation component from the YC. Empirical BRP estimates predicted by the forward rate curve (“C-P BRP”) Cochrane–Piazzesi (2005) find an even better predictor of future bond returns than the YC, loosely related to yield curve curvature.

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Using a control variable besides dividend yield in a regression can uncover such cyclical predictability (e.g., the consumption/wealth ratio or the consumption/dividends ratio). 16.4.2 Relation between yield curve shape and economic growth One series used to be an even better growth predictor than equity market return. Yield curve steepness has had an impressive ability to forecast GDP growth since World War II and inverted yield curves have been the most successful recession predictors. Many other financial series, notably credit spreads, also track business cycles but in a more contemporaneous fashion. The best explanation for the yield curve’s predictive ability is that it proxies for the Fed’s monetary policy stance: a steep (flat/inverted) curve reflects easy (tight) monetary policy.

The Global Money Markets
by Frank J. Fabozzi , Steven V. Mann and Moorad Choudhry
Published 14 Jul 2002

Two common sources of basis risk are index risk and reset risk. Index risk is a type of yield curve risk that arises because the ABS floater’s coupon rate and the interest rate of the underlying collateral are usually determined at different ends of the yield curve. Specifically, the floater’s coupon rate is typically spread off the short-term sector of the yield curve (e.g., U.S. Treasury) while the collateral’s interest rate is spread off a longer maturity sector of the same yield curve or in some cases a different yield curve (e.g., LIBOR). This mismatch is a source of risk. For example, for home equity loan-backed securities in which the collateral is adjustable-rate loans, the reference rate for the loans may be 6-month LIBOR while the reference rate for the bonds is usually 1month LIBOR.

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Both the collateral and the bonds are indexed off LIBOR, but different sectors of the Eurodollar yield curve. The reference rate for some home equity loans is a constant maturity Treasury. Thus, the collateral is based on a spread off the 1-month sector of the Eurodollar yield curve while the bonds are spread off a longer maturity sector of the Treasury yield curve. As another example, for credit cardbacked ABS the interest rate paid is usually a spread over the prime rate (a spread over the Treasury yield curve) while the coupon rate for the bonds is usually a spread over 1-month LIBOR (a spread over the Eurodollar yield curve). Reset risk is the risk associated with the mismatch between the frequency of the resetting of the interest rate on the floating-rate collateral and the frequency of reset of the coupon rate on the bonds.

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We expect LIBOR rates to be higher than the yields on bills of the same maturity because investors in Eurodollars CDs are exposed to default risk. Panel a of Exhibit 3.6 presents a Bloomberg graph of the yield curves for U.S. Treasury bills and LIBOR (out to a maturity of 1 year) on March 13, 2002. The Treasury bill yield curve is the lower curve and is represented by a solid black line. Panel b of the exhibit presents the data used in constructing the two yield curves. The fourth column indicates the spread between LIBOR and the Treasury bill yield for a given maturity. In order to understand the relationship between LIBOR and Treasury bill yields over time, we examine the period January 1, 1987 to December 31, 1999.

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined
by Lasse Heje Pedersen
Published 12 Apr 2015

An example of a classic fixed-income arbitrage trade is to sell short newly issued on-the-run bonds against long positions in older off-the-run bonds. Other classic trades include yield curve trades called butterflies, swap spread trades, mortgage trades, and fixed-income volatility trades. Before we get into the details of these trades, we first consider the fundamentals of bond yields and bond returns. The collection bond yields across all maturities are called the “yield curve” or the “term structure of interest rates.” Fixed-income arbitrage traders are obsessed with the yield curve. We discuss how the yield curve is characterized by its level, slope, and curvature, where the level is set by the central bank, and the slope and curvature are determined by expected future central bank rates and risk premiums.

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See also standard deviation (σ) volatility trades, fixed-income, 241, 262 Volcker, Paul, 206 Volcker Rule, 314 volume-weighted average price (VWAP), 67, 68–69 Waddell & Reed Financial, Inc., 155, 156f warrant, 269 Weil, Jonathan, 124 Whitehead, John, 313 Winton Capital Management, 225 Wood Mackenzie, 225 yield curve, 242–43, 243f; bond returns and, 245f (see also bond returns); hedging the risk of parallel moves in, 246; in overheated economy, 191; preferred habitat theory of, 249; Scholes on segmented clienteles concerned with, 263; speculating on the slope of, 190. See also bond yields; term structure of interest rates yield-curve carry trade, 187 yield curve trading, 13, 241, 264–65 yield to maturity (YTM), 179–80, 242, 243f; of corporate bond, 260; determinants of, 248–49; of swap, 259. See also yield curve zero-coupon bond yields, 242–43, 244, 247

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• Bond carry trade: A bond’s carry is its yield-to-maturity in excess of the financing rate. For example, a 10-year Japanese government bond has a high carry if the Japanese yield curve is steep. Some macro investors trade on bond carry across countries, buying bonds in countries with high carry while shorting bonds in countries with low carry. Such trades can be implemented with cash bonds (financed in repo), bond futures, or interest-rate swaps. • Yield-curve carry trade: Macro investors also trade bonds of different maturities within the same country. This is called a yield-curve trade. Chapter 14 provides more sophisticated measures of bond carry (that include a so-called roll-down effect) and discusses in more detail how to implement bond and yield-curve trades

My Life as a Quant: Reflections on Physics and Finance
by Emanuel Derman
Published 1 Jan 2004

We knew that we had to model the future behavior of all Treasury bonds, that is, the evolution of the entire yield curve. How to set about it was neither obvious nor easy. A stock price is a single number, and when you model its evolution, you project only one number into an uncertain future. In contrast, the yield curve is a continuum, a string or rubber band whose every point, at any instant, represents the yield of a bond with corresponding maturity. As time passes and bond prices change, the yield curve moves, as illustrated in Figure 10.3. To evolve the entire yield curve forward in time is a much more difficult task: Just as you cannot move the different points on a string completely independently of each other, because the string must stay connected, so bonds close to each other must stay connected, too.

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Consistent meant that it had to value all bonds in agreement with their current market prices; if it produced the wrong bond prices, it was pointless to use it to value options on those bonds. Finally, realistic meant that the model's future yield curves should move through ranges similar to those experienced by actual yield curves. Figure 10.3 Yield curves can vary during the day. When physicists build models, they often first resort to a toy representation of the world in which space and time are discrete and exist only at points on a lattice-it makes picturing the mathematics much easier.

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The initial one-year rate, as shown in Figure 10.4, was known from the current yield curve. As you looked further out into the future, rates could range over progressively wider values. Figure 10.4 The Black-Derman-Toy model focuses on the distribution of future short-term rates. Here, each dot corresponds to a particular value of the future one-year rate. The more time passes, the greater the uncertainty of future rates. Figure 10.5 How the distribution of future one-year rates is deduced from the current yield curve in the Black-Derman-Toy model. The two-year yield to maturity fixes the distribution of one-year rates after one year, the threeyear yield to maturity fixes the distribution of one-year rates after two years, and so on.

Frequently Asked Questions in Quantitative Finance
by Paul Wilmott
Published 3 Jan 2007

Thomas Ho and Sang-Bin Lee found a way around this, introducing the idea of yield curve fitting or calibration. See Ho and Lee (1986). 1992 Heath, Jarrow and Morton Although Ho and Lee showed how to match theoretical and market prices for simple bonds, the methodology was rather cumbersome and not easily generalized. David Heath, Robert Jarrow and Andrew Morton took a different approach. Instead of modelling just a short rate and deducing the whole yield curve, they modelled the random evolution of the whole yield curve. The initial yield curve, and hence the value of simple interest rate instruments, was an input to the model.

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The advantage of these models is that they are easy to solve numerically by many different methods. But there are several aspects to the downside. First, the spot rate does not exist, it has to be approximated in some way. Second, with only one source of randomness the yield curve is very constrained in how it can evolve, essentially parallel shifts. Third, the yield curve that is output by the model will not match the market yield curve. To some extent the market thinks of each maturity as being semi independent from the others, so a model should match all maturities otherwise there will be arbitrage opportunities. Models were then designed to get around the second and third of these problems.

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This allowed for a richer structure for yield curves. And an arbitrary time-dependent parameter (or sometimes two or three such) was allowed in place of what had hitherto been constant(s). The time dependence allowed for the yield curve (and other desired quantities) to be instantaneously matched. Thus was born the idea of calibration, the first example being the Ho & Lee model. The business of calibration in such models was rarely straightforward. The next step in the development of models was by Heath, Jarrow & Morton (HJM) who modelled the evolution of the entire yield curve directly so that calibration simply became a matter of specifying an initial curve.

The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett
by Jack (edited By) Guinan
Published 27 Jul 2009

An SEC yield is the percentage yield on a mutual fund based on a 30-day period. 323 324 The Investopedia Guide to Wall Speak Related Terms: • Annual Percentage Yield—APY • Dividend Yield • Yield to Maturity—YTM • Current Yield • Yield Curve Yield Curve Yield What Does Yield Curve Mean? The line on a chart that plots the interest rates, at a set point in time, of bonds that have equal credit quality but different maturity dates. The most frequently reported yield curve compares 3-month, 2-year, 5-year, and 30-year U.S. Treasury debt. This yield curve is used as a benchmark for other debt in the market, such as mortgage rates and bank lending rates. The curve also can be used to predict changes in economic output and growth. Maturity Copyright © 2006 Investopedia.com Investopedia explains Yield Curve The shape of the yield curve is scrutinized closely because it can indicate future changes in interest rates and economic activity.

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Related Terms: • Accrual Accounting • Cost of Goods Sold—COGS • Inventory • Asset Turnover • Gross Profit Margin Inverted Yield Curve Yield What Does Inverted Yield Curve Mean? An interest rate environment in which long-term debt instruments have lower yields than do short-term debt instruments of the same credit quality. This type of yield curve is the rarest of the three main curve types and is considered a predictor of economic recession. Maturity Copyright © 2006 Investopedia.com Partial inversion occurs when only some of the short-term Treasuries (5 or 10 years) have higher yields than the 30-year Treasuries; an inverted yield curve sometimes is referred to as a negative yield curve. Investopedia explains Inverted Yield Curve Historically, inversions of the yield curve have preceded many U.S. recessions.

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Investopedia explains Inverted Yield Curve Historically, inversions of the yield curve have preceded many U.S. recessions. Because of this historical correlation, the yield curve often is seen as an accurate indicator of the turning points of the business cycle. An inverse yield curve predicts lower interest rates in the future as longer-term bonds are being demanded, sending the yields down. The Investopedia Guide to Wall Speak 147 Related Terms: • Interest Rate • Treasury Bond—T-Bond • Yield Curve • Treasury Bill—T-Bill • Treasury Note Investment Bank (IB) What Does Investment Bank (IB) Mean? A financial intermediary that performs a variety of investment services, including underwriting, acting as an intermediary between an issuer of securities and the investing public, facilitating mergers and other corporate reorganizations and also acting as a broker for institutional clients.

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation
by Richard Bookstaber
Published 5 Apr 2007

At regular intervals the U.S. government issues bonds of varying maturities, from 30 days up to 30 years, with the longer-term bonds typically yielding higher interest rates than the shorter-term ones, to reflect the risk of having your money tied up longer. Plotting these payouts forms the well-known yield curve. Although the prices of the bonds and their respective yields vary as circumstances change—inflation, recession, war—each interest rate along the yield curve is flexibly but securely tethered to its neighboring rates in a way that can be described mathematically. CRUNCH TIME AT MORGAN STANLEY The job of the quants descending on Wall Street was to exploit the relationships along the yield curve, to develop mathematical models that would tease a higher return out of a bond portfolio or a bond trading operation than the green-eyeshade gang could.

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Meanwhile, in Orange County, California, treasurer Robert Citron had been structuring trades with the help of friends at Merrill Lynch to borrow on the short end of the yield curve to finance positions in the usually higher-yielding intermediate-term rates. Citron’s strategy depended on short-term interest rates remaining relatively low when compared with medium-term interest rates. This they did in the early 1990s, so Citron’s yield curve bet made money and everyone was happy, with no questions asked. Even in early 1994, when his strategy began to go south, he survived an election that focused attention on his financial management, convincing voters that the criticisms were just so much politically motivated rhetoric.

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Markets either go up, go down, or stay the same, so if you are losing money in one there are bound to be others that will be losing at the same time. That does not mean the two are functionally linked. Another possibility was that the arb model did not pick up all of the factors affecting interest rates. The model was a proprietary yield curve model dubbed the “two plus” because it looked at the yield curve as two factors, plus a parameter to signal the effects of Federal Reserve policy shifts. The two-plus model was the citadel of intellectual capital for the group. It was a closely guarded secret, although, despite the group’s best efforts, it found its way to a number of other firms as talent was periodically bid away. 85 ccc_demon_077-096_ch05.qxd 2/13/07 A DEMON 1:45 PM OF Page 86 OUR OWN DESIGN The model was developed by Bill Krasker in the mid-1980s shortly after he came to Salomon from a brief stint teaching at Harvard.

The Financial Crisis and the Free Market Cure: Why Pure Capitalism Is the World Economy's Only Hope
by John A. Allison
Published 20 Sep 2012

The inflation rate using the “old” CPI is significantly higher than that using Greenspan’s calculation.13 Could the Fed be making improper decisions based on miscalculating the CPI? At best, the calculation of the CPI is more art than science. After he became chairman of the Federal Reserve in early 2006, Bernanke rapidly raised interest rates and created an inverted yield curve. An inverted yield curve is one in which short-term rates are higher than long-term rates, and even Fed researchers acknowledge that an inverted yield curve tends to trigger recessions.14 Because bankers had been misled by Greenspan’s often-spoken concern about deflation, many of them had extended their bond portfolios, as this was one of the few areas where they could make long-term profits based on Greenspan’s deflation scenario.

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Also, the unanticipated pace and magnitude of rising interest rates left bankers in a very difficult position. Inversions of yield curves are an unusual phenomenon. Typically, investors will invest for a longer duration only if they can earn a higher interest rate, because, other things being equal, the longer the investment, the greater the risk and the lower the liquidity. Markets practically never invert yield curves. It is interesting that Bernanke’s decision to both raise short-term interest rates (to a peak of 5.25 percent) and invert the yield curve must have reflected his realization that Greenspan’s policies had been inflating the economy and leading to misinvestment (overinvestment in housing).

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What is sad, however, is that even though at some level Bernanke knew that the Fed had made major mistakes, this is not what he discussed publicly. He said repeatedly that the inverted yield curve would not cause a recession, but would simply slow the rate of inflation. While he mentioned the housing market occasionally, mostly by claiming that there was no bubble,15 his focus was primarily on commodity prices. He held the inverted yield curve for more than a year (from July 2006 to January 2008), one of the longest yield-curve inversions ever. The subsequent Great Recession, which lasted through June 2009 (and, practically speaking, continues in December 2011), began in December 2007.

Inside the House of Money: Top Hedge Fund Traders on Profiting in a Global Market
by Steven Drobny
Published 31 Mar 2006

I have never seen a yield curve that was as mispriced as the yen curve at that time. Other great trades over the years were curvature and conditional steepener type trades on the U.S. yield curve back in 2001 when nobody understood them. Now everyone understands them so there is not much juice left in it. The trade is where you buy a receiver swaption or a call on the oneyear interest rate one-year forward, and sell the same on the 10-year interest rate.There is a slight macro bias to this trade as it is a pure curve trade, which I consider more macro than RV. We built models of the whole yield curve out to 30 years to see what we thought the shape of the curve would be at any given rate level, how convex we thought the curve should be, why it should be that convex, and so on.

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Because as a control freak, you’re always looking out ahead of you, you’re looking out ahead for trouble, and that’s exactly what you have to do in markets, is try to look forward. So much of market talk, market analysis, and trading is based on what’s happened in the past.“The yield curve is flat, therefore it tells you it’s a recession,” or “The yield curve is steep, which tells you there’s going to be a recovery.”Those types of historical examples are of very little value, so a control freak is always trying to look forward and trying to look ahead. What do you think differentiates a good analyst and a good trader?

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Our risk is not limited to Barclays’ outstanding liabilities.We are actively managing risk and seeking a positive absolute return while being limited by the firm’s value at risk (VAR) model, regulatory capital limits, and balance sheet limits. We look to maximize current income for a given unit of risk. As a result, we tend to be in the front end of the yield curve as opposed to the back end because it’s better to roll one billion one-year notes for 10 years than to buy 100 million 10-year bonds ceteris paribus.The VAR would be the same if they had the same volatility but with the one-year notes, you get much more current income. By concentrating risk in the front end of the yield curve, the only thing that can really make me right or wrong is a central bank. A central bank has the ability to enhance or diminish my carry, and we want carry.

Investing Amid Low Expected Returns: Making the Most When Markets Offer the Least
by Antti Ilmanen
Published 24 Feb 2022

The bond risk premium (BRP), or term premium, is the (realized or expected) excess return of a long-term government bond over cash. It is thus the reward for duration extension, for bearing interest rate risk. The simplest forward-looking measure of this premium is yield curve steepness or the term spread, for example, between 10-year Treasury bonds and 1-month Treasury bills. The yield curve reflects both the required BRP and market's interest rate expectations. Yield curve steepness is thus a noisy measure of either part. Better BRP proxies try to strip out the unobservable rate expectations from the curve. Figure 4.10 US Long- and Short-Term Treasury Yields and Their Spread, Jan 1900–Sep 2021 Sources: AQR, FRED (St.

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For some institutions, the long bond is arguably the riskless (liability-matching) asset. 27 Logically, the survey-based BRP is a better predictor of future bond returns than the term spread (yield curve steepness) since it subtracts the expectations-related noise and should give a better risk premium measure. Yet, empirically the yield curve has been the better predictor of near-term returns. Apparently, expectational errors have contributed to yield curve's predictive ability, besides time-varying term premia. Ex-post predictability of forecast errors may not have been irrational or easy to identify in real time. They may reflect structural changes that investors could not foresee at the time.

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For now, real bond yields are surely lower than real growth expectations, and this improves fiscal space (the sustainability of a given amount of government deficits and debts) and is clearly influencing today's policymakers around the world. Current Outlook Low or negative bond yields sound bad for bond investors, let alone if one expects some mean reversion to more normal yields or a meaningful uptick in inflation. However, yield curve steepness matters more than yield level for near-term excess bond returns or for currency-hedged bond returns, and most countries' yield curves are likely to remain upward sloping. The diversification argument remains strong as long as one believes that government bond yields can fall further in those crucial equity bear market scenarios when the safe-haven service is most valuable.

Fed Up!: Success, Excess and Crisis Through the Eyes of a Hedge Fund Macro Trader
by Colin Lancaster
Published 3 May 2021

The first panel is focused on the fixed income markets. They’re talking about the massive yield curve flattening we’ve witnessed over the past two months. This is not normal, they explain: A normal yield curve should have a nice positive upward slope. Longer-term yields should be higher than shorter-term yields. A nice positive upward slope means that you’re paying a higher rate to borrow money for a longer period of time than for a shorter period of time. A sign of a healthy market. Simply put, a flat yield curve means that you pay the same to borrow money for one year as you do for ten or thirty years.

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One of the panelists offers an explanation: An upward sloping yield curve means that folks expect growth to continue into the future, a sign of optimism and a healthy economy. The banking system lies at the center of the economy, and an upward sloping curve helps them fulfill their role as lenders: they pay you to borrow your deposits and then lend at higher rates further out the curve. A flattening yield curve indicates that the yield spread between long-term and short-term bonds is decreasing. Flat (or even worse, inverted) yield curves mean the economy is slowing and the central banks need to cut rates.

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We’re in a ten-year bull market and are starting to make money again. A lot of money. It’s been a while since we had a month like this. It’s time to celebrate. Even the recent yield curve inversions, such as the three-month/ten-year Treasury spread, are back to positive.1 These positives might just be a nail in the coffin in terms of the predicted upcoming recession. After all, they say the market is the best predictor of recessions, and yield curve inversions like this don’t lie. They’re never wrong. But not today. The Federal Reserve—the world’s biggest central bank—is pivoting. Jerome (Jay) Powell, the head of the Fed, is making a mid-cycle adjustment that will drive stocks higher.

The Lords of Easy Money: How the Federal Reserve Broke the American Economy
by Christopher Leonard
Published 11 Jan 2022

Investors can buy a portion of the CLO, and then collect the payments that are made on the underlying loans. If the loans default, investors can lose their money. CLOs fared much better during the crash of 2008, which made them an attractive investment during the 2010s. COMPRESS THE YIELD CURVE: This is what the Fed did through quantitative easing, and it refers to the yield curve on U.S. Treasury bills (which basically affect the yield curve of everything else). In normal times, the yield curve rises on Fed Treasurys as they go out into the future, meaning the rates are higher on Treasurys out into the future. A Treasury due in ten years pays a higher rate, or yield, than a Treasury due in three months.

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This pushes the bank to search for earnings out there in the risky wilderness. A riskier loan might pay a higher interest rate, or a higher “yield,” as the bankers call it. When banks start hunting for yield, they are moving their cash further out on the yield curve, as they say, into the riskier investments. Life at the zero bound pushes banks way down the yield curve. What does a bank have to lose? A risky bet beats nothing. And this isn’t just a side effect of keeping rates at zero. “That’s the whole point,” Hoenig explained, many years later. “The point was to get people willing to take greater risk, to get the economy started again.

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If I am a super-sketchy borrower, then I might need to offer someone a 19 percent rate to convince them to lend me money. If I am the U.S. government, I might only have to offer someone 1.1 percent to persuade them to lend me money. INVERTED YIELD CURVE: A condition in which debt markets enter the rare state when interest rates (or yields, as they call them) paid for long-term debt become lower than interest rates paid for short-term debt. Most people interpret an inverted yield curve as a signal that a recession is about to happen. JUNK BOND DEBT: A form of corporate bond that is so risky it is considered “junk.” Junk debt carries high interest rates to compensate for the high risk of making the loan.

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
by Satyajit Das
Published 15 Nov 2006

Nero would have instantly recognized the leverage in the structure. The trade was very sensitive to interest rates. If rates increased across the yield curve, then the spread increased. If the yield curve flattened (the difference in rates between the five year CMT and the 30 year Treasury bond decreased), then the spread increased. An increased spread resulted in P & G’s cost of funding increasing. If the spread increased above 75 bps, then the benefit of the swap was eroded and P & G’s cost of funds rose above CP rates. P & G had exposure to the slope of the yield curve (in particular to changes in the five year CMT rate). If the price of the 30 Treasury bond is 98.5 and the five year CMT rate is 5.85% pa, then the spread is 118 bps.

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There are subtle problems. Is the income on the asset a known known? In the case of shares, dividends are a known unknown and tend to cause heartache. Also we need a yield curve; that is, the interest rates for borrowing and lending for different dates. Interest rates are frequently not available for every maturity. Quants have elaborate models for creating ‘complete’ and ‘parsimonious’ yield curves. I have no idea why the yield curve has to be stingy, that is, parsimonious. The rocket scientists emphasize that this is important, citing Occam’s razor. Occam was a fourteenth century logician and Franciscan friar in the English county of Surrey.

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Budi’s excitement was palpable. ‘Bank advise us,’ Adewiko added quickly. ‘Bank give us detail presentation. They say dollar yield curve very steep. Get value from steep curve using arrears swap.’ Adewiko displayed surprising animation. ‘Bank know Greenspan. Play tennis with him.’ I must have looked surprised. ‘Bank advise us,’ Adewiko said gloomily, remembering the script. I referred to my notes. ‘Then, you terminated the arrears swap.’ ‘Take profit, take profit,’ Budi interrupted. ‘Dollar yield curve flatten. We take profit.’ DAS_C01.QXD 5/3/07 11:45 PM Page 7 P ro l o g u e 7 I could imagine what had happened.

The Concepts and Practice of Mathematical Finance
by Mark S. Joshi
Published 24 Dec 2003

Develop an analytic formula for its price if the forward rate follows geometric Brownian motion. 14 The pricing of exotic interest rate derivatives 14.1 Introduction The critical difference between modelling interest rate derivatives and equity/FX options is that an interest rate derivative is really a derivative of the yield curve and the yield curve is a one-dimensional object whereas the price of a stock or an FX rate is zero-dimensional. One might be tempted to think that as most movements of the yield curve are up and down it is unnecessary to model the one-dimensional behaviour. However, the yield curve can and does change shape over time, and we shall see that for certain options these changes are the source of most of the option's value. From time to time, yield curves also undergo qualitative changes in shape. For example, the UK yield curve changed from being upward-sloping to being humped in the early 1990s.

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There are, in fact, many yield curves for each currency whose levels depend on the riskiness of the instruments involved. We discuss the curves for sterling but the issues are essentially the same for the euro and US dollar curves. We will generally talk about constructing discount curves rather than yield curves, as the discount curve is just the price of a zero-coupon bond as a function of maturity which is what we generally want. On the other hand, the yield curve is a notional measure of the effective annual interest rate which we would receive for investing in such a bond. The yield curve is useful from a qualitative point of view as it strips out redundant information by converting everything to interest rates, but to work mathematically with the yield curve is simply annoying.

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The interesting thing about the reversing pair is that its value is very insensitive to changes in the overall level of the yield curve. If interest rates go up by 1%, then we gain on the first forward-rate agreement but lose a similar amount on the 319 320 The pricing of exotic interest rate derivatives second. If, however, the shape of the yield curve changes so that the first rate goes down and the second rate goes up, then we lose on the first and lose on the second. Thus the value of the reverse contract reflects changes in the shape but not the level of the yield curve. In particular, the reverse contract is sensitive to the slope of the curve: a change in slope means money won or lost.

The Money Machine: How the City Works
by Philip Coggan
Published 1 Jul 2009

To understand why, we must look at the yield curve. The Yield Curve We have already proposed a general principle of finance – that lesser liquidity demands greater reward. That being the case, longer-term instruments should always bear a higher interest rate than short-term ones. This is not always true. Long-term rates can be the same as, or lower than, those of short-term instruments. A curve can be drawn which links the different levels of rates with the different maturities of debt. If long-term rates are above short-term ones, this is described as a positive or upward-sloping yield curve. If short-term rates are higher, the curve is described as negative or inverted.

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They may do so because they fear that they will need the funds suddenly but will be unable to obtain them, or they may be worried about the possibility of default. Borrowers (in particular, businesses) will be prepared to pay higher interest rates in order to secure long-term funds for investment. Thus, other things being equal, the yield curve will be upward-sloping. The expectations theory holds that the yield curve represents investors’ views on the likely future movement of short-term interest rates. If one-year interest rates are 10 per cent and an investor expects them to rise to 12 per cent in a year’s time, he will be unwilling to accept 10 per cent on a two-year loan. It would be more profitable for him to lend for one year and then re-lend his money at the higher rate.

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It would be more profitable for him to lend for one year and then re-lend his money at the higher rate. A two-year loan will therefore have to offer at least 11 per cent a year before the investor will be attracted. Thus if interest rates are expected to rise, the yield curve will be upward-sloping. If investors expect short-term interest rates to fall, however, they will seek to lend long-term. That will increase the supply of long-term funds and bring down their price (i.e. long-term interest rates). Thus the yield curve will be downward-sloping. What determines investors’ expectations of future interest-rate movements? Much may depend on future inflation rates. If inflation is set to rise, then price rises will absorb much of an investor’s interest income.

The Long Good Buy: Analysing Cycles in Markets
by Peter Oppenheimer
Published 3 May 2020

In the absence of inflation pressures, monetary policy may remain much looser and reduce the risks of recession and, by association, bear markets. The yield curve. Related to the point about inflation, tighter monetary policy often leads to a flattening, or even inverted, yield curve. Because many, although by no means all, bear markets are preceded by periods of monetary policy tightening, we find that flat yield curves, prior to inversion, are also followed by low returns or bear markets. In recent years the impact of QE and falling inflation expectations (term premia), may have weakened the reliability of this signal.4 As a consequence, we use the 3-month to 10-year measure, with a focus on the short end of the yield curve (0–6 quarter).

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This is particularly true – as in the recent cycle – when the starting level of interest rates is very low as rising bond yields, alongside growth expectations, may reflect more confidence that policy is working and that recessionary risks are fading. By the same token, a steepening yield curve (long-term bond yields rising above the levels of short-term interest rates) would generally imply a supportive central bank monetary policy, and an inverted yield curve, when bond yields are below short-term, policy-driven interest rates, would tend to reflect a restrictive monetary stance. Note 1 The output gap is usually described as the amount by which the actual output of an economy falls short of its potential output.

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Available at https://www.bis.org/publ/work114.html 3 Oppenheimer, P., and Bell, S. (2017). Bear necessities: Identifying signals for the next bear market. London, UK: Goldman Sachs Global Investment Research. 4 A useful discussion about the value of the yield curve in predicting recessions can be found in Benzoni, L., Chyruk, O., and Kelley, D. (2018). Why does the yield-curve slope predict recessions? Chicago Fed Letter No. 404. 5 A discussion of a broad recession risk indicator and the private sector imbalance can be found in Struyven, D., Choi, D., and Hatzius, J. (2019). Recession risk: Still moderate. New York, NY: Goldman Sachs Global Investment Research.

The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal
by Ludwig B. Chincarini
Published 29 Jul 2012

This is also a mortgage trade, one that caused a lot of trouble for hedge funds in 2008. LTCM’s fixed-income portfolio included butterfly yield curve trades. A butterfly trade is typically one in which a trader is long the 30-year bond and the 5-year bond, but short the 10-year bond. The trade is neutral to general interest rate movements, but takes a view that the yield curve will become more hump shaped. A trader could take the other view by changing the long positions to short positions. Either view could apply to any part of the yield curve, not just the 5-10-30 combo. In 1998, LTCM had a relative butterfly trade on in Germany and the UK.

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Box 2.2 Salomon Arb Group Interview Question Question: Your portfolio group strongly believes that the yield curve is going to flatten very soon. It could be that short-term rates will rise or long-term rates will fall or some combination of the two. Suppose also that you have three instruments available: a 30-year zero-coupon bond, a 1-year Treasury bill, and a cash account. Suppose the modified duration of the 30-year is 28 and the modified duration of the 1-year is 1. What strategy should you pursue to benefit from your beliefs? Suggested Solution: The investor would ideally like to have no interest-rate exposure, but take a view on the flattening yield curve. Thus, one would like to hedge parallel yield curve shifts, but take advantage of the nonparallel moves.

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They could implement it with government securities or swaps, but typically executed it with swaps. The trade is short the 30-year and 5-year areas of the yield curve and long the 10-year part of the curve. It’s constructed to eliminate interest-rate risk (duration neutral) and eliminate curve-slope risk. This position lost quite a bit in 2008. PGAM (and others) had a large position in this trade across a variety of different currencies. For PGAM, this was a hedge position, designed to diversify its holdings. This trade should have done well in a crisis, when the yield curve typically steepens and the 10- to 30-year part of the curve steepens more than the 5- to 10-year area.

What's Next?: Unconventional Wisdom on the Future of the World Economy
by David Hale and Lyric Hughes Hale
Published 23 May 2011

It also shows a certain degree of confidence that Asian central bankers always seemed to lack. So, on a structural basis, it is encouraging. However, the hawkishness of Asia’s central banks also means that while OECD yield curves are steep and likely to remain so for the foreseeable future, Asian yield curves are now flattening rapidly all across the board. One amazing development is that the US (and German) yield curves have, since 2009, continued to shift lower in spite of the economic recovery. In Asia, we are seeing exactly the opposite, with yield curves flattening (in Malaysia, Indonesia, China, Thailand, Australia, etc.) or shifting higher (India), a divergence in trend that can only logically be explained by the differences in monetary policy.

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In Asia, we are seeing exactly the opposite, with yield curves flattening (in Malaysia, Indonesia, China, Thailand, Australia, etc.) or shifting higher (India), a divergence in trend that can only logically be explained by the differences in monetary policy. And, of course, this should logically have an impact on currency markets since steep yield curves often weaken currencies, while flat or inverted yield curves strengthen them (cash becomes harder to find, thereby inviting companies and individuals to repatriate capital from abroad, etc.). In other words, the differences in monetary policies between the East and the West should ensure that Asian currencies remain well bid. But it also means that most Asian indices face some new headwinds. Indeed, most Asian equity indices are typically comprised of 20–25 percent of exporting stocks (which should struggle as Asian currencies move higher) and 30–35 percent of Asian financials (for whom the flattening yield curves could prove a headwind).

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Indeed, most Asian equity indices are typically comprised of 20–25 percent of exporting stocks (which should struggle as Asian currencies move higher) and 30–35 percent of Asian financials (for whom the flattening yield curves could prove a headwind). In other words, investors into Asia who decide to solely get exposure through benchmark ETFs are likely investing more than half of their money in what should prove to be “dead money.” Asia’s very different cyclical and policy outlook argues against investing in indices and instead for concentrating on the parts of the market that will benefit from the higher currencies and lower long-term interest rates. This of course includes long-dated Asian government bonds, high-dividend yield-paying stocks (which tend to always outperform when yield curves flatten and/or invert), utility stocks, local consumption stocks, and all the “stable growth” stocks, whether pharmaceuticals, consumer staples, software and tech stocks, and so on.

A Primer for the Mathematics of Financial Engineering
by Dan Stefanica
Published 4 Apr 2008

BONDS. 72 which is equivalent to flB ~ -fly D. (2.59) B In other words, the percentage change in the price of the bond can be approximated by the duration of the bond multiplied by the parallel shift in the yield curve, with opposite sign. For very small parallel shifts in the yield curve, the approximation formula (2.59) is accurate. For larger parallel shifts, convexity is used to better capture the effect of the changes in the yield curve on the price of the bond. Definition 2.5. The convexity C of a bond with price B and yield y is 1 82 B C=B8 y 2· 2.8. NUMERICAL IMPLEMENTATION OF BOND MATHEMATICS 73 From (2.62) and (2.64), we conclude that y = r(O, T).

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(J" Thus, the implied volatility approximate value is within 0.015% of the volatility used to price the call option, which is remarkably good accuracy. 0 I(J" - (J"imp,approxl CHAPTER 5. TAYLOR'S FORMULA. TAYLOR SERIES. 170 5.6 Connections between duration and convexity Recall from section 2.7 that bond duration measures the change in the price of a bond with respect to changes in the yield curve, while bond convexity measures the change of the duration of a bond with respect to changes in the yield curve, i.e., D= 1 82B C = B 8 y 2' 1 8B and B 8y (5.94) Also, recall that the value B of a bond with yield y paying cash-flows Ci and time t i , i = 1 : n, is B = 2:7=1 Cie-yti. To emphasize that the value of the bond is a function of its yield, we denote B by B (y), i.e., n B(y) = L Cie- yti

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The value at time of B(t) currency units at time t is r(t) = lim ~ . B(t + dt) - B(t) = B'(t). dt-70 dt B(t) B(t) ----------------------2We note, and further explain this in section 2.7.1, that r(O,t) is the yield of a zero~ coupon bond with maturity t. The zero rate curve is also called the yield curve. r(T) dT), V t > 0; (2.39) from (2.39) is called the discount factor. r(O, t) = ~ t rt r(T) dT. (2.40) 10 In other words, the zero rate r(O, t) is the average of the instantaneous rate r (t) over the time interval [0, t] . If r( t) is continuous, then it is uniquely determined if the zero rate curve r(O, t) is known.

The Volatility Smile
by Emanuel Derman,Michael B.Miller
Published 6 Sep 2016

Figure 8.4 shows the implied volatility surface for the S&P 500 on December 31, 2015. Just as the yield curve at a given time is a concise description of bond prices and the bond market, so, for a particular underlier at a given time, the implied volatility surface provides a summary description of its options market. Whereas bonds are distinguished by their time to maturity, options are distinguished by both a time to expiration and a strike, and so require a surface rather than a curve. As with the yield curve, describing a natural volatility surface mathematically can be challenging, especially because one has to worry about how to interpolate from discrete observations to a continuous surface without violating no-arbitrage constraints.

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When we extend the BSM model to 135 The Smile 0.35 Implied Volatility 0.3 0.25 0.2 0.15 0.1 0 0.5 Time to Expiration (years) 1 1.5 2 1.3 1.2 1.1 1 0.9 0.8 Strike/Index FIGURE 8.4 Volatility Surface, S&P 500, December 31, 2015 Source: Bloomberg. incorporate the smile, we shall see that many of the approaches take their inspiration from stochastic yield curve models. It’s often convenient to be able to describe the characteristic shape of a volatility surface in terms of one number, a spread, similar to the way one characterizes the slope of the yield curve in terms of the 10-year–2-year spread. A popular quotable spread for options is the so-called volatility skew, the change in implied volatility between two different strike prices. Figure 8.5 shows two volatility smiles.

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To understand why, first consider the behavior of short-term interest rates in one-factor short-rate term structure models. A typical yield curve is upward sloping for short maturities and flattens beyond about 20 years. As a result, in a one-factor term structure model (e.g., Black-Derman-Toy, 1990), the initial calibration requires that average shortterm rates in the interest rate tree increase in the near term and then stop increasing beyond 20 years. This means that within the calibrated model, the yield curve in 20 years becomes relatively flat rather than upward sloping. It’s disturbing to have a term structure model that makes consistently biased predictions of a relatively flat term structure in 20 years when yield curves are generally upward sloping.

The Deficit Myth: Modern Monetary Theory and the Birth of the People's Economy
by Stephanie Kelton
Published 8 Jun 2020

Anyone who tells you that fiscal deficits must force interest rates higher has forgotten their World War II history and ignored recent experience, and not just in the United States. Since 2016, Japan’s central bank has been explicitly targeting its yield curve.31 That means the BOJ isn’t just controlling the overnight interest rate (as the Fed does in the US) but also effectively setting long-term rates as well. The practice is known as yield curve control because it literally involves controlling the yield on ten-year government bonds. Today, the BOJ is committed to holding the ten-year rate at around zero percent. To do that, the central bank simply buys bonds in whatever quantity is necessary to prevent yields from rising above zero.

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To do that, the central bank simply buys bonds in whatever quantity is necessary to prevent yields from rising above zero. It’s a bit akin to quantitative easing in that lower interest rates are the objective. However, yield curve control is a stronger form of commitment since the quantity of bonds the BOJ will buy in any given time period is not determined ahead of time. Yield curve control is about committing to an interest rate (price) target rather than committing to purchase a certain amount (quantity) of bonds. The BOJ’s policy clearly demonstrates that the central bank can set both short-term and long-term interest rates, even as government borrowing rises.

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Coordination with fiscal policy officially ended in 1951, with an agreement known as the Treasury–Federal Reserve Accord, which freed the Fed to pursue independent monetary policy.31 Elsewhere, central banks are returning to explicit coordination of fiscal and monetary policy.32 For more than three years, the BOJ has been engaged in a policy known as yield curve control. In addition to anchoring the short-term interest rate, the BOJ committed to pinning rates on ten-year government bonds (known as Japanese Government Bonds or JGBs) near zero. In carrying out that policy, the BOJ has purchased massive amounts of government debt, buying up ¥6.9 trillion in June 2019 alone.33 As a result of its aggressive bond-buying program, the BOJ now holds roughly 50 percent of all Japanese government bonds.

Market Risk Analysis, Quantitative Methods in Finance
by Carol Alexander
Published 2 Jan 2007

To Walter Ledermann Contents List of Figures xiii List of Tables xvi List of Examples xvii Foreword xix Preface to Volume I I.1 Basic Calculus for Finance I.1.1 Introduction I.1.2 Functions and Graphs, Equations and Roots I.1.2.1 Linear and Quadratic Functions I.1.2.2 Continuous and Differentiable Real-Valued Functions I.1.2.3 Inverse Functions I.1.2.4 The Exponential Function I.1.2.5 The Natural Logarithm I.1.3 Differentiation and Integration I.1.3.1 Definitions I.1.3.2 Rules for Differentiation I.1.3.3 Monotonic, Concave and Convex Functions I.1.3.4 Stationary Points and Optimization I.1.3.5 Integration I.1.4 Analysis of Financial Returns I.1.4.1 Discrete and Continuous Time Notation I.1.4.2 Portfolio Holdings and Portfolio Weights I.1.4.3 Profit and Loss I.1.4.4 Percentage and Log Returns I.1.4.5 Geometric Brownian Motion I.1.4.6 Discrete and Continuous Compounding in Discrete Time I.1.4.7 Period Log Returns in Discrete Time I.1.4.8 Return on a Linear Portfolio I.1.4.9 Sources of Returns I.1.5 Functions of Several Variables I.1.5.1 Partial Derivatives: Function of Two Variables I.1.5.2 Partial Derivatives: Function of Several Variables xxiii 1 1 3 4 5 6 7 9 10 10 11 13 14 15 16 16 17 19 19 21 22 23 25 25 26 27 27 viii Contents I.1.5.3 Stationary Points I.1.5.4 Optimization I.1.5.5 Total Derivatives I.1.6 Taylor Expansion I.1.6.1 Definition and Examples I.1.6.2 Risk Factors and their Sensitivities I.1.6.3 Some Financial Applications of Taylor Expansion I.1.6.4 Multivariate Taylor Expansion I.1.7 Summary and Conclusions I.2 Essential Linear Algebra for Finance I.2.1 Introduction I.2.2 Matrix Algebra and its Mathematical Applications I.2.2.1 Basic Terminology I.2.2.2 Laws of Matrix Algebra I.2.2.3 Singular Matrices I.2.2.4 Determinants I.2.2.5 Matrix Inversion I.2.2.6 Solution of Simultaneous Linear Equations I.2.2.7 Quadratic Forms I.2.2.8 Definite Matrices I.2.3 Eigenvectors and Eigenvalues I.2.3.1 Matrices as Linear Transformations I.2.3.2 Formal Definitions I.2.3.3 The Characteristic Equation I.2.3.4 Eigenvalues and Eigenvectors of a 2 × 2 Correlation Matrix I.2.3.5 Properties of Eigenvalues and Eigenvectors I.2.3.6 Using Excel to Find Eigenvalues and Eigenvectors I.2.3.7 Eigenvalue Test for Definiteness I.2.4 Applications to Linear Portfolios I.2.4.1 Covariance and Correlation Matrices I.2.4.2 Portfolio Risk and Return in Matrix Notation I.2.4.3 Positive Definiteness of Covariance and Correlation Matrices I.2.4.4 Eigenvalues and Eigenvectors of Covariance and Correlation Matrices I.2.5 Matrix Decomposition I.2.5.1 Spectral Decomposition of a Symmetric Matrix I.2.5.2 Similarity Transforms I.2.5.3 Cholesky Decomposition I.2.5.4 LU Decomposition I.2.6 Principal Component Analysis I.2.6.1 Definition of Principal Components I.2.6.2 Principal Component Representation I.2.6.3 Case Study: PCA of European Equity Indices I.2.7 Summary and Conclusions 28 29 31 31 32 33 33 34 35 37 37 38 38 39 40 41 43 44 45 46 48 48 50 51 52 52 53 54 55 55 56 58 59 61 61 62 62 63 64 65 66 67 70 Contents I.3 Probability and Statistics I.3.1 Introduction I.3.2 Basic Concepts I.3.2.1 Classical versus Bayesian Approaches I.3.2.2 Laws of Probability I.3.2.3 Density and Distribution Functions I.3.2.4 Samples and Histograms I.3.2.5 Expected Value and Sample Mean I.3.2.6 Variance I.3.2.7 Skewness and Kurtosis I.3.2.8 Quantiles, Quartiles and Percentiles I.3.3 Univariate Distributions I.3.3.1 Binomial Distribution I.3.3.2 Poisson and Exponential Distributions I.3.3.3 Uniform Distribution I.3.3.4 Normal Distribution I.3.3.5 Lognormal Distribution I.3.3.6 Normal Mixture Distributions I.3.3.7 Student t Distributions I.3.3.8 Sampling Distributions I.3.3.9 Generalized Extreme Value Distributions I.3.3.10 Generalized Pareto Distribution I.3.3.11 Stable Distributions I.3.3.12 Kernels I.3.4 Multivariate Distributions I.3.4.1 Bivariate Distributions I.3.4.2 Independent Random Variables I.3.4.3 Covariance I.3.4.4 Correlation I.3.4.5 Multivariate Continuous Distributions I.3.4.6 Multivariate Normal Distributions I.3.4.7 Bivariate Normal Mixture Distributions I.3.4.8 Multivariate Student t Distributions I.3.5 Introduction to Statistical Inference I.3.5.1 Quantiles, Critical Values and Confidence Intervals I.3.5.2 Central Limit Theorem I.3.5.3 Confidence Intervals Based on Student t Distribution I.3.5.4 Confidence Intervals for Variance I.3.5.5 Hypothesis Tests I.3.5.6 Tests on Means I.3.5.7 Tests on Variances I.3.5.8 Non-Parametric Tests on Distributions I.3.6 Maximum Likelihood Estimation I.3.6.1 The Likelihood Function I.3.6.2 Finding the Maximum Likelihood Estimates I.3.6.3 Standard Errors on Mean and Variance Estimates ix 71 71 72 72 73 75 76 78 79 81 83 85 85 87 89 90 93 94 97 100 101 103 105 106 107 108 109 110 111 114 115 116 117 118 118 120 122 123 124 125 126 127 130 130 131 133 x Contents I.3.7 Stochastic Processes in Discrete and Continuous Time I.3.7.1 Stationary and Integrated Processes in Discrete Time I.3.7.2 Mean Reverting Processes and Random Walks in Continuous Time I.3.7.3 Stochastic Models for Asset Prices and Returns I.3.7.4 Jumps and the Poisson Process I.3.8 Summary and Conclusions I.4 Introduction to Linear Regression I.4.1 Introduction I.4.2 Simple Linear Regression I.4.2.1 Simple Linear Model I.4.2.2 Ordinary Least Squares I.4.2.3 Properties of the Error Process I.4.2.4 ANOVA and Goodness of Fit I.4.2.5 Hypothesis Tests on Coefficients I.4.2.6 Reporting the Estimated Regression Model I.4.2.7 Excel Estimation of the Simple Linear Model I.4.3 Properties of OLS Estimators I.4.3.1 Estimates and Estimators I.4.3.2 Unbiasedness and Efficiency I.4.3.3 Gauss–Markov Theorem I.4.3.4 Consistency and Normality of OLS Estimators I.4.3.5 Testing for Normality I.4.4 Multivariate Linear Regression I.4.4.1 Simple Linear Model and OLS in Matrix Notation I.4.4.2 General Linear Model I.4.4.3 Case Study: A Multiple Regression I.4.4.4 Multiple Regression in Excel I.4.4.5 Hypothesis Testing in Multiple Regression I.4.4.6 Testing Multiple Restrictions I.4.4.7 Confidence Intervals I.4.4.8 Multicollinearity I.4.4.9 Case Study: Determinants of Credit Spreads I.4.4.10 Orthogonal Regression I.4.5 Autocorrelation and Heteroscedasticity I.4.5.1 Causes of Autocorrelation and Heteroscedasticity I.4.5.2 Consequences of Autocorrelation and Heteroscedasticity I.4.5.3 Testing for Autocorrelation I.4.5.4 Testing for Heteroscedasticity I.4.5.5 Generalized Least Squares I.4.6 Applications of Linear Regression in Finance I.4.6.1 Testing a Theory I.4.6.2 Analysing Empirical Market Behaviour I.4.6.3 Optimal Portfolio Allocation 134 134 136 137 139 140 143 143 144 144 146 148 149 151 152 153 155 155 156 157 157 158 158 159 161 162 163 163 166 167 170 171 173 175 175 176 176 177 178 179 179 180 181 Contents I.4.6.4 Regression-Based Hedge Ratios I.4.6.5 Trading on Regression Models I.4.7 Summary and Conclusions xi 181 182 184 I.5 Numerical Methods in Finance I.5.1 Introduction I.5.2 Iteration I.5.2.1 Method of Bisection I.5.2.2 Newton–Raphson Iteration I.5.2.3 Gradient Methods I.5.3 Interpolation and Extrapolation I.5.3.1 Linear and Bilinear Interpolation I.5.3.2 Polynomial Interpolation: Application to Currency Options I.5.3.3 Cubic Splines: Application to Yield Curves I.5.4 Optimization I.5.4.1 Least Squares Problems I.5.4.2 Likelihood Methods I.5.4.3 The EM Algorithm I.5.4.4 Case Study: Applying the EM Algorithm to Normal Mixture Densities I.5.5 Finite Difference Approximations I.5.5.1 First and Second Order Finite Differences I.5.5.2 Finite Difference Approximations for the Greeks I.5.5.3 Finite Difference Solutions to Partial Differential Equations I.5.6 Binomial Lattices I.5.6.1 Constructing the Lattice I.5.6.2 Arbitrage Free Pricing and Risk Neutral Valuation I.5.6.3 Pricing European Options I.5.6.4 Lognormal Asset Price Distributions I.5.6.5 Pricing American Options I.5.7 Monte Carlo Simulation I.5.7.1 Random Numbers I.5.7.2 Simulations from an Empirical or a Given Distribution I.5.7.3 Case Study: Generating Time Series of Lognormal Asset Prices I.5.7.4 Simulations on a System of Two Correlated Normal Returns I.5.7.5 Multivariate Normal and Student t Distributed Simulations I.5.8 Summary and Conclusions 185 185 187 187 188 191 193 193 195 197 200 201 202 203 I.6 Introduction to Portfolio Theory I.6.1 Introduction I.6.2 Utility Theory I.6.2.1 Properties of Utility Functions I.6.2.2 Risk Preference I.6.2.3 How to Determine the Risk Tolerance of an Investor I.6.2.4 Coefficients of Risk Aversion 225 225 226 226 229 230 231 203 206 206 207 208 210 211 211 212 213 215 217 217 217 218 220 220 223 xii Contents I.6.2.5 I.6.2.6 I.6.2.7 I.6.3 I.6.4 I.6.5 I.6.6 Some Standard Utility Functions Mean–Variance Criterion Extension of the Mean–Variance Criterion to Higher Moments Portfolio Allocation I.6.3.1 Portfolio Diversification I.6.3.2 Minimum Variance Portfolios I.6.3.3 The Markowitz Problem I.6.3.4 Minimum Variance Portfolios with Many Constraints I.6.3.5 Efficient Frontier I.6.3.6 Optimal Allocations Theory of Asset Pricing I.6.4.1 Capital Market Line I.6.4.2 Capital Asset Pricing Model I.6.4.3 Security Market Line I.6.4.4 Testing the CAPM I.6.4.5 Extensions to CAPM Risk Adjusted Performance Measures I.6.5.1 CAPM RAPMs I.6.5.2 Making Decisions Using the Sharpe Ratio I.6.5.3 Adjusting the Sharpe Ratio for Autocorrelation I.6.5.4 Adjusting the Sharpe Ratio for Higher Moments I.6.5.5 Generalized Sharpe Ratio I.6.5.6 Kappa Indices, Omega and Sortino Ratio Summary and Conclusions 232 234 235 237 238 240 244 245 246 247 250 250 252 253 254 255 256 257 258 259 260 262 263 266 References 269 Statistical Tables 273 Index 279 List of Figures A linear function The quadratic function fx = 4x2 + 3x + 2 I.1.3 The reciprocal function I.1.4 The inverse of a function I.1.5 The exponential function I.1.6 The natural logarithmic function I.1.7 Definition of the first derivative I.1.8 Two functions I.1.9 The definite integral I.1.10 The h-period log return is the sum of h consecutive one-period log returns I.1.11 Graph of the function in Example I.1.8 I.2.1 A matrix is a linear transformation I.2.2 A vector that is not an eigenvector I.2.3 An eigenvector I.2.4 Six European equity indices I.2.5 The first principal component I.3.1 Venn diagram I.3.2 Density and distribution functions: (a) discrete random variable; (b) continuous variable I.3.3 Building a histogram in Excel I.3.4 The effect of cell width on the histogram shape I.3.5 Two densities with the same expectation I.1.1 I.1.2 4 5 6 7 8 I.3.6 9 I.3.8 10 12 15 I.3.9 24 27 I.3.7 I.3.10 I.3.11 I.3.12 I.3.13 48 I.3.14 49 50 67 I.3.15 I.3.16 69 75 I.3.17 77 78 I.3.18 78 I.3.19 I.3.20 but different standard deviations (a) A normal density and a leptokurtic density; (b) a positively skewed density The 0.1 quantile of a continuous random variable Some binomial density functions A binomial tree for a stock price evolution The standard uniform distribution Two normal densities Lognormal density associated with the standard normal distribution A variance mixture of two normal densities A skewed, leptokurtic normal mixture density Comparison of Student t densities and standard normal Comparison of Student t density and normal with same variance Comparison of standardized empirical density with standardized Student t density and standard normal density The Excel t distribution function Filtering data to derive the GEV distribution A Fréchet density 80 83 84 86 87 89 90 93 95 97 98 99 99 100 102 103 xiv List of Figures I.3.21 Filtering data in the peaks-over-threshold model I.3.22 Kernel estimates of S&P 500 returns I.3.23 Scatter plots from a paired sample of returns: (a) correlation +075; (b) correlation 0; (c) correlation −075 I.3.24 Critical regions for hypothesis tests I.3.25 The dependence of the likelihood on parameters I.3.26 The likelihood and the log likelihood functions I.3.27 FTSE 100 index I.3.28 Daily prices and log prices of DJIA index I.3.29 Daily log returns on DJIA index I.4.1 Scatter plot of Amex and S&P 500 daily log returns I.4.2 Dialog box for Excel regression I.4.3 Unbiasedness and efficiency I.4.4 Distribution of a consistent estimator I.4.5 Billiton share price, Amex Oil index and CBOE Gold index I.4.6 Dialog box for multiple regression in Excel I.4.7 The iTraxx Europe index and its determinants I.4.8 Residuals from the Billiton regression I.5.1 Method of bisection I.5.2 Setting Excel’s Goal Seek I.5.3 Newton–Raphson iteration I.5.4 104 107 I.5.5 I.5.6 I.5.7 I.5.8 I.5.9 113 I.5.10 125 I.5.11 130 I.5.12 131 133 I.5.13 I.5.14 137 138 I.5.15 I.5.16 145 I.5.17 153 I.5.18 156 I.5.19 157 I.5.20 162 I.6.1 164 I.6.2 172 I.6.3 178 187 189 189 I.6.4 I.6.5 Convergence of Newton–Raphson scheme Solver options Extrapolation of a yield curve Linear interpolation on percentiles Fitting a currency smile A cubic spline interpolated yield curve FTSE 100 and S&P 500 index prices, 1996–2007 Sterling–US dollar exchange rate, 1996–2007 Slope of chord about a point Discretization of space for the finite difference scheme A simple finite difference scheme A binomial lattice Computing the price of European and American puts Simulating from a standard normal distribution Possible paths for an asset price following geometric Brownian motion A set of three independent standard normal simulations A set of three correlated normal simulations Convex, concave and linear utility functions The effect of correlation on portfolio volatility Portfolio volatility as a function of portfolio weight Portfolio risk and return as a function of portfolio weight Minimum variance portfolio 190 191 193 195 197 200 204 204 206 209 210 210 216 218 220 221 222 229 239 241 242 243 I.6.6 I.6.7 I.6.8 Solver settings for Example I.6.9 The opportunity set and the efficient frontier Indifference curves of risk averse investor List of Figures xv Indifference curves of risk loving investor I.6.10 Market portfolio I.6.11 Capital market line I.6.12 Security market line 249 251 251 253 I.6.9 246 247 248 List of Tables I.1.1 Asset prices I.1.2 Portfolio weights and portfolio value I.1.3 Portfolio returns I.2.1 Volatilities and correlations I.2.2 The correlation matrix of weekly returns I.2.3 Eigenvectors and eigenvalues of the correlation matrix I.3.1 Example of the density of a discrete random variable I.3.2 Distribution function for Table I.3.1 I.3.3 Biased and unbiased sample moments I.3.4 The B(3, 1/6) distribution I.3.5 A Poisson density function I.3.6 A simple bivariate density I.3.7 Distribution of the product I.3.8 Calculating a covariance I.3.9 Sample statistics I.4.1 Calculation of OLS estimates I.4.2 Estimating the residual sum of sqaures and the standard error of the regression I.4.3 Estimating the total sum of squares I.4.4 Critical values of t3 I.4.5 Some of the Excel output for the Amex and S&P 500 model 18 18 26 56 68 68 75 75 82 86 88 110 110 111 127 147 149 150 152 154 I.4.6 ANOVA for the Amex and S&P 500 model I.4.7 Coefficient estimates for the Amex and S&P 500 model I.4.8 ANOVA for Billiton regression I.4.9 Wald, LM and LR statistics I.5.1 Mean and volatility of the FTSE 100 and S&P 500 indices and the £/$ FX rate I.5.2 Estimated parameters of normal mixture distributions I.5.3 Analytic vs finite difference Greeks I.5.4 Characteristics of asset returns I.6.1 Two investments (outcomes as returns) I.6.2 Two investments (utility of outcomes) I.6.3 Returns characteristics for two portfolios I.6.4 Two investments I.6.5 Sharpe ratio and weak stochastic dominance I.6.6 Returns on an actively managed fund and its benchmark I.6.7 Statistics on excess returns I.6.8 Sharpe ratios and adjusted Sharpe ratios I.6.9 Kappa indices 154 154 164 167 205 205 208 221 227 228 237 258 259 261 262 262 264 List of Examples I.1.1 I.1.2 I.1.3 I.1.4 I.1.5 I.1.6 I.1.7 I.1.8 I.1.9 I.1.10 I.1.11 I.2.1 I.2.2 I.2.3 I.2.4 I.2.5 I.2.6 I.2.7 I.2.8 I.2.9 I.2.10 I.2.11 Roots of a quadratic equation Calculating derivatives Identifying stationary points A definite integral Portfolio weights Returns on a long-short portfolio Portfolio returns Stationary points of a function of two variables Constrained optimization Total derivative of a function of three variables Taylor approximation Finding a matrix product using Excel Calculating a 4 × 4 determinant Finding the determinant and the inverse matrix using Excel Solving a system of simultaneous linear equations in Excel A quadratic form in Excel Positive definiteness Determinant test for positive definiteness Finding eigenvalues and eigenvectors Finding eigenvectors Using an Excel add-in to find eigenvectors and eigenvalues Covariance and correlation matrices 5 12 14 16 18 20 25 28 30 31 32 40 42 43 45 45 46 47 51 53 54 56 I.2.12 Volatility of returns and volatility of P&L I.2.13 A non-positive definite 3 × 3 matrix I.2.14 Eigenvectors and eigenvalues of a 2 × 2 covariance matrix I.2.15 Spectral decomposition of a correlation matrix I.2.16 The Cholesky matrix of a 2 × 2 matrix I.2.17 The Cholesky matrix of a 3 × 3 matrix I.2.18 Finding the Cholesky matrix in Excel I.2.19 Finding the LU decomposition in Excel I.3.1 Building a histogram I.3.2 Calculating moments of a distribution I.3.3 Calculating moments of a sample I.3.4 Evolution of an asset price I.3.5 Normal probabilities I.3.6 Normal probabilities for portfolio returns I.3.7 Normal probabilities for active returns I.3.8 Variance and kurtosis of a zero-expectation normal mixture I.3.9 Probabilities of normal mixture variables I.3.10 Calculating a covariance I.3.11 Calculating a correlation I.3.12 Normal confidence intervals 57 59 60 61 62 63 63 64 77 81 82 87 90 91 92 95 96 110 112 119 xviii List of Examples I.3.13 One- and two-sided confidence intervals I.3.14 Confidence interval for a population mean I.3.15 Testing for equality of means and variances I.3.16 Log likelihood of the normal density I.3.17 Fitting a Student t distribution by maximum likelihood I.4.1 Using the OLS formula I.4.2 Relationship between beta and correlation I.4.3 Estimating the OLS standard error of the regression I.4.4 ANOVA I.4.5 Hypothesis tests in a simple linear model I.4.6 Simple regression in matrix form I.4.7 Goodness-of-fit test in multiple regression I.4.8 Testing a simple hypothesis in multiple regression I.4.9 Testing a linear restriction I.4.10 Confidence interval for regression coefficient I.4.11 Prediction in multivariate regression I.4.12 Durbin–Watson test I.4.13 White’s heteroscedasticity test I.5.1 Excel’s Goal Seek I.5.2 Using Solver to find a bond yield I.5.3 Interpolating implied volatility I.5.4 Bilinear interpolation I.5.5 120 I.5.6 123 I.5.7 127 131 I.5.8 I.5.9 132 147 147 148 150 151 160 I.5.10 I.6.1 I.6.2 I.6.3 I.6.4 I.6.5 I.6.6 164 165 165 168 I.6.7 I.6.8 I.6.9 169 177 I.6.10 I.6.11 177 188 I.6.12 191 I.6.13 I.6.14 194 194 I.6.15 Fitting a 25-delta currency option smile Interpolation with cubic splines Finite difference approximation to delta, gamma and vega Pricing European call and put options Pricing an American option with a binomial lattice Simulations from correlated Student t distributed variables Expected utility Certain equivalents Portfolio allocations for an exponential investor Higher moment criterion for an exponential investor Minimum variance portfolio: two assets Minimum variance portfolio on S&P 100 and FTSE 100 General formula for minimum variance portfolio The Markowitz problem Minimum variance portfolio with many constraints The CML equation Stochastic dominance and the Sharpe ratio Adjusting a Sharpe ratio for autocorrelation Adjusted Sharpe ratio Computing a generalized Sharpe ratio Omega, Sortino and kappa indices 196 198 208 212 215 222 227 228 235 236 241 242 244 245 246 252 258 260 261 263 264 Foreword How many children dream of one day becoming risk managers?

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For instance, suppose the monthly spot rates from 1 month to 36 months are as shown in Figure I.5.6. How should we ‘extrapolate’ these data to obtain the spot rates up to 48 months? Since the yield curve is not a straight line, we need to fit a quadratic or higher order polynomial in order to extrapolate to the longer maturities. UK Short Spot Curve, 31 May 2002 5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 3.50 0 4 m 8 m 12 m 16 m 20 m 24 m 28 m 32 m 36 m 40 m 44 m Figure I.5.6 Extrapolation of a yield curve I.5.3.1 Linear and Bilinear Interpolation Given two data points, x1  y1  and x2  y2  with x1 < x2 , linear interpolation gives the value of y at some point x ∈ x1  x2 as x − x1  y1 + x − x1  y2 y= 2 (I.5.11) x2 − x1  7 See http://en.wikipedia.org/wiki/Conjugate_gradient_method. 194 Quantitative Methods in Finance For an example of linear interpolation, consider the construction of a constant maturity 30-day futures series from traded futures.

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If further data on 10-delta strangles and risk reversals are available, two more points can be added to the implied volatility smile: 10 = 50 + ST10 + 21 RR10  90 = 50 + ST10 − 21 RR10 (I.5.13) A more precise interpolation and extrapolation method is then to fit a quartic polynomial to the ATM, 25-delta and 10-delta data: this is left as an exercise to the reader. I.5.3.3 Cubic Splines: Application to Yield Curves Spline interpolation is a special type of piecewise polynomial interpolation that is usually more accurate than ordinary polynomial interpolation, even when the spline polynomials have quite low degree. In this section we consider cubic splines, since these are the lowest degree splines with attractive properties and are in use by many financial institutions, for instance for yield curve fitting and for volatility smile surface interpolation. We aim to interpolate a function fx using a cubic spline.

The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money
by Steven Drobny
Published 18 Mar 2010

Looking at real assets first entails major supply and demand analysis of all goods, services, and commodities, rather than just focusing on boilerplate economic analysis. Using this lens has given me an edge. For example, we were ahead of the game in predicting that the yield curve would invert during the Greenspan conundrum era (see box on page 276). We realized that the world had switched from one of supply constriction in commodities to one of demand pull, and that a bull market in commodities (with the associated switch from backwardation into contango in commodity futures curves) would be reflected in an inverted yield curve. In a deflationary consumer environment with an inflationary real asset environment, the real asset inflationary aspects affect the short end of the curve, but the long end remains locked down.

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With productivity gains and no real inflation feeding through to core CPI—because core excludes food and energy—we bought bonds on the long end and put on yield curve inversion trades, which practically everyone scoffed at. We caught that move not by being smarter than everyone else, but by interpreting events through a commodity lens and being able to predict their effect on interest rate curves. (See Figure 10.1.) Figure 10.1 U.S. Treasury Yield Curve, 2004 and 2006 SOURCE: Bloomberg. The Greenspan Conundrum Speech, 2005 There is little doubt that, with the breakup of the Soviet Union and the integration of China and India into the global trading market, more of the world’s productive capacity is being tapped to satisfy global demands for goods and services.

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It’s easy to replicate and model portfolios with leveraged government bond positions or bond option positions, and the most interesting thing about this kind of leverage is that historically, it adds value to portfolios. It’s like receiving free insurance because the bond risk premium is positive. If you buy a portfolio of government bonds and fund it by borrowing cash, if there is an upward sloping yield curve on average, over the business cycle or over any long period of time, that portfolio will make money. Hence you are buying insurance that, on average, makes you money. It is an incredibly interesting idea because normally insurance costs you money. In 2007, we were looking at all kinds of things to hedge an equity portfolio in a bad event.

Corporate Finance: Theory and Practice
by Pierre Vernimmen , Pascal Quiry , Maurizio Dallocchio , Yann le Fur and Antonio Salvi
Published 16 Oct 2017

An entire body of financial research is devoted to understanding movements in interest rates and, in particular, how different maturities are linked. This is the study of how the yield curve, which at a point in time relates the yield to maturity to the maturity (or duration) of bonds, is formed. 1. The various yield curves By charting the interest rate for the same categories of risk at all maturities, the investor obtains the yield curve that reflects the anticipation of all financial market operators. The concept of premium helps explain why the interest rate of any financial asset is generally proportional to its maturity. Generally speaking, the yield curve reflects the market’s anticipation regarding: long-term inflation; the central bank’s monetary policy; and the issuing country’s debt management policy.

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Investors preferring liquidity will require a liquidity premium if they are to invest for the long term. Hence, long-term rates will be the geometric average of anticipated short-term rates increased by a liquidity premium normally increasing with maturity. Even if investors anticipate fixed short-term rates, the yield curve will slope upward due to the liquidity premiums. 4. Yield curves and valuation of securities After having studied the yield curve, it is easier to understand that the discounting of all the cash flows from a fixed-income security at a single rate, regardless of the period when they are paid, is an oversimplification, although this is the method that will be used throughout this text for stocks and capital expenditure.

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Like the CAPM, the APT assumes that the required rate of return no longer depends on a single market rate; however, it considers a number of other variables too, such as the difference between government bonds and Treasury bills, unanticipated changes in the growth rate of the economy or the rate of inflation, etc. Rates of return on bonds with different maturity dates can be plotted on a graph known as the yield curve. In order to avoid distortions linked to coupon rates of bonds, it is better to analyse zero-coupon curves that can be reconstituted on the basis of the yield curve. The shape of the yield curve depends on changes in expectations about short-term rates and the liquidity premium that investors will require for making a long-term investment. In a risk-free environment, the long-term rate at n years is a geometric average of short-term rates anticipated for future periods.

Derivatives Markets
by David Goldenberg
Published 2 Mar 2016

So we need the current (t=0) spot LIBOR yield curve. It gives the rates to be applied to zero-coupon Eurobonds for alternative maturities. Assume that it is as in Table 8.8. Our long position in the fixed-rate bond can be decomposed as the sum of three zero-coupon bonds, and one NP repayment bond as indicated in the multi-level cash flow diagram, Figure 8.15. TABLE 8.8 LIBOR Yield Curve (Spot Rates) Maturity Zero-Coupon Bond Yields 1 year 6.0% 2 years 6.5% 3 years 7.0% FIGURE 8.15 The Implicit Fixed-Rate Bond in a Swap, Written in Terms of Zero-Coupon Bonds The LIBOR zero-yield curve says that the appropriate discount rate to apply to the cash flow from Bond 1 is 6.00%, the appropriate discount rate to apply to the cash flow from Bond 2 is 6.5%, and the appropriate discount rate to apply to the cash flows from Bond 3 and from Bond 4 is 7.0%.

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The weights add up to 1.0 and are the current prices of 1, 2, and 3-year unit discount LIBOR bonds each expressed as a percentage of the sum of the values of those bonds, Interpretation 2 This representation is equivalent to that given in section 8.9.4 of the par swap rate as To establish this equivalence, all we have to do is to show that, Re-write LIBOR1,0 as r1 ,where r1 is the LIBOR zero yield curve rate used to price is the LIBOR zero yield curve rate used to price , and r3 is the LIBOR zero yield curve rate used to price . Using the definitions of the IFRs we obtain that the right hand side of the required equality, , is equal to, This is what we wanted to demonstrate because it is the left side of Interpretation 3 There is a third useful interpretation of the par swap rate that follows from basic bond finance.

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That is, it is the rate, denoted by IFR1,1, such that (1+LIBOR2,0)2= (1+LIBOR1,0)*(1+IFR1,1). The IFR1,1 is given by, Similarly, the Implied Forward Rate on one-year loans two years from today, denoted by IFR1,2, is defined as the artificial rate such that, Implied Forward Rates are obtained from the LIBOR yield curve, or from the prices of Eurodollar futures contracts. For example, based on the LIBOR yield curve given in Table 8.8, we can imply 1-year forward rates one year from today and two years from today. ■ CONCEPT CHECK 6 a. Calculate, based upon Table 8.8, the IFR for 1-year loans one year from today, IFR1,1. b. Also, calculate the IFR for 1-year loans two years from today, IFR1,2.

Wall Street: How It Works And for Whom
by Doug Henwood
Published 30 Aug 1998

The trading day ends when New York closes. Treasury debt falls into three categories — bills, with maturities running from three months to one year; notes, one year to 10; and bonds, over 10. Most trading occurs in the two- to seven-year range. Shown on p. 26 are three "yield curves," plots of interest rates at various maturities. Normally the yield curve slopes gently upward, with interest rates rising as maturities lengthen. The reason for this is pretty simple — the longer a maturity, the more possibility there is for something to go wrong (inflation, financial panic, war), so investors require a sweeter return to tempt them into parting with their money.

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At business cycle peaks, the process is thrown into reverse gear, with interest rates steadily rising and the stock market flattening and finally sinking. Note that short-term rates move far more dramatically in both directions than long-term rates; the yield curve normally flattens or even goes negative as the economy approaches recession, then turns steeply positive as the slowdown ends. In fact, the yield curve "significantly outperforms other financial and macroeconomic indicators in predicting recessions two to six quarters ahead" (Estrella and Mishkin 1996) — and not only in the U.S., but in most of the rich industrial countries (Bernard and Gerlach 1996).

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In the early 1980s, the curve was negative, as Volcker's Fed drove rates up to record levels to kill inflation; in the early 1990s, it was quite steep, and Greenspan's Fed forced rates down to keep the financial system from imploding. It's likely that investors assumed that both extremes were not sustainable, and that short rates would return to more "normal" levels, which is why the longer end of the curve never got so carried away. 16% 14% 12% 10% 8% 6% 4% 2% 0% U.S. Treasury yield curves Jan 1997 Dec 1980 Oct 1992 3-mo 1 2 3 5 7 10 30 years to maturity mums Federal government bonds aren't the only kind, of course. Cities and states sell tax-exempt municipal bonds, which help retired dentists to shelter income and local governments to build sewers and subsidize shopping malls in the name of "industrial development."

The New Science of Asset Allocation: Risk Management in a Multi-Asset World
by Thomas Schneeweis , Garry B. Crowder and Hossein Kazemi
Published 8 Mar 2010

First, the signals must make economic sense; that is, one should be able to explain in simple terms why the model is able to forecast relative performance of various asset classes. For example, one of the most reliable signals about future performance of equities relative to fixed income instruments has been the slope of the yield curve. An upward sloping yield curve is generally consistent with a period of rising stock prices. The reason behind this is that an upward sloping yield curve is generally observed at the beginning of economic expansion. By examining the economic foundation of the signal, one can avoid using results that have resulted from data mining, that is, the generated signals that are not likely to perform well out of sample.

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However, for those who focus on risk measures beyond standard deviation of return, risk analysis at the portfolio level includes a wide range of analysis, including:9 34 ■ ■ ■ ■ ■ ■ THE NEW SCIENCE OF ASSET ALLOCATION Market Risk Analysis (changes in the yield curve or other marketrelated variables) on the performance of the portfolio as well as the primary asset sectors. Changes in factors such as interest rate movements, yield curve shifts, and other economic factors provide additional information on the macro sensitivity of the portfolio to economic factors. Performance Attribution: Attribution analysis, which measures the sources of return on an asset class as well as sector selection as a percentage of total return.

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How they could or should be priced in a single-factor or even a multi-factor model framework was explored, but a solution was rarely found.9 Option Pricing Models and Growth of Futures Markets We have spent a great deal of time focusing on the equity markets. During this period of market innovation, considerable research also centered on direct arbitrage relationships. Arbitrage relationships in capital and A Brief History of Asset Allocation 11 corporate markets were explored during the 1930s (forward interest rates implied in yield curve models)10 and in the 1950s (corporate dividend policy and debt policy). Similarly, cost of carry arbitrage models had long been the focal point of pricing in most futures based research. In the early 1970s Fischer Black and Myron Scholes (1973) and Merton (1973) developed a simple-to-use option pricing model based in part on arbitrage relationships between investment vehicles.

Infonomics: How to Monetize, Manage, and Measure Information as an Asset for Competitive Advantage
by Douglas B. Laney
Published 4 Sep 2017

This leads us to a examination of information yield (a concept loosely inspired by the traditional yield curve6) for expressing the rate of improved value per unit of information-related investment. The information yield curve brings together, conceptually, the concepts of information monetization, management, and measurement. As we all know, information asset management (IAM) involves numerous moving parts. And as enumerated in chapter 5, many factors exert upward or downward pressure on information maturity. But what does this maturation curve look like? And where are you on it? The information yield curve which my Gartner colleagues Andrew White, Joe Bugajski, Frank Buytendijk, and I devised a few years ago is intended to answer these questions.

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How understanding the marginal utility of information for both human and technology-based consumers of information should drive business and architecture decisions. How the opportunity costs of certain information assets must be factored into selecting and publishing them. How the information production possibility frontier affects information-related behavior and investments. How to use Gartner’s information yield curve to conceptually integrate the concepts of information monetization, management, and measurement for improved information-related and business strategies. The Supply and Demand of Information Information is an unruly asset. As pointed out earlier, it does not deplete when consumed, it can be used simultaneously, it is representative of some other entity or activity, it costs comparatively little to store or transmit, and it can instantly transform or disappear.

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The information yield curve which my Gartner colleagues Andrew White, Joe Bugajski, Frank Buytendijk, and I devised a few years ago is intended to answer these questions. Not computationally, but more along the lines of how the popular Gartner Hype Cycle7 sets maturity expectations for technology users and suppliers, the information yield curve sets expectations for how information-related investments affect IAM maturity—and thereby your information’s rate of return. In short, low-maturity organizations will see accelerating improvements in the rate of return on their information assets from information-related investments, while high-maturity organizations will see decelerating rates of return as they approach an optimization ceiling.

Asset and Risk Management: Risk Oriented Finance
by Louis Esch , Robert Kieffer and Thierry Lopez
Published 28 Nov 2005

If we describe P (s) as the issue price of a zero-coupon bond with maturity s and R(s) as the rate observed on the market at moment 0 for this type of security, called the spot rate, these two values are clearly linked by the relation P (s) = (1 + R(s))−s . The value R(s), for all the values of s > 0, constitutes the term interest-rate structure at moment 0 and the graph for this function is termed the yield curve. The most natural direction of the yield curve is of course upwards; the investor should gain more if he invests over a longer period. This, however, is not always the case; in practice we frequently see flat curves (constant R(s) value) as well as increasing curves, as well as inverted curves (decreasing R(s) value) and humped curves (see Figure 4.4).

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xix xix xxi PART I THE MASSIVE CHANGES IN THE WORLD OF FINANCE Introduction 1 The Regulatory Context 1.1 Precautionary surveillance 1.2 The Basle Committee 1.2.1 General information 1.2.2 Basle II and the philosophy of operational risk 1.3 Accounting standards 1.3.1 Standard-setting organisations 1.3.2 The IASB 2 Changes in Financial Risk Management 2.1 Definitions 2.1.1 Typology of risks 2.1.2 Risk management methodology 2.2 Changes in financial risk management 2.2.1 Towards an integrated risk management 2.2.2 The ‘cost’ of risk management 2.3 A new risk-return world 2.3.1 Towards a minimisation of risk for an anticipated return 2.3.2 Theoretical formalisation 1 2 3 3 3 3 5 9 9 9 11 11 11 19 21 21 25 26 26 26 vi Contents PART II EVALUATING FINANCIAL ASSETS Introduction 3 4 29 30 Equities 3.1 The basics 3.1.1 Return and risk 3.1.2 Market efficiency 3.1.3 Equity valuation models 3.2 Portfolio diversification and management 3.2.1 Principles of diversification 3.2.2 Diversification and portfolio size 3.2.3 Markowitz model and critical line algorithm 3.2.4 Sharpe’s simple index model 3.2.5 Model with risk-free security 3.2.6 The Elton, Gruber and Padberg method of portfolio management 3.2.7 Utility theory and optimal portfolio selection 3.2.8 The market model 3.3 Model of financial asset equilibrium and applications 3.3.1 Capital asset pricing model 3.3.2 Arbitrage pricing theory 3.3.3 Performance evaluation 3.3.4 Equity portfolio management strategies 3.4 Equity dynamic models 3.4.1 Deterministic models 3.4.2 Stochastic models 35 35 35 44 48 51 51 55 56 69 75 79 85 91 93 93 97 99 103 108 108 109 Bonds 4.1 Characteristics and valuation 4.1.1 Definitions 4.1.2 Return on bonds 4.1.3 Valuing a bond 4.2 Bonds and financial risk 4.2.1 Sources of risk 4.2.2 Duration 4.2.3 Convexity 4.3 Deterministic structure of interest rates 4.3.1 Yield curves 4.3.2 Static interest rate structure 4.3.3 Dynamic interest rate structure 4.3.4 Deterministic model and stochastic model 4.4 Bond portfolio management strategies 4.4.1 Passive strategy: immunisation 4.4.2 Active strategy 4.5 Stochastic bond dynamic models 4.5.1 Arbitrage models with one state variable 4.5.2 The Vasicek model 115 115 115 116 119 119 119 121 127 129 129 130 132 134 135 135 137 138 139 142 Contents 4.5.3 The Cox, Ingersoll and Ross model 4.5.4 Stochastic duration 5 Options 5.1 Definitions 5.1.1 Characteristics 5.1.2 Use 5.2 Value of an option 5.2.1 Intrinsic value and time value 5.2.2 Volatility 5.2.3 Sensitivity parameters 5.2.4 General properties 5.3 Valuation models 5.3.1 Binomial model for equity options 5.3.2 Black and Scholes model for equity options 5.3.3 Other models of valuation 5.4 Strategies on options 5.4.1 Simple strategies 5.4.2 More complex strategies PART III GENERAL THEORY OF VaR Introduction vii 145 147 149 149 149 150 153 153 154 155 157 160 162 168 174 175 175 175 179 180 6 Theory of VaR 6.1 The concept of ‘risk per share’ 6.1.1 Standard measurement of risk linked to financial products 6.1.2 Problems with these approaches to risk 6.1.3 Generalising the concept of ‘risk’ 6.2 VaR for a single asset 6.2.1 Value at Risk 6.2.2 Case of a normal distribution 6.3 VaR for a portfolio 6.3.1 General results 6.3.2 Components of the VaR of a portfolio 6.3.3 Incremental VaR 181 181 181 181 184 185 185 188 190 190 193 195 7 VaR Estimation Techniques 7.1 General questions in estimating VaR 7.1.1 The problem of estimation 7.1.2 Typology of estimation methods 7.2 Estimated variance–covariance matrix method 7.2.1 Identifying cash flows in financial assets 7.2.2 Mapping cashflows with standard maturity dates 7.2.3 Calculating VaR 7.3 Monte Carlo simulation 7.3.1 The Monte Carlo method and probability theory 7.3.2 Estimation method 199 199 199 200 202 203 205 209 216 216 218 viii Contents 7.4 Historical simulation 7.4.1 Basic methodology 7.4.2 The contribution of extreme value theory 7.5 Advantages and drawbacks 7.5.1 The theoretical viewpoint 7.5.2 The practical viewpoint 7.5.3 Synthesis 8 Setting Up a VaR Methodology 8.1 Putting together the database 8.1.1 Which data should be chosen?

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As the second-degree term C(r)2 /2 of the approximation formula is always positive, it therefore appears that when one has to choose between two bonds with the same return (actuarial rate) and duration, it will be preferable to choose the one with Bonds 129 the greater convexity regardless of the direction of the potential variation in the rate of return. 4.3 DETERMINISTIC STRUCTURE OF INTEREST RATES13 4.3.1 Yield curves The actuarial rate at the issue of a bond, as defined in Section 4.1.2 is obviously a particular characteristic to the security in question. The rate will vary from one bond to another, depending mainly on the quality of the issuer (assessed using the ratings issued by public rating companies) and the maturity of the security.

Hedge Fund Market Wizards
by Jack D. Schwager
Published 24 Apr 2012

Instead of expressing this trade idea only through long short-term interest rate instrument positions, O’Shea also implemented the trade as a yield curve spread: long short-term rate instruments/short long-term rate instruments. His reasoning was that the yield curve at the time was relatively flat, implying that a rate decline would most likely be concentrated on the short-term end of the yield curve. If, however, rates went up, the flat yield curve implied that long-term rates should go up at least as much as short-term rates and probably more. The yield curve spread provided most of the profit potential with only a fraction of the risk. In essence, it provided a much better return-to-risk ratio than a straight long position in short-term rates alone.

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Add liquidity and cut rates. That was the policy response we expected. So that was our trade at the time: Rates would go lower and the yield curve would steepen. So you put on long positions in short-term rate instruments? Yes, but we coupled it with short positions on the long end because it was a better risk/reward trade. The yield curve was flat at the time and priced to stay flat. The market wasn’t pricing in any risk that there would be a major problem. So you bet on lower short-term rates through a yield curve spread rather than a long position in short-term rate instruments because you felt it was a safer way to do the trade.

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Can you think of an example where the market response to the news was counter to what you expected and impacted your trade? In 2009, I was long 2-year notes/short 10-year notes one-year forward, looking for the yield curve to widen, and a lot of news came out that I thought would hurt me. One news item after another, I saw the screen and thought, I am going to get screwed in this position. But I didn’t. After a number of these instances, I thought, the yield curve just can’t get any flatter no matter what comes out. So I quadrupled my position. It was a great trade. The spread went from 25 basis points to 210, although I got out at 110.

How I Became a Quant: Insights From 25 of Wall Street's Elite
by Richard R. Lindsey and Barry Schachter
Published 30 Jun 2007

We hired an academic to build a pricing model. The model provided Black-Scholes type prices, but with a couple of simplifications. To be able to obtain real-time prices at the beginning of each day, the head trader (me) had to select the values to assign to each of two parameters. The first parameter was yield-curve shape, and the choices of parameter values were “relatively flat” and “relatively steep.” The second parameter was spot volatility (no JWPR007-Lindsey 90 May 28, 2007 15:39 h ow i b e cam e a quant vol surface here!). The choices were “relatively high” and “relatively low.” This model was more sophisticated at the time than models used elsewhere in the bank and among our competitors for cap pricing.

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I believe that I was the first in the industry to answer this question with the delta-gamma approach (see Wilson (1994b)), based on the observation that a quadratic form of normal variables is distributed as the sum of noncentral chi-squared variables for which numerical solutions are available. How many independent factors are practically required to capture the risk of a multicurrency fixed income trading book? The dimensionality of VaR calculations for a global trading book quickly becomes too large to be calculated efficiently, especially if each point on the yield curve is modeled separately. A logical place to look for a reduction in the dimensionality was therefore in the modeling of multicurrency interest rates. My answer (see Wilson (1994a)) compared both factor analysis and eigenvalue decompositions of multicurrency term structures and attempted to characterize the required number of factors and the stability of the parameter estimates over time.

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I guess it was for most of us the first time that we had been involved in building what amounted to a whole derivatives pricing JWPR007-Lindsey 174 May 18, 2007 21:24 h ow i b e cam e a quant system from scratch. Everything had to be coded from the ground up: ISDA day counting and accrual conventions, holiday calendar handling, volatility quotation conventions, settlement delays, yield curve stripping, simple analytical convexity corrections, a whole host of simple option analytics (the usual suspects: baskets, barriers, etc.), number generators, multithreaded Monte Carlo simulation, variance reduction techniques, multidimensional tree solvers for diffusion-based models, general finite differencing solvers for jump-diffusion based models, multifactor HullWhite models, LIBOR market models with global calibration, Bermudan Monte Carlo techniques, serialization of any of model or product objects for possible storage or distribution, distributed valuation framework, etc.

Big Debt Crises
by Ray Dalio
Published 9 Sep 2018

tightening: Policy moves that reduce the availability of money and credit, which has the effect of slowing economic growth, usually by increasing interest rates, allowing money supplies to shrink, cutting government spending, or changing rules to restrict bank lending. yield curve: The difference between shorter-term interest rates and longer-term interest rates. If short rates are above longer-term rates, the yield curve is said to be inverted, meaning short-term interest rates are priced to fall. If short rates are below longer-term rates, short-term interest rates are priced to rise. 48 Debt Crises This section goes through each of the 48 debt crises we examined, so that you can live through them on your own.

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Runs from risky assets to less risky assets pick up, contributing to a broadening of the contraction. Typically, in the early stages of the top, the rise in short rates narrows or eliminates the spread with long rates (i.e., the extra interest rate earned for lending long term rather than short term), lessening the incentive to lend relative to the incentive to hold cash. As a result of the yield curve being flat or inverted (i.e., long-term interest rates are at their lowest relative to short-term interest rates), people are incentivized to move to cash just before the bubble pops, slowing credit growth and causing the previously described dynamic. Early on in the top, some parts of the credit system suffer, but others remain robust, so it isn’t clear that the economy is weakening.

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Typically capital inflows dry up, falling fast (by more than 5 percent of GDP in less than 12 months) Capital outflows continue (at a pace of -3 to -5 percent of GDP) Typically the pullback in capital is not offset much by the central bank printing money, as printing risks enabling more people to get out of the currency, worsening capital flight. Weaker growth causes investors to pull their money out anyway; the assets that had been seen as a fabulous treasure a short time ago now look like trash. They quickly go from overbought to oversold and prices plummet. Nominal short rates rise (typically by about 20 percentage points) and the yield curve inverts. Printing is limited (1 to 2 percent of GDP, on average). Equities in local currency terms fall (on average by around 50%). They perform even worse in foreign currency terms, as the currency decline exacerbates the equity sell-off. One of the most important asset/liability mismatches is foreign-denominated debt.

Investing Demystified: How to Invest Without Speculation and Sleepless Nights
by Lars Kroijer
Published 5 Sep 2013

As a reward for taking the interest rate risk associated with the longer-term bonds they typically yield more than the short-term bonds, as illustrated in Figure 4.1.2 So if you need a product that will not lose money over the next year, pick short-term bonds to match that profile. However, if you – like most people – are after a product that will provide a secure investment further into the future, pick longer-term bonds and accept the attendant interest-rate risk. Figure 4.1 The typical bond yield curve You should therefore consider the time horizon of your portfolio and select the maturity of your minimal risk bonds accordingly. If you are matching needs far in the future (like your retirement spending) there is certainly merit in adding long-term bonds or even inflation-protected bonds (see below) to your portfolio.

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You will have to accept interest rate risk even if you avoid inflation risk by buying inflation-adjusted bonds. 1 For those who don’t think government bonds can default I would encourage you to read This Time is Different: Eight Centuries of Financial Folly by Carmen Reinhart and Kenneth Rogoff (Princeton University Press, 2011). The authors make a mockery of the belief that governments rarely default and that we are somehow now protected from the catastrophic financial events of the past. 2 There are cases where the yield curve is reversed and shorter-term bonds yield more than longer-term ones, but these cases are less frequent. 3 Imagine the scenario where you want to hold one-month government bonds. Tomorrow the bonds are no longer one-month to maturity, but 29 days. Is this ok? How about 2 days hence? How much you are willing for the maturity to deviate from exactly 30 days is up to you, but in reality there is a trading and administrative cost associated with trading bonds.

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While interesting (different countries often have very different results) these surveys have been criticised for being heavily sentiment driven and more about a desired return than one actually expected. 5 While the historical risk premium was calculated as a premium to short-term debt, the minimal risk asset return expectation of 0.5% is not as short-term (highly rated real short-term debt returns at the time of writing have negative yields). However, historically the short-term real return has been closer to 0.5% and this is what the equity risk premium is based on. Also, the current yield curve suggests that the negative real interest rate will not last forever. chapter 6 * * * The risk of equity markets Understanding the risk you take to get returns It seems that every pre-bubble period is characterised by an abundance of changing paradigm stories or that ‘this time it’s different’, only for history to repeat itself and markets falling.

All About Asset Allocation, Second Edition
by Richard Ferri
Published 11 Jul 2010

Figure 8-3 shows the changing interest-rate spread between 1-year Treasury bills and 10-year Treasury notes since the early 1950s. Most of the time, a 10-year Treasury note has had a higher yield than the 1-year T-bill. These are periods with a “normal” yield curve, so called because under normal conditions short-term T-bills are expected to yield less than intermediate-term Treasury notes. A “flat” yield curve occurs when the yield on T-bills and T-notes is the same. If T-bills have a higher yield than Treasury notes, this is known as an “inverted” yield curve. There is a school of thought that believes that when the curve is inverted, the economy is slowing and the stock market will likely go down. There appears to be some support for this theory, although CHAPTER 8 152 FIGURE 8-3 Treasury Term Spread, 1-Year T-Bills, and 10-Year Treasury Notes 4.0 Normal yield curve (long-term rates higher than short-term rates) 3.0 Yield difference 2.0 1.0 0.0 Feb. 89 ⫺1.0 Apr. 00 Jan. 06 ⫺2.0 ⫺3.0 Dec-10 Dec-05 Dec-00 Dec-95 Dec-90 Dec-85 Dec-75 Dec-70 Dec-65 Dec-60 Dec-55 ⫺4.0 Dec-80 Inverted yield curve (short-term rates higher than long-term rates) the timing is sketchy at best.

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There appears to be some support for this theory, although CHAPTER 8 152 FIGURE 8-3 Treasury Term Spread, 1-Year T-Bills, and 10-Year Treasury Notes 4.0 Normal yield curve (long-term rates higher than short-term rates) 3.0 Yield difference 2.0 1.0 0.0 Feb. 89 ⫺1.0 Apr. 00 Jan. 06 ⫺2.0 ⫺3.0 Dec-10 Dec-05 Dec-00 Dec-95 Dec-90 Dec-85 Dec-75 Dec-70 Dec-65 Dec-60 Dec-55 ⫺4.0 Dec-80 Inverted yield curve (short-term rates higher than long-term rates) the timing is sketchy at best. Sometimes the curve becomes inverted a couple of years before stocks correct during a recession, and sometimes it inverts after the market has already started to pull back.

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Wash Sale Rule The IRS regulation that prohibits a taxpayer from claiming a loss on the sale of an investment if that investment or a substantially identical investment is purchased within 30 days before or after the sale. Yankee Dollars/Bonds Debt obligations, such as bonds or certificates of deposit, bearing U.S. dollar denominations and issued in the United States by foreign banks and corporations. Yield Curve A line plotted on a graph that depicts the yields of bonds of varying maturities, from short term to long term. The line, or “curve,” shows the relationship between short-term interest rates and long-term interest rates. Yield-to-Maturity The rate of return an investor would receive if the securities held in his or her portfolio were held until their maturity dates. 

Trillion Dollar Triage: How Jay Powell and the Fed Battled a President and a Pandemic---And Prevented Economic Disaster
by Nick Timiraos
Published 1 Mar 2022

In May 2019, yields on ten-year government notes—which tend to go down when investors become risk-averse or pessimistic about growth—slid from 2.5 percent to 2.13 percent. When the long-term yield slips below the level of three-month Treasury bills, it creates a dreaded Wall Street dynamic known as the “inversion of the yield curve.” Essentially, investors expect central bankers may need to lower short-term rates in response to a slowdown. Inverted yield curves have frequently preceded recessions by one or two years. Before an early June speech at the Federal Reserve Bank of Chicago, Powell huddled with Clarida and Williams. They agreed on adding a key phrase to his introductory remarks: Powell pledged the Fed would “act as appropriate” to sustain the expansion.

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Date 2020 Covid-19 Cases Covid-19 Deaths Dow Jones Average VIX Fear Index Wednesday, March 18 12,934 152 19,898 (↓ 1,338) 76.45 (↑.54) Triage Powell emailed Clarida first thing the next morning, March 19, unspooling his latest thinking. We’ve got to go bigger on Treasuries and mortgages, the Fed chair said. The global riptide meant markets were on the verge of collapse, said Powell, and he asked Clarida again for his thoughts on yield-curve control. At 11:30 p.m. the night before, Australia’s central bank had rolled out its own yield-curve-control program by committing to buy government debt in whatever amounts were needed to hold near zero the yields on debt with maturities of up to three years. Then Powell vented another brainstorm: Should the Fed come up with a 13(3) facility that would purchase existing corporate bonds?

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Now he acknowledged the obvious to Powell: “Our purchases are massive, but they’re not working.” Rates on the most recently issued Treasury securities continued to diverge from older issues, an important danger sign that the Fed’s purchases were falling short. Powell sighed. “Are you saying we should move to yield-curve control?” he asked. Yield control would mean buying as much debt as necessary to achieve a certain yield—an open-ended commitment the Fed had not made since the Second World War. “I’m not recommending it now, but failure is not an option,” Clarida responded. “So at a minimum, we’ve gotta do more, and we’ve gotta get the ten-year yield under control.”

After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead
by Alan S. Blinder
Published 24 Jan 2013

The good news was that Bernanke and the FOMC doves were firmly in control. The bad news was that the Fed was nearly out of bullets. Eyes would now turn to fiscal policy. THE EXPECTATIONS THEORY OF THE YIELD CURVE The idea that intermediate-and long-term interest rates depend on beliefs (or expectations) about what overnight interest rates (like the federal funds rate) will be in the future is called the expectations theory of the yield curve. It is the basis for Federal Reserve policies that make implicit or explicit commitments about future interest rates. Here’s a simple example: If one-day money costs 2 percent (annualized) today, and the market expects one-day money to cost 3 percent tomorrow, how much should two-day money cost today?

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While the federal funds rate was already down to a superlow 1 percent, the FOMC could lower it still further. The markets thought a 50-basis-point cut most likely. Second, the Committee could try to reduce longer-term interest rates by committing to holding its overnight rate low for a long time. Some called that “open-mouth policy.” The idea is based on the expectations theory of the yield curve, which is explained in the accompanying box. Third, the Fed could keep on expanding its balance sheet, which had already soared from $924 billion the week before Lehman to $2,262 billion on December 11. Which option would the Fed choose? It turned out to be all of the above. In the FOMC’s own language, it decided to use “all available tools” to fight the recession.

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See European Central Bank (ECB) euro, problem of, 418–19, 425–26 financial leadership countries, 417–19 Greece as problem, 380–83, 413–18 as sovereign crisis, 169, 409, 412, 419, 425–26 U.S. economy, impact on, 381–83, 409 European Stability Mechanism, 426 Evans, Charles, 383–84 Excess reserves, reducing rate on, 246–47, 386 Exchange Stabilization Fund (ESF), 146, 180 Exchange-traded derivatives, 61, 281, 436 Executive compensation, 81–84 AIG bonuses after bailout, 137–38, 297 Dodd-Frank provisions, 309 golden parachute to O’Neal (Stan), 152 regulatory efforts, rejection of, 83–84 regulatory needs for, 283–85, 297, 437 risk-based rewards, 81–83, 284 TARP restrictions, 183, 188–91, 202 Exit strategy of Fed, 367–79 European crisis and delay of, 381–83, 409 excess reserves, dealing with, 369–72, 378, 431 and inflation level, 374–75, 378 interest rates, normalizing, 372–74, 378, 431 timing of, 374–75, 378–79 unconventional policy, continuation of, 384–86 Expectations theory of yield curve, 221–23 Fannie Mae/Freddie Mac, 115–19 competitive edge of, 116 conservatorship, 118–19, 287n federal safety net for, 115–16, 118 financial crisis, role in, 117–18 functions of, 115, 324 future view for, 287–88, 297–98, 309 mortgage default, low rate, 72 QE1 asset-purchase, 206–7, 251 in shadow banking system, 60 and subprime mortgages, 71–72, 116–17 vulnerabilities of (2007), 116–17 Farkas, Lee, 355 Federal budget deficit, 387–408 and Bush administration actions, 388–91, 394 and creditworthiness of U.S., 395–96, 400, 401 economic danger of, 395 future view for, 400–408, 430 growth in dollars, 387–88, 392–93 and health care costs, 390, 398, 404, 406 national debt ceiling, raising, 400 Obama attempts to address, 396–400 public opinion of, 393–95 and recovery programs, 234–36, 350–51, 359–61, 392–93 Simpson-Bowles plan, 397, 401–2, 405–8, 430 Federal Deposit Insurance Act (1991), 162 Federal Deposit Insurance Corporation (FDIC) history of, 144, 146–47 marketable debt guarantee, 161–62 money market funds, not insured, 144 receivership authority of, 298, 306, 310 regulatory failure of, 58 systemic risk exception invoked, 162–63 Temporary Liquidity Guarantee Program (TLGP), 161–62, 208, 242 Federal Deposit Insurance Corporation Improvement Act, 306 Federal Housing Finance Agency (FHFA), 118 home price index, 17–18, 18n, 34 Federal Open Market Committee (FOMC) communication problems of, 373–74 funds rate cuts (2007), 96–97, 172 funds rate cuts (2008), 221–23, 244 growth versus exit actions (2011), 381–85 initial response to crisis, 91–93, 95, 171 landmark meeting (2008), 221–23 Operation Twist, 383–84 Federal Reserve anti-Fed sentiments, 276–77, 293–94, 348–49, 352–53, 358–59 bailouts, 105–19, 136–40 balance sheet (2007–2011), 368–72, 431 and bond bubble burst, 44–45 chairman during crisis.

Beyond Diversification: What Every Investor Needs to Know About Asset Allocation
by Sebastien Page
Published 4 Nov 2020

Suppose a bond portfolio has a duration (interest rate sensitivity) of five years. If rates unexpectedly spike by +0.5%, the portfolio should go down about –2.5% (5 × –0.5%). However, we now earn +0.5% more on the portfolio than we did before the rate shock. If we ignore several less important subtleties, such as yield curve effects and the timing of the rate shock, we can expect to recover the 2.5% over roughly five years (5 × +0.5%). This offset effect works no matter the size of the rate shock. It explains why, historically, the initial yield to maturity has been a remarkably good predictor of forward return for bonds, and the sweet spot of our ability to forecast, or close enough, is when the investment horizon matches the portfolio’s duration.

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However, contrary to conventional wisdom, this example illustrates how rising rates are good for bonds: higher rates mean higher reinvestment rates and, ultimately, higher expected returns. In an excellent paper titled “Bond Investing in a Rising Rate Environment” (2014), my former colleagues Helen Guo and Niels Pedersen go beyond this simple example. They account for the timing of the rate shock(s), and they model nonparallel yield curve shifts. They find that if rates rise gradually, or if the increase occurs later in the investment horizon, then it takes longer for the reinvestment effect to heal the price shock(s). They derive rules of thumb to predict when the convergence will occur for these special cases. Their results are remarkably intuitive, simple, and quite interesting (again, if you’re into geeky bond math).

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As rates rise, the investor reinvests coupons and principals at higher yields, and vice versa when rates decline. Principal gets reinvested when maturity is reached, as well as within the investment horizon to maintain duration and/or earn the roll down. The roll down component is measured based on the steepness of the curve, and we assume a one-year holding period. If the yield curve slopes upward (as it does most of the time), and nothing else changes (the level of yields remains constant, defaults remain constant, etc.), a bond will appreciate in price over time. The intuition is as follows: One year from now, the bond will be one year closer to maturity. Since a bond with shorter maturity is discounted at a lower rate, its price will go up.

Valuation: Measuring and Managing the Value of Companies
by Tim Koller , McKinsey , Company Inc. , Marc Goedhart , David Wessels , Barbara Schwimmer and Franziska Manoury
Published 16 Aug 2015

Small irregularities in the current yield curve can lead to large spikes and dents in the forward rate curves, which 776 BANKS EXHIBIT 34.11 Yield Curve and Future Interest Rates Interest rate, % Current yield curve Forward 1-year rates Forward 3-year rates Forward 5-year rates Forward 10-year rates 6 5 4 3 2 1 0 2015 2020 2025 2030 2035 2040 would produce large fluctuations in net interest income forecasts. As a practical solution, use the following procedure. First, obtain the forward one-year interest rates from the current yield curve. Then smooth these forward oneyear rates to even out the spikes and dents arising from irregularities in the yield curve. Finally, derive the two-year and longer-maturity forward rates from the smoothed forward one-year interest rates.

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The rates are all derived from the current yield curve. To illustrate, the expected three-year interest rate in 2016 follows from the current three- and six-year yield: [ r2016−2019 ] 13 [ ] 13 (1 + 2.82%)6 = −1 = − 1 = 4.0% (1 + Y2016 )3 (1 + 1.66%)3 (1 + Y2019 )6 where r2016–2019 is the expected three-year interest rate as of 2016, Y2016 is the current three-year interest rate, and Y2019 is the current six-year interest rate. In practice, forward rate curves derived from the yield curve will rarely follow the smooth patterns of Exhibit 34.11. Small irregularities in the current yield curve can lead to large spikes and dents in the forward rate curves, which 776 BANKS EXHIBIT 34.11 Yield Curve and Future Interest Rates Interest rate, % Current yield curve Forward 1-year rates Forward 3-year rates Forward 5-year rates Forward 10-year rates 6 5 4 3 2 1 0 2015 2020 2025 2030 2035 2040 would produce large fluctuations in net interest income forecasts.

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However, following the expectations theory of interest rates, long-term rates move higher when short-term rates are expected to increase, and vice versa. Following this theory, it is necessary to ensure that our expectations for interest rates in future years are consistent with the current yield curve. Exhibit 34.11 shows an example of a set of future one-, three-, five-, and ten-year interest rates that are consistent with the yield curve as of 2014. The forecasts for a bank’s interest income and expenses should be based on these forward rates, which constitute the matched-opportunity rates for the different product lines. For example, if the bank’s deposits have a three-year maturity on average, you should use the interest rates from the forward three-year interest rate curve minus an expected spread for the bank to forecast the expected interest rates on deposits in your DCF model.

The Only Game in Town: Central Banks, Instability, and Avoiding the Next Collapse
by Mohamed A. El-Erian
Published 26 Jan 2016

El-Erian, “What We Need from the IMF/World Bank Meetings,” Financial Times, October 6, 2013, http://blogs.ft.com/the-a-list/2013/10/06/what-we-need-from-the-imfworld-bank-meetings/. CHAPTER 23: THE BELLY OF THE DISTRIBUTION OF POTENTIAL OUTCOMES 1. “The World in 2015,” Economist, December 2014. 2. Michael J. Casey, “Flattening Yield Curve Latest Complication for Fed,” Wall Street Journal, April 12, 2015, http://blogs.wsj.com/moneybeat/2015/04/12/flattening-yield-curve-latest-complication-for-fed/?mod=WSJ_hps_MIDDLE_Video_Third. 3. Mohamed A. El-Erian, “The Instability in Central Bank Divergence,” Financial Times, February 26, 2014, http://blogs.ft.com/the-a-list/2014/02/26/the-instability-in-central-bank-divergence/.

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In the span of a few weeks, the Swiss National Bank would suddenly dismantle a key element of its exchange rate system, and do so in what proved to be an incredibly disruptive manner for markets; Singapore would alter its own exchange rate system; and Denmark would declare that it would refrain from issuing any more government bonds. The next few weeks would also witness a market collapse in government yields, including negative levels all the way out to the nine-year point in the German yield curve and the benchmark ten-year bond there trading at just five basis points (that is, 0.05 percent). They would see investors rush to buy many newly issued bonds directly from some European governments, agreeing to pay (rather than receive) interest income for doing so. And they would witness large banks actively discourage depositors from keeping money with them.

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This discomfort relates to the growing difficulties that both national economies and the global system face (and will face) in reconciling in a relatively stable manner five trends that I believe will become more pronounced in the period ahead—namely: • Multi-speed growth; • Multi-track central banking policies; • Growing pricing anomalies, from negative nominal interest rates to the unusual position of having “the U.S. yield curve…now shaped as much by foreign monetary policy as the Fed’s”;2 • Non-economic headwinds; and • The impact of certain disruptive innovations going macro. Together they suggest that, as opposed to the consensus view of a relatively stable low-growth world, we are looking at increasing economic and policy divergences among countries, which, together with prospects for national political and geopolitical disruptions, will make the belly of the distribution a lot less stable.

How to Speak Money: What the Money People Say--And What It Really Means
by John Lanchester
Published 5 Oct 2014

From the point of view of listening to the news, the thing to remember is that yields going up means the debt is being seen as more risky. yield curve The yield projected into the future. If you lend money, the general rule is that longer you’re lending it for, the more your money is at risk. This means that longer loans should offer a higher yield: more risk means the yield has to be more tempting to get you to lend money. The graph of time plotted against risk is called the yield curve, and over time, it goes up, as the risk and yield go up. Sometimes, though, when things are weird and the economy is hitting hard times, investors think that the long-term rates currently on offer are better than the ones they’ll be getting in a few months’ time.

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Now that I know more about it, I think everybody else should too. Just as C. P. Snow said, in the late 1950s, that everyone should know the second law of thermodynamics,* everyone should know about interest rates, and why they matter, and also what monetarism is, and what GDP is, and what an inverted yield curve is, and why it’s scary. From that starting point, of language, we begin to have the tools to make up an economic picture, or pictures. That’s what I want this book to do: to give the reader tools, and my hope is that after reading it you’ll be able to listen to the economic news, or read the money pages, or the Wall Street Journal, and know what’s being talked about and, just as importantly, have a sense of whether you agree or not.

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They pile into long-term debt, taking the opportunity to get these good rates while they’re still available. The price of those long-term debts goes up. Because price and yield are inversely correlated, the rising price makes the yield on those debts go down: that can mean that the longer-term debt ends up with a lower yield than short-term debt. This is known as an inverted yield curve, and it is a sure sign that the market thinks there is severe trouble just ahead. yuan and renminbi Observers of China refer to both the renminbi and the yuan in talking about the country’s currency. They’re the same thing: renminbi means “the people’s currency,” and it was the name given the new currency at the foundation of the People’s Republic of China in 1949.

The Four Pillars of Investing: Lessons for Building a Winning Portfolio
by William J. Bernstein
Published 26 Apr 2002

On the other hand, the excess return earned by extending bond maturities is minimal, as shown by the “yield curve” for the U.S. Treasury market I’ve plotted in Figure 13-2. Notice that you get about 4% of extra return by extending your maturity from 30 days out to 30 years. This is about as “steep” as the yield curve gets. Much of the time, the curve is much less steep—perhaps 1% to 1.5% difference between long and short yields—and there are even times when the yield curve is “inverted,” i.e., when long rates are lower than shorter rates. Table 13-4. Bond and Bond Index Funds Figure 13-2. U.S. Treasury yield curve. (Source: The Wall Street Journal, 3/14/02.)

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(Source: The Wall Street Journal, 3/14/02.) In Figure 13-2, note that you get the most “bang for the buck” by about a five-year maturity. This is the steepest part of the yield curve—the part that rewards you the most. Beyond that, the extra return diminishes, with continually increasing risk. The stock portion of your portfolio is the place to take risk, not the bond portion, where the purpose is to shelter you from market downturns and provide ready liquidity. The curve is steepest in the first year or two. For the most part, then, you should keep the maturity of your bond portfolio between one and five years. There are a wide variety of bond funds that will accomplish this.

Trading Risk: Enhanced Profitability Through Risk Control
by Kenneth L. Grant
Published 1 Sep 2004

In the case of the former, a prudent risk manager might want to know what happens to this portfolio if interest rates continue to move in nonintuitive ways that are adverse to the portfolio, and he or she might design a set of scenarios to cover the following such contingencies: 1. Relative Value Fixed Income. • Interest rates change by the same magnitude across the yield curve (called a parallel shift). • Rates at earlier maturities increase at a faster rate than those at further out maturities (flattening twist), or vice versa (steepening twist). • Rates at both ends of the yield curve remain relatively constant, while those in between these endpoints either increase or decrease. By using scenario analysis, one can determine the exposures associated with these types of subtle price movements with a great deal more precision than by using other methods of exposure estimation.

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For example, you may want to calculate your average return on longs versus shorts in order to determine whether there is a discernible bias in your market orientation. Similarly, you can compare your averages across market sectors (for equities), underlying markets (for futures), segments of the yield curve (for fixed income trading), and so on. Look carefully here for differences in your unit performance. Are they tied to external factors such as market conditions or perhaps to areas of expertise or trading comfort? By calculating averages across these factors, you can begin to form an idea of what is working in your portfolio and what isn’t.

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In the case of relative value plays involving instruments of differing credit quality, the designers of scenario analysis routines will typically try to estimate the impact of changes in credit spreads, defined as the premium that lenders will demand of borrowers of lesser credit quality. Like the yield curve manipulations mentioned immediately earlier, these exercises are likely to capture risks that are assumed away by the aggregations embedded in the VaR calculation. 2. Convertible Bond Arbitrage. The typical configuration of a convertible bond arbitrage portfolio is one under which the portfolio contains inventories of bonds that are convertible into stock, as hedged by short positions in the cash equity securities of the same corporations.

The Corona Crash: How the Pandemic Will Change Capitalism
by Grace Blakeley
Published 14 Oct 2020

Instead, the main effect of low interest rates was to inflate a debt bubble three times the size of global GDP.10 The problem was clear: capitalism had lost all momentum. Many economists were predicting that a recession would hit the US, the UK and the Eurozone by 2022.11 The yield curve, which shows the returns on US Treasuries of different maturities, had inverted for the first time since 2007 – meaning that short-term government bonds had higher yields than long-term bonds.12 An inverted yield curve has augured every major recession for the last half century. In the end, the recession came earlier – and hit unimaginably harder – than expected. All over the world, capitalists were already looking to nation-states to save them from the overlapping crises of secular stagnation, populism and climate breakdown.

The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction
by Richard Bookstaber
Published 1 May 2017

I have seen this issue repeatedly in risk management, and it is one reason any risk management model will not cover all risks. Once the model is specified, the traders will try to find a way around it. Are you measuring interest rate risk? Well, fine, then I will do a trade that is interest rate neutral but bets on the slope of the yield curve. Now you’re measuring yield curve risk? Fine, then I will do a trade that is both interest rate and yield curve neutral, but rests on the curvature of the yield curve—a butterfly trade. And as this game is being played, the complexity and thus endogenous risk is increasing with each iteration. One of the problems with the standard risk measures is that they become exposed to multiple dimensions for such gaming, and for gaming in a way that is harder to detect.

High-Frequency Trading
by David Easley , Marcos López de Prado and Maureen O'Hara
Published 28 Sep 2013

Relationships between different stocks are at best weak. As a consequence, quant researchers in equity markets have focused intensively on the details of the execution process. By contrast, fixed-income products are inherently complex, and quantitatively minded researchers in this area have focused on such aspects as yield curve modelling and day counts. Asset managers have not traditionally focused on measuring or managing execution costs, and have few effective tools to do so. However, the Securities Industry and Financial Markets Association (SIFMA) noted that “It is clear that the duty to seek best execution imposed on an asset manager is the same regardless of whether the manager is undertaking equity or fixed-income transactions” (SIFMAAsset Management Group 2008). 43 i i i i i i “Easley” — 2013/10/8 — 11:31 — page 44 — #64 i i HIGH-FREQUENCY TRADING This chapter discusses some details of the fixed-income markets that present special challenges for best execution in general and automated trading in particular.

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. • Information events: interest rates markets are strongly af- fected by events such as economic information releases and government auctions. In contrast to earnings releases in the equities markets, these events generally happen in the middle of the trading day and we must have a strategy for trading through them. • Cointegration: interest rates products generally differ only in their position on the yield curve. Thus, they move together to a much greater degree than any collection of equities. To achieve efficient execution in a single product, we must monitor some subset of the entire universe of products. • Pro rata matching: because futures products are commonly traded on a single exchange (in contrast to the fragmentation in the equities markets), the microstructural rules of trading can be much more complex.

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A systematic test of the accuracy of the cointegration prediction shows that it is far less than perfectly accurate, but still effective enough to add value to real-time trading. Figure 3.8 shows the principal components for the full set of four price series shown in Figure 3.4. This corresponds to what would be obtained by a traditional analysis of yield curve dynamics, but here on an intra-day timescale. The first component represents the overall market motion, while the other components represent shifts 57 i i i i i i “Easley” — 2013/10/8 — 11:31 — page 58 — #78 i i HIGH-FREQUENCY TRADING Figure 3.7 Short-term price predictor, using the projections shown in Figures 3.5 and 3.6 A B C D 04.00 06.00 E F G H I ZBH3 ZNH3 00.00 02.00 08.00 10.00 12.00 14.00 16.00 CST on Tuesday December 11, 2012 Black lines are the raw price series as in Figure 3.4.

Financial Modelling in Python
by Shayne Fletcher and Christopher Gardner
Published 3 Aug 2009

+ccy+".hw" mr = env.retrieve constant(key) if mr <> 0: term var *= (math.exp(2.0*mr*t)-1.0)/(2.0*mr) else: term var *= t return math.sqrt(term var) The Hull–White Model 101 def local vol(self, t, T, ccy, env): assert t <= T key = "cv.mr."+ccy+".hw" mr = env.retrieve constant(key) return math.exp(-mr*t)-math.exp(-mr*T) The requestor class uses the class environment implemented in the ppf.market.environment module. The purpose of this class is to provide access to market data objects such as yield curves, volatility surfaces, correlation surfaces, etc. Refer to section 5.3 for the details. The following code snippets illustrate how to construct a requestor and make a request for a discount factor and a term volatility: >>> import math >>> import ppf.market >>> from ppf.math.interpolation import loglinear >>> times = [0.0, 0.5, 1.0, 1.5, 2.0] >>> factors = [math.exp(-0.05*t) for t in times] >>> c = ppf.market.curve(times, factors, loglinear) >>> env = ppf.market.environment() >>> key = "zc.disc.eur" >>> env.add curve(key, c) >>> r = requestor() >>> t = 1.5 >>> print r.discount factor(t, "eur", env) 0.927743486329 >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> 0.1 import math import ppf.market from numpy import zeros expiries = [0.1, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0] tenors = [0, 90] values = zeros((8, 2)) values.fill(0.04) surf = ppf.market.surface(expiries, tenors, values) env = ppf.market.environment() key = "ve.term.eur.hw" env.add surface(key, surf) key = "cv.mr.eur.hw" env.add constant(key, 0.0) r = requestor() t = 0.25 print r.term vol(t, "eur", env) 8.1.2 State When pricing a financia instrument we frequently need to know about the state of the world – the world being both define and modelled by the chosen model.

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Unit tests for the exercise component are provided in the module ppf.test.test hull white. The method test explanatory variables on the class exercise tests checks that the computed explanatory variables, the LIBOR and swap rates, The Hull–White Model 117 match the corresponding rates taken from the yield curve for the case when the Hull–White volatilities are all zero. def test explanatory variables(self): from ppf.math.interpolation import loglinear times = [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0] factors = [math.exp(-0.05*t) for t in times] c = ppf.market.curve(times, factors, loglinear) expiries = [0.0, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0] tenors = [0, 90] values = numpy.zeros((8, 2)) surf = ppf.market.surface(expiries, tenors, values) from ppf.date time \ import date, shift convention, modified following, basis act 360, months pd = date(2008, 01, 01) env = ppf.market.environment(pd) key = "zc.disc.eur" env.add curve(key, c) key = "ve.term.eur.hw" env.add surface(key, surf) key = "cv.mr.eur.hw" env.add constant(key, 0.0) r = ppf.model.hull white.requestor() s = ppf.model.hull white.monte carlo.state(10) sx = s.fill(0.25, r, env) f = ppf.model.hull white.fill(3.0) flows = ppf.core.generate flows( start = date(2008, 01, 01) , end = date(2010, 01, 01) , duration = months , period = 6 , shift method = shift convention.modified following , basis = "ACT/360" , pay currency = "EUR") lg = ppf.core.leg(flows, ppf.core.PAY) ex = ppf.model.hull white.monte carlo.cle exercise(lg) t = env.relative date(flows[1].accrual start date())/365.0 T = env.relative date(flows[1].accrual end date())/365.0 ret = ex(t, f, sx, r, env) dft = c(t) dfT = c(T) expected libor = (dft/dfT-1.0)/flows[1].year fraction() pv01 = 0.0 for fl in flows[1:]: T = env.relative date(fl.pay date())/365.0 dfT = c(T) pv01 += fl.year fraction()*dfT T = env.relative date(flows[-1].accrual end date())/365.0 dfT = c(T) expected swap = (dft-dfT)/pv01 118 Financial Modelling in Python expected libors = numpy.zeros(10) expected libors.fill(expected libor) expected swaps = numpy.zeros(10) expected swaps.fill(expected swap) actual libors = ret[:, 0] actual swaps = ret[:, 1] assert seq close(actual libors, expected libors) assert seq close(actual swaps, expected swaps) 8.2 THE MODEL AND MODEL FACTORIES The model class brings all the components from the preceding sections together into one place.

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.; mathematics; NumPy; ppf package basics 193–205 batch interpreter mode 193–4 benefit 1–4 built-in data types 1, 195–7 C++/Python ‘Hybrid Systems’ 4, 159–63 C API routines 19–26, 161–3 C/C++ interoperability benefit 2, 3–4, 7–9, 11–26, 157 class basics 2–3, 201–3 COM servers 4, 5–6, 98, 165–89 concepts 1–4, 193–205 control fl w statements 197–200 dictionaries 119–22, 181, 196–7, 215–16 dynamic type system 2–3 encapsulation support 2–3, 58–61, 209 expressiveness aspects 1 extensibility aspects 1–4, 7–9, 11–26 financia engineering 1–4, 11–26 function basics 2–3, 200–1 functional programming idioms 1 GUI toolkits 2 high-level aspects 1 indented code 198–200 inheritance basics 122, 202–3, 209–11 interactive interpreter mode 193–4 interoperability aspects 1–4, 7–9, 11–26, 157 interpreters 2, 24–6, 45–6, 193–4, 208–9 list basics 3, 196–7, 215 Microsoft Excel 4, 165–89 misconceptions 2–3 module basics 203–5 overview of the book 3–4 package basics 1, 203–5 productivity benefit 1 simple expressions 194–5 Index standard libraries 1 structure misconceptions 2–3 tuples 131, 195–7, 200–1, 215 visualisation software integration 2 whirlwind tour 193–205 white space uses 198–200 Python Distutils package 9 Python Programming on Win32 (Hammond & Robinson) 165 Python Scripting for Computational Science (Langtangen) 2 python.hpp 214–15 python -i command 193 PyUnit testing module, concepts 6–7, 9 quadratic roots, concepts 3, 46–9 quadratic fo 132–42 quadratic roots 46–9 quantitative analysis 1–4, 27–61, 123–43, 165–89 raise 15–16, 30–1, 35–6, 40–1, 43–5, 50–8, 66–7, 78, 81–3, 85–7, 88, 89, 91, 98, 102, 105–6, 113, 118–19, 131, 133, 134–6, 166–9, 170–6 random 27–8, 45–6 random number generation, concepts 3, 27–8, 45–6, 112–22 random variables, expectation calculations 3, 49–61 range function, Python basics 197–8 ratio 48–9 rcv flows 89–91, 96–8, 120–2 redemption cap 153–6 redemption floor 153–6 reference counts 20–6 references, C++ 212–14 reg clsid 169–76, 177–87, 188–9 register com class 169–76 register date... 11–16, 160–3 register date more.cpp 160 register numpy.cpp 23 register special functions 18–19 reg progid 169–76, 177–89 regression schemes 4, 132–42, 150–2, 219–20 regression model 136–42, 150–2 regressions 132–42 regrid 55–61 regridder 58–61 regrid fs 55–7 regrid xT 58–61 regrid yT 58–61 relative date 66–7, 105–22, 125–8, 146–57 233 requestor 100–22, 124–8, 129–42, 146–57 requestor component, pricing models 100–22, 124–8, 129–42 reset currencies, concepts 70–9, 96–8, 105–22 reset dates 69–79, 95–8 see also observables reset basis 72–9, 89–91, 96–8, 120–2, 178–87 reset ccy 69–79, 90 reset currency 71–9, 89–90, 96–8, 105–22, 177–87 reset date 69–79, 95–8 reset duration 73–9, 89–91, 96–8, 120–2 reset holiday centres 72–9 reset id 69–79, 93–8, 146–57 reset lag 72–9 reset period 73–9, 89–91, 96–8, 120–2 reset shift method 72–9, 89–91, 96–8, 120–2, 178–87 retrieve 66–7, 97–8, 124–8, 169–76, 179–87, 188–9 retrieve constant 67, 100–22 retrieve curve 66–7, 100–22, 148–57 retrieve surface 67, 100–22 retrieve symbol... 97–8, 124–8, 131–42, 149–52 return statements, Python basics 200–5 risk the Greeks 142–3 management systems 4 Robinson, Andy 165 rollback 57–61, 108–22, 124–8 rollback component, pricing models 108–22, 124–8, 177–87 rollback max 57–61, 108–22, 124–8 rollback tests 109–22 roll duration 72–9, 84–5, 89–91, 96–8, 120–2, 177–87 roll end 72–9, 81–3, 84–5, 86–91 roll period 72–9, 84–5, 89–91, 96–8, 120–2, 177–87 rolls 14–16, 72–3 roll start 77–8, 81–3, 86–91 root-findin algorithms bisection method 35–6, 37 concepts 3, 35–7 Newton–Raphson method 36–7 root finding 35–7 roots 46–9, 53–7 RuntimeError 30–1, 35–6, 40–1, 43–5, 50–8, 66–7, 77, 81–3, 85–7, 88, 89, 90, 98, 102, 104–5, 113, 118–19, 131, 133, 134–6, 147–8, 169, 170–6, 177–8, 202–3 sausage Monte-Carlo method 143 Schwartz, E.S. 219 234 Index SciPy 1, 3, 8 see also NumPy scope guard techniques 20 SDEs 218 second axis 64–5 seed 112–22, 150–2 self 31–4, 45–6, 51–61, 63–7, 69–79, 93–122, 124–8, 130–42, 146–57, 178–89 semi-analytic conditional expectations, concepts 57–61 semi analytic domain integrator 57–61 server 166–89 set event 126–8, 130–42 set last cfs 135–42 sgn 46–9 shape 43–6, 50–1, 58–61, 81–3, 103–22, 133–42 shared ptr hpp 20–4 shift 14–16, 72–9, 86–8, 111–22 shift convention 14–16, 73–9, 80–2, 83–91, 96–8, 120–2, 151–2 shift method 14–16, 73–9, 80–2, 83–91, 120–2 short rates 101–2 sig 42–6, 65 sign 35–6 simple expressions, Python basics 194–5 sin 205 singular value decomposition of a matrix see also linear algebra concepts 42–6 singular value decomposition back substitution 42–6 solve tridiagonal system 2–3, 34, 39–40 solve upper diagonal system 17–19, 40–4, 50–1 solving linear systems see also linear algebra concepts 39–40 solving tridiagonal systems see also linear algebra concepts 2–3, 34, 39–40 solving upper diagonal systems see also linear algebra concepts 17–19, 40–4, 49–51 sort 48–9 special functions 17–18, 27–61 spread 70–9, 154–6 sqrt 48–9, 52–7, 59–61, 100–22 square tridiagonal matrices 33–4, 40–1 standard deviations 44–6, 51–7, 102–22, 133–42, 188–9 standard libraries 1 standard normal cumulative distributions see also N concepts 3, 27–9, 31, 51–7, 102–22 start 80–3, 83–91, 96–8, 120–2, 177–87, 198–200 start date 83–4 start of to year 16 state 59–61, 102–22, 124–8, 129–42, 146–57 state component, pricing models 101–22, 124–8, 129–42, 145–52 stddev 53–7, 102–22 step, Python basics 198–200 STL functions, C++ 29 stochastic volatility 113–14 stop, Python basics 198–200 str 71–9, 80–3, 86–7, 94, 166–8, 170–6 string literals, Python basics 194–6 structure misconceptions, Python 2–3 sum array 23–6 surf 101–22 surface 64–7, 101–22 surfaces see also environment concepts 3, 63, 64–7, 100–22, 170–6 definitio 64 volatility surfaces 3, 6, 63–7, 100–22 surface tests 64–7 svd 42–4 see also singular value decomposition of a matrix swap rates 70–9, 104–5, 115–22 swap obs 105–22 swap rate 74–9, 116–22 swaps 4, 70–9, 101–2, 104–5, 115–22, 123–8, 132–42, 145–52, 157 swap tests 149–52 swaptions 4, 101–2, 115–16, 126–8, 132–42, 145–52, 157 symbol table 97–8, 124–8, 129–42 symbol table listener 125–8, 129–42 symbol value pair 130–42, 155–6 symbol value pairs to add 130–42, 155–6 sys 27–8 table 82–4, 169 tables, adjuvants 82–4, 147–52, 153–6, 177–87 tag 169–76, 177–89 target redemption notes (TARNs) 4, 101–2, 145, 152–7 concepts 152–7 definitio 152 pricing models 4, 101–2, 145, 152–7 target indicator 153–6 tarn coupon leg payoff 152–6 tarn funding leg payoff 154–6 Index TARNs see target redemption notes tarn tests 155–6 templates 18–26, 159–63 tenor duration 72–9 tenor period 72–9 tenors 67, 84–5, 101–22, 170–6 term 28–9, 103–22 term structure of interest rates see yield curves term volatility, Hull–White model 100–22 terminal T 104–22 term var 100–22 term vol 100–22 test 6–7, 9, 17–19, 59–61, 64–7, 109–22, 148–57 test bond 115–22 test bond option 111–22 test bound 30–1 test bound ci 31 test constant 111–22 test discounted libor rollback 109–22 test explanatory variables 117–22 test hull white 67, 109–22 testing concepts 6–7, 9, 17–19 test lattice pricer 148–57 test market 64–7 test math 59–61 test mean and variance 114–22 test monte carlo pricer 154–6 test value 149–52 theta 48–9, 205 throw error already set 21–6 timeline 94–8, 125–8, 129–42 see also events Tk 2 tline 96–8 to ppf date 168–9, 178–87 tower law 60 tower law test 60–1 trace 23–6 Traceback 195–7, 202–3 trade 87–91, 94–8, 125–8, 129–42, 150–7, 177–87 trade representations, concepts 3, 69–91, 93–8 trade server, COM servers 176–87 trade utilities, concepts 88–91 trade VBA client 181 trade id 188–9 trades see also exercise...; fl ws; legs concepts 3, 69, 87–91, 93–8, 123–43, 176–87 definitio 69, 88 TradeServer 176–87, 188–9 trade server 176–87, 188–9 235 trade utils 89–91, 129–42, 153–6, 176–87 transpose 41–4 tridiagonal systems 2–3, 33–4, 39–40 try 27–8, 171–6, 177–87 Trying 6–7 tuples, Python basics 131, 195–7, 200–1, 215 TypeError 195–7 Ubuntu... 8 underlying 127–8, 130–42 unicode 172 unit fo 132–42 update indicator 134–42 update symbol 97–8, 126–8, 131–42 upper bound 29–31 USD 70–83, 152 utility 6–7, 29–61, 64–7 utility functions 17–26, 29–61 utils 168–76, 187–9 values 101–22 vanilla financia instruments, pricing approaches 99, 123–8, 145–57 var 102–22 variance 51–61, 102–22 variates 103–22 varT 102–22 Vasicek models 217–18 see also Hull–White model VB... see Microsoft... vector 41, 44–6, 133–42, 212 vectorize 133–42 visualisation software integration, Python benefit 2 vol 51–7, 59–61, 114–22 volatility Hull–White model 100–22 piecewise polynomial integration 51–61 surfaces 3, 6, 63–7, 100–22 vols 65 volt 59–61, 59–61 weekdays 15–16, 159–63 while statements, Python basics 199–200 white space, Python basics 198–200 win32 165–89 Win32 Python extensions 165–89 xh 52–7 xl 52–7 xprev 53–7 xs 56–61 xsT 60–1 xT 58–61, 108–22 xtT 58–61, 108–22 xt 58–61, 108–22 

The Simple Path to Wealth: Your Road Map to Financial Independence and a Rich, Free Life
by J L Collins
Published 17 Jun 2016

Accordingly, long-term bonds are seen as having higher risk and pay more. If you are a bond analyst, you’ll graph this on a chart and create what is called a yield curve. The chart on the left is fairly typical. The greater the difference between short, mid and long-term rates, the steeper the curve. This difference varies and sometimes things get so wacky short-term rates become higher than long-term rates. The chart for this event produces the wonderfully named Inverted Yield Curve and it sets the hearts of bond analysts all aflutter. You can see what that looks like in the illustration on the right. Stage 7 Inflation is the biggest risk to your bonds.

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Your money is worth less. A big factor in determining the interest rate paid on a bond is the anticipated inflation rate. Since some inflation is almost always present in a healthy economy, long-term bonds are sure to be affected. That’s a key reason they typically pay more interest. So, when we get an Inverted Yield Curve and short-term rates are higher than long-term rates, investors are anticipating low inflation or even deflation. Stage 8 Here are a few other risks: Credit downgrades. Remember those rating agencies we discussed above? Maybe you bought a bond from a company rated AAA. This is the risk that sometime after you buy the company gets in trouble and those agencies downgrade its rating.

Investment: A History
by Norton Reamer and Jesse Downing
Published 19 Feb 2016

Some are rather risk averse, seeking to buy attractive debt securities that deliver healthy and uninterrupted payments. Others have far more complicated schemes to garner returns, such as exploiting aberrations in yield curves. This can occur when the yield curve adopts an unusual geometry (often a flat or steep slope at the extreme) and managers place long and short positions that profit when the yield curve shifts. One of the most common fixed income strategies is the “swap spread,” which involves collecting the difference between Treasury rates and the swap rate. Others invest in mortgage-backed securities, like those packaged by Fannie Mae and Freddie Mac.

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These models have a wide spectrum of sophistication. Some of them are simple, trying to capitalize on well-studied sources of risk premium in the stock market like momentum, value, and small market capitalization. Others are more complicated, analyzing convergence-divergence patterns, steepness or flatness of yield curves or futures curves, or even sifting through press releases and conference calls for information on a stock that the market has neglected. The quant fund faces a few difficulties that the best groups are able to overcome. The first is to ensure that the models are not overfitted to historical patterns.

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(Rozanov), 128 whole life insurance, 132 Wickham, Richard, 46–47 Wiggin, Albert, 190–91 William and Flora Hewlett Foundation, 127 William III (king of England), 73, 97 William of Orange (stadtholder of Dutch Republic), 86 Williams, John Burr, 4, 232–33 Williams, Ted, 311–12 Wilsonian internationalism, 199 Wisselbank, 85 “World’s Largest Hedge Fund Is a Fraud, The” (Markopolos), 152 World War I: impacts of, 95, 162; inflation during, 198; transition out of, 197–98 436 Investment: A History World War II: bull market after, 92, 143; economy and, 275; impacts of, 96; mutual funds during postwar period, 142–44; price and wage fixing of, 110 Wujinzang (Buddhist temples’ wealth), 29 Wu Zetian, 29 Xenophon, 18 Yale University, 257, 296, 328, 332 yield curves, aberrations in, 266 Zarossi, Luigi, 156 Zhiku lending institution, 29–30 

Triumph of the Optimists: 101 Years of Global Investment Returns
by Elroy Dimson , Paul Marsh and Mike Staunton
Published 3 Feb 2002

We can gain further clues by looking at the yield curve, and at the difference between the redemption yield at which long bonds are trading, and the yield on short-term bills. This data was presented graphically in Figure 6-2, which showed that for the first twenty or so years of the last century, US short-term interest rates were typically above long-term bond yields. Over the eighty years from 1921–2000, however, long bond yields have generally been above short rates by an average of around 1.3 percent per year, with mid-maturity bonds typically lying in between. There has thus normally been an upward sloping yield curve, with yields rising with term to maturity.

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There has thus normally been an upward sloping yield curve, with yields rising with term to maturity. There can be at least two reasons for an upward sloping yield curve. First, short-term interest rates may be expected to rise. Alternatively, investors may require some form of liquidity or risk premium for holding long bonds to compensate them for uncertainty about the real interest rate, inflation, or both. Since US interest rates in the early 1920s were similar to those at end-2000, it seems most likely that the tendency for the yield curve to have sloped upward over this period is related to some form of risk premium. While we cannot measure investors’ ex ante requirements or expectations relating to this risk premium, we can measure the bond maturity premia actually achieved.

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McL., 229 Lansdown, A., xii Lanstein, R., 141 Large capitalization stocks, 125–6, 133–6, 143, 146, 148, 212 Latin America, 15, 21, 22 Lebanon, 20 Lehavy, R., 188 Lettau, M., 57, 118 Levy, H., 56, 182 Index Li, B., 145 Li, H., 42 Li, L., 116, 117, 118, 123 Liquidity, 17, 18, 20, 81, 301 Litzenberger, R.H., 140 Loeb, G.M., 205 Lognormal distribution, 56, 182, 184, 203 London, xi, xii, 19, 22, 23, 27, 37, 38, 39, 43, 48, 122, 126, 142, 160, 279, 284, 299 London Business School (LBS), xi, xii, 27, 126, 299 London Share Price Database (LSPD), xii, 37, 142, 299, 300 London Stock Exchange (LSE), 19, 23, 39, 142, 160 Long bonds, 46, 49, 54, 74–90, 163, 169, 171, 173, 174, 239, 300, 301, 306 Look-ahead bias, 35, 41, 142, 222, 299 Longin, F., 117 Lorie, J.H., 38 Low yield stocks, 139–48 Lund, J., 244 Luxembourg, 20 Lynch, A.W., 35 Lystbaek, B., 244 Maddison, A., 22, 228 Maier, J., 254 Malaysia, 20 Malkiel, B., 57, 118 Manufacturing, 19, 24, 26–8 Marcus, A.J., 185, 239 Market development, 5, 18–28 Market failure, 41, 42 Market risk, 56, 105, 108, 118, 122, 164, 166, 179, 180, 181, 184, 188, 195, 205, 215 Market timing, 110 337 Market-to-book ratio, see book-to-market ratio Markowitz, H., xi Marquis, D.R.P., 224 Marsh, P.R., iii, v, xi, xii, 27, 35, 126, 130, 138, 184, 193, 299 Marston, F.C., 188 Maturity premium, 6, 74, 81–84, 89, 101, 204 Maynes, E., 239 McCulloch, J.H., 84 McLeod, H., 42, 279 Meghen, P.J., 259 Mehra, R., 180, 202 Merrett, A., 36 Merrill Lynch, 14, 15, 16, 17, 84 Mexico, 20, 21, 121 Michaely, R., 159, 160, 162 Michie, R.C., 19, 22 Micro capitalization stocks, 125–7, 130–2, 136, 137 Mid-capitalization stocks, 134, 146 Middle East War (1973), 50 Mid-maturity bonds, 75, 78, 81, 85–7 Miller, M.H., 218 Mitchell, B.R., 228, 234, 244, 284 Modigliani, F., 218 Moller, B., 289 Momentum, 208 Monetary system, international, 93–5 Murphy’s Law, 124, 131– 5, 138, 147–8 Mutual funds, 28, 35, 205– 8 Mutual fund fees, 205, 207–8 Myers, S.C., 185, 211, 218, 239 Nagel, S., xii, 142 Naik, N.Y., xi, 35 Nasdaq, 11, 23, 46, 158, 306 Nationalization, 17, 25, 26, 41 Nelson, C.R., 70 Netherlands, The, 200, 274–8 see also cross-country comparisons New York, 11, 19, 23, 24, 38, 43, 58, 124, 306 New York Stock Exchange (NYSE), 11, 19, 23, 24, 46, 48, 124, 125, 126, 133, 136, 142, 158, 306 New Zealand, 20, 21, 84 Nielsen, S., 244 Nigeria, 20 Nokia, 29 Normal distribution, 54– 6, 168, 182, 185 Norway, 20 NTT, 199 O’Brien, P., xii, 239 O’Shaughnessy, J., 140 Odean, T., 207 Odell, K.A., 20 Officer, R.R., 229 Oil, 25, 47, 50, 97, 117, 142 OPEC, 47, 50 Optimists, xi, 156, 176, 179, 185, 188, 224 Otten, R., xii, 274 Pakistan, 20 Panetta, F., xii, 264 Panjer, H.H., 239 Paredaens, J., 234 Paris, 19, 22, 122 Park, A., 35, 198 Parum, C., xii, 244 Passive management, 207–8 see also buy-and-hold strategies, indexation, index funds Payout, see dividend payout Peng, L., 23, 306 Pension plan, 216–7 Pettit, J., 198 Philippines, 20 Poland, 20, 21, 41, 67, 222 Portfolio risk, 108 338 Portugal, 20 Prescott, E., 180, 202 Primary market, 18–9 Privatization, 25, 26 Productivity, 43, 48, 97, 189, 223, 224 Purchasing Power Parity (PPP), 7, 91, 95–104, 219 Railroads, 19, 20, 24, 25, 26, 28, 37, 168 Rajan, R.G., 22 Ramaswamy, K., 140 Random walk, 153, 161 Ratzer, E., 294 Rau, P.R., 160, 161 Real exchange rates, 7, 91, 96–103, 105–8 Real interest rates, 68–73 see also interest rates, bond yields Real term premium, 74, 84–7 Recession, 50, 212 Regional exchanges, 20 Regional stock markets, 20 Regulated businesses, 216–7 Regularities, see anomalies Regulation, 3, 18, 163, 186, 216, 217 Reid, K., 141 Reinganum, M., 131 Reward-to-risk ratio, see Sharpe ratio Repurchases, 143, 149, 158–63, 177, 191 Risager, O., 244 Risk, 54–62 see also currency risk, default risk, market risk, portfolio risk, risk premium, volatility Risk aversion, 163, 179– 81, 188 Risk Measurement Service, 27 Risk premium, 4, 8–10, 34–44, 45, 53, 55, 61, 63, Triumph of the Optimists: 101 Years of Global Investment Returns 74, 81, 88, 89, 195–210, 211–9, 220–4 Risk premium, historical, 163–75 Risk premium, prospective, 176–94 Risk premium, relative to bills, 163–8 Risk premium, relative to bonds, 169–73 Risk-free rate puzzle, 202 Roden, D., 38 Romania, 20 Rose, H.B., xi Rosenberg, B., 141 Ross, S., 41, 211, 212 Rouwenhorst, K.G., 116, 117, 118, 123 Rowley, I., 145 Royal Dutch Shell, 29 Russia, 20, 21, 22, 41, 67, 222 Ryan, R., 156 Sallee, P., 249 San Francisco, 20 Sandez, M., 284 Schaefer, S.M., xi, 85 Scherbina, A., 177 Scheurkogel, A.E., 279 Schumann, C.G.W., 279 Schwartz, D., 135 Schwartz, E.S., 35 Schwartz, S.S., 199, 269 Schwert, G.W., 39, 70 Seasonality, 7, 8, 124, 135– 8, 223 Secondary market, 18–9 Second World War, 36, 58, 70, 71, 73, 76, 79, 94, 98, 116, 122, 152, 189, 195, 221, 224 Sectors, 4, 17, 23–28, 35, 36, 37, 138, 188, 299 Sell-in-May, 135, 138, September 11th 2001, 47, 58, 117, 168, 177, 178, 213 Shares, see equities Sharpe ratio, 105, 111–4, 208 Sharpe, K.P., 239 Sharpe, W.F., xi, 105, 111, 112, 113, 145, 180 Shell, 29 Shiller, R.J., 84, 158, 161, 176, 179 Shleifer, A., 141, 147, 180 Siegel, J.J., xi, 40, 126, 141, 156, 176, 195, 197, 201, 206, 222 Siegel, L.B., 206 Siegel’s constant, 195–202 Singapore, 20 Sinquefield, R., 88, 306 Size effect, xi, 4, 7, 8, 124– 38, 142, 144, 208, 223 Size premium, 8, 124–39, 142, 144 Slovenia, 20, 21 Small capitalization stocks, xi, 124–38, 144, 148, 212 see also size effect Small-cap reversal, 131–5 Smithers, A., 195 Solnik, B., 117, 118, 122 South Africa, 279–83 see also cross-country comparisons South Korea, 12, 15 Spain, 284–8 see also cross-country comparisons Spoerer, M., 254 Sri Lanka, 20, 21 Standard & Poors (S&P), 38, 239 Standard errors, 167, 168, 174, 182, 188 Stattman, D., 141 Stehle, R., xii, 254 Stewart, G.B., 181 Stock markets, 3–5, 11–4, 18–33, 40–4, 155–8, 188–94 Stock repurchases, see repurchases Stocks, see equities Stock-level data, 7, 38, 139 Stolper, G., 66 Suarez, J.L., 284 Index Success bias, 6, 34, 36–8, 42–4, 174, 197 Sui, J.A., 211 Sullivan, T., xii Summer effect, 135, 138 Surveys, 179, 185–7, 188 Survivorship bias, 34–8, 41, 142, 173–5, 202, 222, 299 Sweden, 289–93 see also cross-country comparisons Switzer, L., xii, 239 Switzerland, 294–8 see also cross-country comparisons Taiwan, 12, 20, 133, 161 Tax-loss selling, 135–8 Tax management, 205–6 Taxes, 9, 44, 46, 85, 104, 122, 135–8, 140, 158–62, 193, 205–7, 209, 212, 214, 218, 219, 254, 301 Taylor, A.M., 97, 99 Taylor, B., xii Technological change, 23–4, 189, 223–4 Technology, 23, 25, 26, 28, 199 Term premium, 74, 84–7 Terrorism, 3, 4, 58, 168, 210, 213 Thaler, R., 176 Thomas, J., 188 Thomas, W.A., 259 Time-of-the-day effect, 135 Timmermann, A., xii, 244 Transactions costs, 46, 189, 207 Treasury bills, see bills Treasury inflationprotected securities (TIPS), 74, 84–7, 90, 212 Treynor, J.L., xi, 207, 208 Triangles, 227, 228 Triumph of the Optimists, xi, 176, 224 Turkey, 20, 21, 22 Turn-of-the-year effect, 135–9 339 Twenty-first century, 17, 118, 119, 158, 184, 190, 195, 210 United Kingdom, 23–32, 36–8, 48–50, 63–5, 78, 84–7, 95, 126–9, 135–8, 142–5, 149–53, 190–3, 198–9, 299–305 see also cross-country comparisons United States, 23–32, 45– 7, 54–61, 63–5, 68–70, 74–8, 81–2, 84–9, 95, 124–6, 135–8, 139–42, 149–53, 158–61, 163–6, 169–71, 186–7, 190–3, 196–7, 306–10 see also cross-country comparisons Uppal, R., 117 Urquhart, M.C., 239 Uruguay, 20 US economy, 3, 35, 62, 166, 222 Valbuena, S.F., xii, 284 Valuation, 18, 139, 149, 155, 161, 162, 177–9, 191, 211–7 Value investing, 139–48 Value-growth effect, 139– 48 Value-growth premium, 139–48 Value stocks, 8, 139–48 van Nieuwerburgh, S., 234 van Schaik, F., xii, 274 Vandellos, J.A., 284 Velioti, A.M., xii Venezuela, 20, 21 Vermaelen, T., 160, 161 Violi, R., 264 Vishny, R., 141 Vodafone, 18, 23, 28, 30, 31, 218 Volatility, 54–62, 77–83, 91–9, 105–8, 114, 123, 144, 152, 161, 163, 178– 84, 187, 195–210, 219, 221 see also risk Wada, K., xii, 269 Wall Street Crash, 22, 47, 58, 116, 122, 224 Warnock, F.E., 120, 121 Weekend effect., 135 Weights, 24, 40, 279, 311 Weil, P., 202 Weisbach, M.S., 159 Welch, I., 185–7, 188 Westerfield, R.W., 211, 212 Weston, F., 211 Whelan, S., 259 White, E.N., 19 Williams, J.B., 139 Wilshire Associates, 46, 58, 306 Wilshire 5000, 46, 58, 306 Wilson, J.W., xii, 35, 39, 46, 306 Window-dressing, 135–6, Woodward, G.T., 85 World Bank, 12, 15, 93 World Index, 7, 10, 39–40, 108–14, 119, 123, 166, 167, 168, 171–5, 184–5, 187, 192, 193, 202, 216, 219, 220, 223, 311–5 World ex-US index, 109– 11 World markets, 5, 11–4, 32, 50–1, 123, 138 World Trade Center, see September 11th 2001 World wars, 36, 37, 44, 47, 58, 69, 70, 71, 73, 75, 76, 79, 93, 94, 98, 116, 122, 123, 152, 153, 189, 195, 221, 224 see also First World War and Second World War Wright, S., 195 Wydler, D., xii, 294 Xu, Y., 42, 57, 118 Yield, see bond yield and dividend yield Yield curve, 81 Yugoslavia, 20 Ziemba, W.T., 199, 269 Zingales, L., 22 

Getting a Job in Hedge Funds: An Inside Look at How Funds Hire
by Adam Zoia and Aaron Finkel
Published 8 Feb 2008

This category includes interest rate swap arbitrage, U.S. and non-U.S. government bond arbitrage, forward yield curve arbitrage, and mortgage-backed securities (MBS) arbitrage. The mortgage-backed market is primarily U.S.-based, over-the-counter (OTC), and particularly complex. Note: Fixed income arbitrage is a generic description of a variety of strategies involving investments in fixed income instruments, and weighted in an attempt to eliminate or reduce exposure to changes in the yield curve. Risk Arbitrage Sometimes called merger arbitrage, this involves investment in event-driven situations such as leveraged buyouts (LBOs), mergers, and hostile takeovers.

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I believe I was able to make a case for myself because I knew the theory behind finance and had also taught myself the technical aspects. A lot of bankers know the technical part of finance and are Excel experts, but they don’t have the business intuition that consultants do. In my view, and I’m biased, I’d say a consultant who can understand yield curves, do a DCF analysis, and build a cash flow statement is in great shape to be a hedge fund candidate. My primary advice to someone aspiring to work at a hedge fund is to work to be at the top of your consulting or invest“People have to understand ment banking analyst class. Taking the time to invest in pubwhat each fund does before just lic securities will be a major differentiating factor.

The Rise of Carry: The Dangerous Consequences of Volatility Suppression and the New Financial Order of Decaying Growth and Recurring Crisis
by Tim Lee , Jamie Lee and Kevin Coldiron
Published 13 Dec 2019

Central banks, uniquely, have control over their own funding costs, and it might seem unlikely that they would allow their own carry—the spread between the yields of the assets they hold and their funding cost that they set—to go negative. If an inflationary spiral were to inflict capital losses on them, they could counteract those capital losses by doubling down on their carry trades—buying more, now higher-yielding, bonds—as long as they kept the yield curve positively sloped, that is, kept their policy rate below the rising yields on long bonds. But it seems likely that, in such a spiral, keeping the yield curve positively sloped would exacerbate instead of arrest the spiral. Ultimately, they would then have to choose between restraining the inflation and maintaining their own solvency. The collapse of the central bank carry trade, which could also include carry trades associated with central bank liquidity swaps, could then render central banks insolvent.

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The central bank will be relatively restrictive in its provision of high-powered liquidity (reserves), and this restriction of supply, set against strong bank demand for liquidity deriving from strong demand for credit, will force short-term interest rates upward. If inflation is high, longer-term interest rates will naturally be high also. To be an effective constraint, shorter-term interest rates will need to be at least as high as long-term interest rates (that is, the yield curve will be flat or downward sloping). If short-term interest rates are lower than long-term The Monetary Ramifications of the Carry Regime 111 interest rates, then the demand for credit at the short-term interest rate will still tend to be firm; inflation and growth will keep the demand for credit strong.

Nerds on Wall Street: Math, Machines and Wired Markets
by David J. Leinweber
Published 31 Dec 2008

Many financial conference speakers, including those talking to mixed professional/spousal audiences after open-bar events, are deadly dull; hardly anyone really wants to see yield curves over dessert and that last glass of wine. I started collecting photographs about markets and technology in the early 1990s, and tried to mix in some actual informative content. That, along with the natural sensibilities of a borscht belt comic, made me a popular alternative to the yield curve guys. Given the 20-minute rule for these talks, none of them were as voluminous as this chapter. Still, this is not intended in any way to be a complete history of market technology, but rather an easily digestible introduction.

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Note that these percentages are not referring to total energy consumption, but to the level of total power (the rate of delivering energy) that has to be provided over the year. In the electric world, this is called lowering the peak of the load duration curve. Understanding load duration curves is the first lecture in Power 101 class. If you want to understand bonds, you need to know about the yield curve. The load duration curve is equally important if you want to understand electricity. Figure 14.1 shows a load duration curve and how it would shift with the use of the technologies discussed in this chapter. Lowering the peaks on these curves is important economically, environmentally, and geopolitically, because the plants needed to meet them are expensive, and often oil fueled.

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The state of both means that there are likely to be more than 330 Nerds on Wall Str eet 1 2 Hourly MW Load Reduce Customers’ Peak Loads ⭈ Utility-Controlled Circuit-level Management Discharge Stored Power During Peak ⭈ Clean, Reliable, Efficient ⭈ Targeted Deployments 3 4 Offer Value-Added Optimize Generation Services and T&D Assets ⭈ Online Energy Management ⭈ Charge Energy Storage ⭈ Renewables Integration and PHEVs Off-peak 2 1 3 4 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 Hours Per Year Load duration curve. Result of stored power deployed during peak and charging power during off-peak. Result of reducing customers’ peak loads and energy conservation. ENVIRONMENTAL LEADERSHIP AND GRID RELIABILITY Figure 14.1 Reshaping the load duration curve. Bonds have the yield curve. Power has this. Source: GridPoint. a few readers contemplating this transition. This last chapter is a gentle introduction to and a survey of more in-depth resources on this topic. Accelerating Innovation There are over a million hybrid Toyota Prius vehicles on the road, and in Berkeley, California, it often seems that they are all parked on the same street.

Stolen: How to Save the World From Financialisation
by Grace Blakeley
Published 9 Sep 2019

The implication is that stock markets are overvalued, and three factors suggest that investors know it. Firstly, stock markets are highly volatile — a tell-tale sign of a bubble.59 The second warning sign is what is called the “yield curve” — which shows the interest rates investors will receive on the same government bonds with different maturity dates. Longer-term bonds are supposed to have higher interest rates, because lending for a long time is riskier than for a short time, so investors need to be compensated with higher returns. But the yield curve has now inverted in the US, meaning that short-term yields are higher than long-term yields, indicating that investors are nervous about the future.60 Finally, the Buffett indicator — the market capitalisation to GDP ratio, or how big the stock markets are relative to the “real” economy — suggests that stock markets are overvalued.

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50 Williams, A. (2017) “London House Prices Fall for the First Time Since 2009”, Financial Times, 29 September. 51 Office for National Statistics (2019) “UK House Price Index Summary: November 2018” 52 Office for National Statistics (2018) “Business Investment in the UK: July to September 2018 Revised Results” 53 Office for National Statistics (2019) “Insolvency Statistics — October to December 2018 (Q4 2018)” 54 Blakeley (2019). 55 World Bank (2018) “Gross fixed capital formation (annual % growth)” 56 IMF (2018) “Fiscal Monitor 2018: Capitalising on Good Times” 57 Oguh, C. and Tanzi, A. (2019) “Global Debt of $244 Trillion Nears Record Despite Faster Growth”, Bloomberg, 15 January. 58 Partington, R. (2018) “Wall Street Sets Record for Longest Bull Run in History”, Guardian, 22 August 59 Seeking Alpha (2019) ‘Stocks In 2019: Volatility Is Back’ https://seekingalpha.com/article/4234365-stocks-2019-volatility-back 60 Barrett E and Greifeld K (2019) ‘Treasuries Buying Wave Triggers First Curve Inversion Since 2007’ https://www.bloomberg.com/news/articles/2019-03-22/u-s-treasury-yield-curve-inverts-for-first-time-since-2007 61 Federal Reserve Bank of St Louis (2018) ‘Stock Market Capitalization to GDP for United States’ https://fred.stlouisfed.org/series/DDDM01USA156NWDB 62 Curran, E. (2018) “China’s Debt Bomb”, Bloomberg, 17 September. 63 Moody’s (2018) “Moody’s: China Shadow Banking Activity Increasingly Reveals Challenging Trade-Off Between Growth and Deleveraging”, Moody’s Investors Service, 3 December. 64 BIS (2019) 65 Banerjee, R. and Hofmann, B. (2018) “The Rise of Zombie Firms: Causes and Consequences”, Bank for International Settlements Quarterly Review, September. 66 Colombo, J. (2018) “The US Is Experiencing A Dangerous Corporate Debt Bubble”, Forbes, 29 August. https://www.forbes.com/sites/jessecolombo/2018/08/29/the-u-s-is-experiencing-a-dangerous-corporate-debt-bubble/#547ffa2f600e 67 Heath, M. (2018) “These May Be the World’s 10 Riskiest Housing Markets”, Bloomberg, 13 September. 68 Byres, W. (2012) “Basel III: Necessary, but Not Sufficient”, speech to the Financial Stability Institute’s 6th Biennial Conference on Risk Management and Supervision, Basel, 6 November 69 This account draws on: Laybourn-Langton, L., Rankin, L. and Baxter, D. (2019) “This is a Crisis: Facing up to the Age of Environmental Breakdown”, IPPR. http://www.ippr.org/research/publications/age-of-environmental-breakdown; Intergovernmental Panel on Climate Change (2018) “Global warming of 1.5°C.

The Great Demographic Reversal: Ageing Societies, Waning Inequality, and an Inflation Revival
by Charles Goodhart and Manoj Pradhan
Published 8 Aug 2020

If tax rates should have to rise significantly to finance pensions and medical expenses , will workers start to bargain for post-tax real wages? We would think so, and if we’re right, it would lead to yet further upwards pressures on inflation. Third, real, inflation-adjusted interest rates, particularly at the longer end of the yield curve, may rise (Chapter 6) because of the behaviour of ex-ante (expected) savings and investment. That the elderly will dissave is not controversial. Those who believe real interest rates are likely to fall or stay low clearly believe that investment will fall even further below savings—we disagree.

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Largely because of the political context which we see unfolding, we think it highly likely that short rates will be held below the increase in inflation which we see developing over the next few decades. In contrast, however, as this new, uncomfortable, world emerges into clearer sight, long rates will start rising and very likely rise above the current rate of inflation. So, one of our conclusions is that the yield curve, which is currently flattened to an unusual degree, will probably steepen sharply. So, we are, in a sense, hedging our bets, suggesting that short rates may continue to run at low real levels, but that longer, e.g. ten-year rates, are likely to show rising real rates. Footnotes 1‘About 90 per cent of Chinese seniors rely mainly on family support, 7 per cent on residential community-based care services and 3 per cent on nursing homes, according to the Qianzhan Industry Research Institute, a consultancy’. 2 Rachel and Summers (2019) see recent fiscal deficits as raising the neutral real rate.

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Workers, declining number Workers, high skilled, prosper Working Age Population (WAP) Working classes Working population, slow down in growth World Alzheimer Report (WAR) World Bank World Bank’s Human Capital Index World Bank’s PovcalNet database World Bank Ease of Doing Business index World Dementia Council World Economic Forum World Health Organization (WHO) World Inequality Database World Population Ageing World’s savings ratio World Trade Organisation (WTO) World War I World War II World War II, trends since then World Wars WTO rules X Xiaomi Xu, T. Y Yemen Yen appreciation, after Plaza Accord Yen’s dramatic appreciation Yield curve Young, benefit less from monetary expansion Z Zero Lower Bound (ZLB) ‘Zombie’ firms

The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series)
by Robert P. Baker
Published 4 Oct 2015

They range from about three months to two years. Swaps These are quoted for longer periods extending up to 30 years or beyond. By combining prices for these three sets of instruments, we can derive a yield curve which indicates the yield (or interest rate) against time (see Figure 24.2). 313 Data 7 6 Yield (%) 5 4 3 2 1 0 0 5 10 15 20 Time to maturity (years) 25 30 35 FIGURE 24.2 Yield curve Surfaces Some instruments have three dimensions – two dimensions of data for any time period. In order to look at the shape of market data over time, we need to use a threedimensional object, usually referred to as a surface.

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Bob Steiner (2012) Mastering Financial Calculations: A Step-by-step Guide to the Mathematics of Financial Market Instruments, Financial Times/Prentice Hall. 377 Index 30/360 date calculation 350–1 ABSs see asset backed securities abusive behaviour, traders 223 acceptance testing see user acceptance testing accounting 161–9 balance sheet 161–4 financial reports 168–9 profit and loss account 164–8 accrual accrual convention 349–50 accrued profit and loss 165 actual/actual date calculation 350 advisory services 269, 370 aggregation of calculations 342 trades 101–2 agricultural commodities 56 algorithms 184 amendment to a trade 108 American options 29, 66 amortising bonds 47, 48 analytics 271–2 see also quantitative analysts animal products 56 application programming interface (API) 270 architects, IT 187 asset backed securities (ABSs) 47 asset classes 33–59 bonds and credit 46–53 commodities 29, 53–8 equities 44–5 foreign exchange 40–4 interest rates 33–40 and products 17 trade matrix 71–2 trading across 58–9 asset holdings see holdings asset managers 10, 168–9 at-the-money options 66 audit 191–2 average trades, exotic options 68 back book trading 132 back office (operations) 183, 227, 316 back testing 317 back-to-back trades 152 bad data 105, 317–20 balance sheet 161–4 banks culture and conduct 203 interbank systems 158 reasons for trading 9–10 retail banks 222 traders’ internal accounts 123 Barclays Capital 219 barrier options 68 base rate, interest rates 35 Basel II 144 Basel III 205 baskets exotic options 68 FX trades 41–2 BCP see business continuity planning bearer securities 124 Bermudan options 66 bespoke trades 69–70 bid/offer spread 310 binary options 68–9 black box (mathematical library) 238, 241, 270 black box testing 301 Black Scholes formula 346 board of directors 193–4 bond basis deltas 175 379 380 bonds 27, 28, 29, 46–53 coupon payments 47, 48, 106–7 RABOND project case study 225–35 sovereign debt 46 tradeflow issues 49 types 46–7 bonuses 220–1 booking of a trade 85, 93–4 bootstrapping 348–9 boundary testing 351 breaches, dealing with 155–6 breaks, settlement 356–7 brokers 5–6, 10, 75 buckets (time intervals) 148–9 bullying behaviour 223 business continuity planning (BCP) 373 calculation process 337–52 see also valuation process bootstrapping 348–9 calibration to market 351 dates 349–51 example 337–8 mark-to-market value 339–40 model integration 352 net present value 338–9, 343–8 risks 352 sensitivity analysis 347–8 calibration process, valuation 351 call options 62, 63 cancellation of a trade 109 capital adequacy ratio (CAR) 144 case studies 225–52 EcoRisk project 235–47 OTTC equity confirmation project 247–52 RABOND project 225–35 cash balance sheet item 162 exchange dates 86 exercise 111 settlement 98, 99 cashflows American options 30 asset holdings 117–24 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 INDEX reconciliation 121 risks 124 treatment of 119–20 value of 120–1 credit default swaps 31 deposits 23 discount curve 38–9 equity spot trades 26 fixed bonds 27, 28 floating bonds 27, 28 foreign exchange swaps 25 future trades 20–1 loans 22 options 27–30, 345–6 post booking 96–7 risks 367 spot trades 19 swap trades 24 unknown, options valuation 345–6 zero bonds 27, 29 CDSs see credit default swaps Central Counterparty Clearing (CCP) 210–12 change coping with 260–1, 284 to a trade 105–10 clearing 210–12 Cliquet (ratchet options) 68 collateral 108, 153–4, 156, 212–13 COM (common object model) 246 commodities 29, 53–8 cash settlement 99 characteristics 55–6 currency 57 definition 55 example 53–5 localised production 57 OTC commodities 56 physical settlement 57–8 profit curve 54–5 time lag 57 tradeflow issues 58 types 56 utility of 57 common object model (COM) 246 communication 188, 197–8, 254–5, 259–60, 305, 371 competition analysis 269 compliance officers 192–3 confirmation of a trade 94–6, 247–52, 355 conflicts and tensions 196–7, 198–9, 360–1 381 Index consolidated reporting 122 consolidation of processes 283–4 control see also counterparty risk control; market risk control people involved in 189–99, 224 of report generation 335 conversion, currency 344 correlation risk 131, 363 counterparties changes to a trade 108 correlation between 364 identification of 85 Counterparty Clearing, Central 210–12 counterparty risk control 147–60, 364–5 activities of department 154–7, 190–1 collateral 153–4, 156 counterparty identification 153 default consequences 148 limit imposition 152–3 management interface 157 measurement of risk 149–52, 155, 156 non-fulfilment of obligations 147–8 payment systems 158–60 quantitative analyst role 268 risks in analysing credit risk 157–8 settlement 356 time intervals 148–9 coupon payments, bonds 47, 48, 106–7 credit default swaps (CDSs) 30–1, 51–2, 65–6, 175, 209 credit exposure 150–1 credit quantitative analysts 274 credit rating companies 231–2 credit risk see also counterparty risk control; credit default swaps; credit valuation adjustment bonds 46–53 default 51 definition 50 documentation 50–1 market data 316 measurement of 209 recovery rate 52–3 risks in analysing 157–8 types of risk 131 credit valuation adjustment (CVA) 207–13 debt valuation adjustment 209 definition 208 funding valuation adjustment 209 measurement of 208 mitigation 210 netting 211–12 portfolio-based 213 rehypothication 212–13 credit worthiness 51–2, 155 creditors, balance sheet item 163 CreditWatch 232 culture of banks 203 currency conversion 344 exposure to 4 precious metals as 57 reporting currency 42 value of holdings 120–1 currency swaps, foreign exchange 41 current (live) market data 79, 314 curves, market data 310–13 custodians 98, 124 customer loyalty 199 CVA see credit valuation adjustment data 307–25 absence of 368 authentic data 368 back testing 317 bad data 105, 317–20 bid/offer spread 310 corrections to 321–2 data feeds 226 expectations 309–10 extreme values 317 implied data 323 integrity of 322–4 internal data 321 interpolation 319 market data 107–8, 180, 292, 308–17 processes 286 risks 324–5, 367–8 sources of 320–1, 323 storage 309 testing 302 time series analysis 320 types of 308–10 validity of 307 vendors 321 data cleaning 320 data discovery 319–20 data engineering 319 databases 250–1, 308 382 dates calculation of 349–51 exercise of trades 111 final settlement 113 internal and external trades 102 relating to a trade 86–7 settlement 101, 113 on trade tickets 102 debt, exposure to 127 debt valuation adjustment (DVA) 209 debtors, balance sheet item 162 default 51, 131, 148 see also credit default swaps delivery versus payment (DvP) 98 delta hedging 133 delta risk 130 deltas 175 deposits 23, 35 derivatives 61–72 see also futures and forwards; options; swaps digital options 68–9 directors, role of 193–4 discount curve, interest rates 38–9 discounting, NPV calculation 343–4, 345 diversification 122–3 dividends 105–6 documentation credit risk 50–1 EcoRisk project case study 240–1 legal documents 84–5 processes 287 risks 356, 374 settlement 98 Dodd–Frank Act 206–7 dreaming ahead 131–2 due diligence 192, 292 duties (fees) 97 DVA (debt valuation adjustment) 209 DVO1, risk measure 138 DvP (delivery versus payment) 98 economic data 84 EcoRisk project, case study 235–47 documentation 240–1 functionality 243–4 Graphical User Interface 237–8 mathematical library 238, 241 solution 238–40 testing 239–40 valuation problem debugging 242–3 INDEX electronic exchanges 6 electronic systems 92 email 92 EMIR (European Markets Infrastructure Regulation) 202–3 employees see people involved in trade lifecycle end of day roll 103, 181–2 end of month reports 182 energy products 56 equal opportunities 219–20 equities 26, 44–5, 247–52 errors confirmation process 95 in data 322 P&L corrections 171 post booking 97 in reports 333–4 European Markets Infrastructure Regulation (EMIR) 202–3 European options 29, 66 exceptions, processes 322 exchange price 75 exchanges 6, 86, 320 execution of a trade 89–93 exercise, option trades 64, 110–12, 357–8 exotic options 67–9, 109, 235–47, 346 expected loss 150 exposure 4, 125–8, 130–2, 150–1, 155, 156 fault logging 302–4 fees 97, 169 finance department 191, 316 financial products 17–31 bonds 27, 28, 29, 46–53, 106–7, 225–35 credit default swaps 30–1, 51–2, 65–6, 175, 209 deposits 23, 35 equities 26, 44–5, 247–52 futures 20–1, 35–6, 40–1, 61, 62, 77, 127, 311, 312 FX swaps 25, 41 loans 21–3 options 27–30, 61–9, 77, 109–12, 127, 235–47, 345–6, 357–8 spot trades 18–19, 40, 127 swaps 23–5, 30–1, 36–7, 41, 107, 312–13 financial reports 168–9 financial services industry 8–10 fixed assets, balance sheet item 161 fixed bonds 27, 28, 47, 48 fixed and floating coupons 127 383 Index fixed for floating swaps 23–4 fixed loans 22 fixing date 86 fixings 107–8 float for fixed/float for float 36 floating bonds 27, 28 floating loans 22 floating rate notes (FRNs) 47 flow diagrams 287 FoP (free of payment) 98 foreign exchange (FX) 40–4 baskets 41–2 FX drift 42–3 reporting currency 42 swaps 25, 41 tradeflow issues 43–4 forward rate agreement (FRA) 37–8 see also futures and forwards free of payment (FoP) 98 FRNs (floating rate notes) 47 front book trading 132 front line support staff 186 front office EcoRisk project, case 235–47 market risk control 142 risks 375–6 fugit 112 fund managers 10 funding valuation adjustment (FVA) 209 futures and forwards 20–1, 35–6, 40–1, 61, 62 gold futures 311, 312 leverage 77 risks 127 FVA (funding valuation adjustment) 209 FX see foreign exchange gamma risk 130 gearing 77–8 gold futures 311, 312 governance 204 Graphical User Interface (GUI) 237–8 hedge funds 10, 168–9, 212–13 hedging strategies 133–4 hedging trades 128 help desks 247 historical market data 314 holdings 117–24 asset types 118 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 reconciliation 121 risks 124 value 120–1 human resources see people involved in trade lifecycle human risks 194–9, 359–61 hybrid trades 69–70 identification details, trades 83–4 illiquid products 140 illiquid trades 339 in person trades 92 in-the-money options 66 incentives 195 industrial metals 56 information technology (IT) architects 187 case studies 225–52 communication 259–60 dependency on 284 EcoRisk project 235–47 equity confirmation project 247–52 infrastructure 186 IT divide 253–66 business functions 255–6 business requirements 261–3 coping with change 260–1 do’s and don’ts 263 IT blockers 258 IT requirements 263–4 misuse of IT 256–7 organisational blockers 257–8 problems caused by 255 project examples 265–6 solution 259–60 language of 254 legacy systems 282 operators 188 project managers 187–8 quality control 260 and quantitative analysts 271–4 RABOND project 225–35 risks 375–6 staff 185–9, 197, 217–18, 253–66 testers 188–9 and traders 258 384 infrastructure, IT 186 instantaneous risk measures 138 insurance 30–1, 50 integration testing 300 interbank systems 158 interbank trading (LIBOR) 39 interest rates 21–3, 33–40 base rate 35 credit effects 39 deltas 175 deposits 35 discount curve 38–9 forward rate agreement 37–8 futures 35–6, 311–12 market participants 34–5 option valuation 67 products 35–8 quantitative analysts 274 swaps 23–5, 36–7 time value of money 33–4 tradeflow issues 39–40 vegas 175 interim delivery of projects 259 internal audit 191–2 International Swaps and Derivatives Association (ISDA) 50 investment banks 9–10 investments, balance sheet item 161 ISDA (International Swaps and Derivatives Association) 50 IT see information technology kappa risk 130 knock in/knock out, barrier options 68 knowledge, risks 359–60 legacy IT systems 282 legal department 189, 293, 316 legal documents 84–5 legal risks 50, 369 leverage 64–6, 76–9 LIBOR (interbank trading) 39 libraries 184–5 lifecycle of a trade see trade lifecycle limit orders 129 limits and credit worthiness 155 imposing 152–3 market risk control 141 line managers 222 INDEX linear derivatives 61, 62 liquidity 73–5, 202, 375 litigation 370 live trading 7 loans 21–3 management see also project management; risk management of changes 109–10 counterparty risk control 157 fees 169 market data usage 317 new products 292 responsibilities of 193–4 risks 374 of teams 229–31 margin payments 156 mark-to-market value 339–40 market data 180, 292, 308–17 business usage 315–17 changes as result of 107–8 curves and surfaces 310–13 sets of 314 market participants 4–5 market risk control 135–45, 190, 363–4 allocation of risk 139 balanced approach 143 controlling the risk 140–1 human factor 143 limitations 142–3 market data usage 316 methodologies 135–9 monitoring of market risk 140 need for risk 139 quantitative analyst role 268 regulatory requirements 143–4 responsibilities 141–2 market sentiment 340 matching of records 94–5 mathematical libraries 238, 241, 270 mathematical models evolution of 343 new products 293 parameters 341 prototypes 238–9 quantitative analyst role 183–5 risks 373 validation team 189–90 maturity of a trade 8, 67, 86, 112–13 MBS see mortgage backed securities 385 Index metal commodities 56, 57 middle office (product control) market data usage 316 new products 293 RABOND project, case study 225–35 role of 180–2 missing data 317 mobile phones 92 models see mathematical models Monte Carlo technique 346–7 mortgage backed securities (MBS) 47 multilateral netting 211–12 NatWest Markets, EcoRisk project 235–47 net present value (NPV) 338–9, 343–8 netting 152, 211–12 new products 289–95 checklist 292–3 evolution of 294 market data 292 market risk control 140 process development/improvement 279–88 risks 194, 294–5, 369 testing 291–2 trial basis for 290–2 new trade types 156 nonlinear derivatives 62–9 nostro accounts 99 NPV see net present value official market data 314 offsetting of risks 128 OIS (overnight indexed swap) 39 operational risks 355–8 operations department 183, 227, 316 operators, IT 188 options 27–30, 61–9 credit default swaps 65–6 exercise 110–12 exotic options 67–9, 109, 235–47, 346 leverage 64–6, 77 risks 127, 357–8 terminology 66 trade process 64–6 valuation 67, 345–6 orders 90–1, 357 OTC see over-the-counter trading OTTC equity confirmation project, case study 247–52 out-of-the-money options 66 over-the-counter (OTC) trading 6–7 clearing 210 commodities 56 price 75 overnight indexed swap (OIS) 39 overnight processes 101–5 P&L see profit and loss parallel testing 301 pay 203, 220–1 payment systems 106–7, 158–60, 357 pension funds 10 people involved in trade lifecycle 177–200 see also working in capital markets back office 183, 227, 316 compliance officers 192–3 conflicts and tensions 196–9, 360–1 control functions 189–99 counterparty risk control department 190–1 finance department 191, 316 human risks 194–9 information technology 185–9, 197, 217–18, 253–66 internal audit 191–2 legal department 189, 293, 316 line managers 222 management 193–4 market risk control department 190 middle office 180–2, 225–35, 293, 316 model validation team 189–90 personality and outlook 194–5, 244–5, 273 programmers 187, 244–5 quantitative analysts 183–5, 267–75 researchers 179–80 revenue generation 177–89 sales department 179, 227, 315, 375 senior managers 126 staffing levels 195 structurers 179 supervisors 204 testers 298–9 traders 125–6, 177–8, 218–23, 226–7, 258, 268, 315, 361 trading assistants 178 trading managers 126, 193 training of staff 193 performance reports 169 personality and outlook 194–5, 244–5, 273 PFE (potential future exposure) 151 physical assets, exercise 111 386 physical commodities, settlement 57–8, 99 planning of processes 282–3 recovery plans 203–4 risks 360 post booking processes 96–7 postal trades 92–3 potential future exposure (PFE) 151 power, abuses of 220, 221–2 pre-execution of a trade 89–91 precious metals 56, 311, 312 premiums 31 price 75–6, 138–9 pricing methods EcoRisk project, case study 235–47 short-term pricing 183 process development/improvement 279–88 coping with change 284 current processes 285–7 evolution of processes 280–1 improving the situation 284–7 inertia 287–8 inventory of current systems 282–4 planning 282–3 timing 288 producers 5 product appetite 4 product control see middle office product development see new products profit curve, commodity trading 54–5 profit and loss (P&L) accounts 164–8 accrued and incidental 165 example 165–6 individual trades 166–7 realised and unrealised 165 responsibility for producing 167 risks associated with reporting 167–8 rogue trading 168 attribution reports 171–6 benefits of 171–2 example 173–6 market movements 173, 175 process 172–3 unexplained differences 173 balance sheet item 163 end of day 182 realised and unrealised 122, 165 programmers 187, 244–5 see also quantitative analysts INDEX project management 225–47, 259, 262 project managers 187–8 proprietary (‘prop’) trading 203 prototypes, IT projects 238–9 provisional trades 89–90, 357–8 put options 62, 63 PVO1, risk measure 138 quality control, IT 260 see also testing quantitative analysts (quants) 183–5, 267–75 and IT professionals 271–4 role of 267–9, 270 seating arrangements 270–1 working methods 269–70 RABOND project, case study 225–35 management 229–31 outcome 233–5 reports 227–9 team management 229–31 traders 226–7 random market data 314 rapid application development (RAD) 260, 281 ratchet options (Cliquet) 68 ratings companies 231–2 raw data 323 raw reporting 331 real world of capital markets see working in capital markets realised P&L 122 receipts 156 reconciliation 121 recovery plans 203–4 recovery rates 52–3, 176 redundancy, processes 282 reform of banks 203 registered securities 123–4 regression testing 302 regulation 201–13, 223–4 authorities 202 Basel II and III 144, 205 credit valuation adjustment 207–13 external 192 internal 224 market risk control 143–4 new products 293 problems 204–5 requirements 202–4 387 Index risk-weighted assets 205–7 risks 369 rehypothication 212–13 remuneration 203, 220–1 reporting currency 42 reports 327–36 accuracy 330–1, 368 calculation process 342 configuration 331–2 consolidated reporting 122 content 328–9 control issues 335 dimensions 333 distribution 329–30, 335, 369 dynamic reports 332–3 end of month reports 182 enhancements 335 errors in 333–4 false reporting 375 financial reports 168–9 frame of reference 333 middle office role 180–1 OTTC equity confirmation project 250, 251 performance reports 169 presentation 329 problems 333–4 profit and loss 167, 171–6 RABOND project 227–9 raw reporting 331 readership 328, 329, 368–9 redundancy of 334–5 requirements 328–33 risks 335–6, 368–70 security issues 335, 368 timing 330 types of 330 reputation, risk to 356, 370 research 268, 375 researchers 179–80 reserve accounts 141 reset date 86 resettable strike, exotic options 68 retail banks 222 revenue generation, people involved in 177–89 rho risk 130 risk 13–16 see also counterparty risk control; market risk control advisory services 370 appetite for 4 business continuity planning 373 calculation process 352 cashflows 124, 367 changes to a trade 110 communication 371 confirmation 95–6, 355 control departments 224 correlation 363 data 324–5, 367–8 definition 13 documentation 356, 374 exercise 112 front office 375–6 human risks 194–9, 359–61 information technology 375–6 instantaneous measures 138 legal risks 369 liquidity 74–5, 375 litigation 370 management risks 374 measures 130, 138, 149–52, 155, 156 model approval 373 new products 140, 194, 294–5, 369 operational risks 355–8 orders 91 origin of risks 126–8 payment systems 357 provisional trades 90, 357–8 quantifying 14 regulation 369 reports 335–6, 368–70 reputation 356, 370 risk-weighted assets 205–7 sales 375 settlement 100, 355–7 short-term thinking 360 straight through processing 357 support activities 376 systematic 202–3, 375–6 testing 304–5, 370–1 types 130–2 unexpected charges 356 unforeseen 16, 353 valuation process 352, 373 risk management 13, 15, 125–34 in absence of trader 128–9 dreaming ahead 131–2 EcoRisk project case study 235–47 hedging strategies 133–4 hedging trades 128 388 risk management (continued) offsetting of risks 128 senior managers 126 traders 125–6, 361 trading managers 126 trading strategies 132 rogue trading 168 sales data 84 sales department 179, 227, 315, 375 SBC Warburg, equity confirmation project, case study 247–52 scenario analysis 136, 198–9, 341 scope creep 187, 264 scrutiny of trades 96 securities, custody of 123–4 security issues 181, 335, 368 semi-static data 309 senior managers 126 sensitivity analysis 138, 347–8 settlement 97–101, 147–8 breaks 101, 356–7 commodities 99 dates 101, 113 nostro accounts 99 quick settlement 101 risks 100, 355–7 shares 44–5 see also equities short selling 65 short-term pricing 183 short-term thinking 195–6, 360 silo approach 257 simple products 70–1 smoke testing 301 sovereign debt 46 speculators 5 spot prices 61, 62, 63, 67, 76–7 spot testing 301 spot trades 18–19, 40, 127 spread of bid/offer 310 spreadsheets 184, 238 staff see people involved in trade lifecycle stale data 105, 318 Standard & Poor’s (S&P) ratings 231–2 static data 309 stop-loss hedging 133–4 stop orders 129 storage of data 309 straight through processing (STP) 93–4, 357 INDEX stress, staff 222, 244–5 stress testing 302 strike price, options 67 structured trades 69–70 structurers 179 supervisors 204 support activities, risks 376 surfaces, market data 310–13 swaps credit default 30–1, 51–2, 65–6, 175, 209 fixings 107 foreign exchange 25, 41 interest rate 23–5, 36–7 yield curves 312–13 swaptions 66 synthetic equities (index) 45 systems see also information technology amalgamation 104–5 analytics 271–2 electronic systems 92 integrated 261 legacy IT systems 282 risks 375–6 testing 251–2, 300 tail behaviour, predicting 143, 364 team management 229–31 telephone transactions 91–2 tensions and conflicts 196–9, 360–1 testing 297–305 back testing 317 boundary testing 351 extreme values 352 fault logging 302–4 importance of 298 mathematical models 239 new products 291–2 risks 304–5, 370–1 stages 300–1 testers 188–9, 298–9 types of 301–2 unit testing 300 user acceptance testing 237, 239–40, 252, 264, 301 when to perform 299–300 theft 355 theta risk 130 time intervals (buckets) 148–9 time lag, commodities 57 389 Index time series analysis 320 timeline of a trade 79, 86–7 trade blotters 93 trade lifecycle 89–115 booking 93–4 business functions 11 changes during lifetime 105–10 confirmation 94–6 equity trades 45 example trade 113–15 execution 91–3 exercise 110–12 maturity 112–13 new products 293 overnight processes 101–5 post booking 96–7 pre execution 89–91 settlement 97–101 trade tickets 102 trade/trading 3–12 see also trade lifecycle anatomy 83–7 business functions 11 complicated trades 340 consequences of 7–8 definition 10–12 financial products 17–31 live trading 7 matching of records 94–5 policies 8 reasons for 3, 9–10 timeline 79, 86–7 transactions 5–7 types 132 tradeflow issues bonds 49 commodities 58 foreign exchange 43–4 interest rates 39–40 traders 177–8, 218–22, 223, 226–7, 258, 268 bonuses 220–1 market data usage 315 risk management 125–6, 361 trading assistants 178 trading desks 70–1, 256–7 trading floor 217–18, 235–6 trading managers 126, 193 training of staff 193 tranche correlation 131 treasury desk 71 trials for new products 290–2 trust 197, 222 UAT see user acceptance testing underlying 83 unexplained differences, P&L reports 173 unforeseen risk 16, 353 unit testing 300 unknown cashflows 345–6 unrealised P&L 122 unwinding a trade, cost of 76 user acceptance testing (UAT) 237, 239–40, 252, 264, 301 validation of models 189–90 valuation process see also calculation process calibration to market 351 mark-to-market value calculation 339–40 middle office role 181 NPV calculation 338–9, 343–8 options 67 problem debugging 242–3 risks 352, 364, 373 valuation systems 269 value at risk (VaR) 136–8, 341 vega (kappa) risk 130 vegas 175 vendors, data services 321 volatility 67, 130 volume of a trade, price effect 76 white box testing 301 workarounds 303 working in capital markets 217–24 see also case studies; people involved in trade lifecycle in 1990s 217–19 culture clashes 219 equal opportunities 219–20 office politics 220–2, 246 positive/negative aspects 222–3 yield curves 312–13 zero bonds 27, 29, 47 Index compiled by Indexing Specialists (UK) Ltd WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA. 

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Bob Steiner (2012) Mastering Financial Calculations: A Step-by-step Guide to the Mathematics of Financial Market Instruments, Financial Times/Prentice Hall. 377 Index 30/360 date calculation 350–1 ABSs see asset backed securities abusive behaviour, traders 223 acceptance testing see user acceptance testing accounting 161–9 balance sheet 161–4 financial reports 168–9 profit and loss account 164–8 accrual accrual convention 349–50 accrued profit and loss 165 actual/actual date calculation 350 advisory services 269, 370 aggregation of calculations 342 trades 101–2 agricultural commodities 56 algorithms 184 amendment to a trade 108 American options 29, 66 amortising bonds 47, 48 analytics 271–2 see also quantitative analysts animal products 56 application programming interface (API) 270 architects, IT 187 asset backed securities (ABSs) 47 asset classes 33–59 bonds and credit 46–53 commodities 29, 53–8 equities 44–5 foreign exchange 40–4 interest rates 33–40 and products 17 trade matrix 71–2 trading across 58–9 asset holdings see holdings asset managers 10, 168–9 at-the-money options 66 audit 191–2 average trades, exotic options 68 back book trading 132 back office (operations) 183, 227, 316 back testing 317 back-to-back trades 152 bad data 105, 317–20 balance sheet 161–4 banks culture and conduct 203 interbank systems 158 reasons for trading 9–10 retail banks 222 traders’ internal accounts 123 Barclays Capital 219 barrier options 68 base rate, interest rates 35 Basel II 144 Basel III 205 baskets exotic options 68 FX trades 41–2 BCP see business continuity planning bearer securities 124 Bermudan options 66 bespoke trades 69–70 bid/offer spread 310 binary options 68–9 black box (mathematical library) 238, 241, 270 black box testing 301 Black Scholes formula 346 board of directors 193–4 bond basis deltas 175 379 380 bonds 27, 28, 29, 46–53 coupon payments 47, 48, 106–7 RABOND project case study 225–35 sovereign debt 46 tradeflow issues 49 types 46–7 bonuses 220–1 booking of a trade 85, 93–4 bootstrapping 348–9 boundary testing 351 breaches, dealing with 155–6 breaks, settlement 356–7 brokers 5–6, 10, 75 buckets (time intervals) 148–9 bullying behaviour 223 business continuity planning (BCP) 373 calculation process 337–52 see also valuation process bootstrapping 348–9 calibration to market 351 dates 349–51 example 337–8 mark-to-market value 339–40 model integration 352 net present value 338–9, 343–8 risks 352 sensitivity analysis 347–8 calibration process, valuation 351 call options 62, 63 cancellation of a trade 109 capital adequacy ratio (CAR) 144 case studies 225–52 EcoRisk project 235–47 OTTC equity confirmation project 247–52 RABOND project 225–35 cash balance sheet item 162 exchange dates 86 exercise 111 settlement 98, 99 cashflows American options 30 asset holdings 117–24 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 INDEX reconciliation 121 risks 124 treatment of 119–20 value of 120–1 credit default swaps 31 deposits 23 discount curve 38–9 equity spot trades 26 fixed bonds 27, 28 floating bonds 27, 28 foreign exchange swaps 25 future trades 20–1 loans 22 options 27–30, 345–6 post booking 96–7 risks 367 spot trades 19 swap trades 24 unknown, options valuation 345–6 zero bonds 27, 29 CDSs see credit default swaps Central Counterparty Clearing (CCP) 210–12 change coping with 260–1, 284 to a trade 105–10 clearing 210–12 Cliquet (ratchet options) 68 collateral 108, 153–4, 156, 212–13 COM (common object model) 246 commodities 29, 53–8 cash settlement 99 characteristics 55–6 currency 57 definition 55 example 53–5 localised production 57 OTC commodities 56 physical settlement 57–8 profit curve 54–5 time lag 57 tradeflow issues 58 types 56 utility of 57 common object model (COM) 246 communication 188, 197–8, 254–5, 259–60, 305, 371 competition analysis 269 compliance officers 192–3 confirmation of a trade 94–6, 247–52, 355 conflicts and tensions 196–7, 198–9, 360–1 381 Index consolidated reporting 122 consolidation of processes 283–4 control see also counterparty risk control; market risk control people involved in 189–99, 224 of report generation 335 conversion, currency 344 correlation risk 131, 363 counterparties changes to a trade 108 correlation between 364 identification of 85 Counterparty Clearing, Central 210–12 counterparty risk control 147–60, 364–5 activities of department 154–7, 190–1 collateral 153–4, 156 counterparty identification 153 default consequences 148 limit imposition 152–3 management interface 157 measurement of risk 149–52, 155, 156 non-fulfilment of obligations 147–8 payment systems 158–60 quantitative analyst role 268 risks in analysing credit risk 157–8 settlement 356 time intervals 148–9 coupon payments, bonds 47, 48, 106–7 credit default swaps (CDSs) 30–1, 51–2, 65–6, 175, 209 credit exposure 150–1 credit quantitative analysts 274 credit rating companies 231–2 credit risk see also counterparty risk control; credit default swaps; credit valuation adjustment bonds 46–53 default 51 definition 50 documentation 50–1 market data 316 measurement of 209 recovery rate 52–3 risks in analysing 157–8 types of risk 131 credit valuation adjustment (CVA) 207–13 debt valuation adjustment 209 definition 208 funding valuation adjustment 209 measurement of 208 mitigation 210 netting 211–12 portfolio-based 213 rehypothication 212–13 credit worthiness 51–2, 155 creditors, balance sheet item 163 CreditWatch 232 culture of banks 203 currency conversion 344 exposure to 4 precious metals as 57 reporting currency 42 value of holdings 120–1 currency swaps, foreign exchange 41 current (live) market data 79, 314 curves, market data 310–13 custodians 98, 124 customer loyalty 199 CVA see credit valuation adjustment data 307–25 absence of 368 authentic data 368 back testing 317 bad data 105, 317–20 bid/offer spread 310 corrections to 321–2 data feeds 226 expectations 309–10 extreme values 317 implied data 323 integrity of 322–4 internal data 321 interpolation 319 market data 107–8, 180, 292, 308–17 processes 286 risks 324–5, 367–8 sources of 320–1, 323 storage 309 testing 302 time series analysis 320 types of 308–10 validity of 307 vendors 321 data cleaning 320 data discovery 319–20 data engineering 319 databases 250–1, 308 382 dates calculation of 349–51 exercise of trades 111 final settlement 113 internal and external trades 102 relating to a trade 86–7 settlement 101, 113 on trade tickets 102 debt, exposure to 127 debt valuation adjustment (DVA) 209 debtors, balance sheet item 162 default 51, 131, 148 see also credit default swaps delivery versus payment (DvP) 98 delta hedging 133 delta risk 130 deltas 175 deposits 23, 35 derivatives 61–72 see also futures and forwards; options; swaps digital options 68–9 directors, role of 193–4 discount curve, interest rates 38–9 discounting, NPV calculation 343–4, 345 diversification 122–3 dividends 105–6 documentation credit risk 50–1 EcoRisk project case study 240–1 legal documents 84–5 processes 287 risks 356, 374 settlement 98 Dodd–Frank Act 206–7 dreaming ahead 131–2 due diligence 192, 292 duties (fees) 97 DVA (debt valuation adjustment) 209 DVO1, risk measure 138 DvP (delivery versus payment) 98 economic data 84 EcoRisk project, case study 235–47 documentation 240–1 functionality 243–4 Graphical User Interface 237–8 mathematical library 238, 241 solution 238–40 testing 239–40 valuation problem debugging 242–3 INDEX electronic exchanges 6 electronic systems 92 email 92 EMIR (European Markets Infrastructure Regulation) 202–3 employees see people involved in trade lifecycle end of day roll 103, 181–2 end of month reports 182 energy products 56 equal opportunities 219–20 equities 26, 44–5, 247–52 errors confirmation process 95 in data 322 P&L corrections 171 post booking 97 in reports 333–4 European Markets Infrastructure Regulation (EMIR) 202–3 European options 29, 66 exceptions, processes 322 exchange price 75 exchanges 6, 86, 320 execution of a trade 89–93 exercise, option trades 64, 110–12, 357–8 exotic options 67–9, 109, 235–47, 346 expected loss 150 exposure 4, 125–8, 130–2, 150–1, 155, 156 fault logging 302–4 fees 97, 169 finance department 191, 316 financial products 17–31 bonds 27, 28, 29, 46–53, 106–7, 225–35 credit default swaps 30–1, 51–2, 65–6, 175, 209 deposits 23, 35 equities 26, 44–5, 247–52 futures 20–1, 35–6, 40–1, 61, 62, 77, 127, 311, 312 FX swaps 25, 41 loans 21–3 options 27–30, 61–9, 77, 109–12, 127, 235–47, 345–6, 357–8 spot trades 18–19, 40, 127 swaps 23–5, 30–1, 36–7, 41, 107, 312–13 financial reports 168–9 financial services industry 8–10 fixed assets, balance sheet item 161 fixed bonds 27, 28, 47, 48 fixed and floating coupons 127 383 Index fixed for floating swaps 23–4 fixed loans 22 fixing date 86 fixings 107–8 float for fixed/float for float 36 floating bonds 27, 28 floating loans 22 floating rate notes (FRNs) 47 flow diagrams 287 FoP (free of payment) 98 foreign exchange (FX) 40–4 baskets 41–2 FX drift 42–3 reporting currency 42 swaps 25, 41 tradeflow issues 43–4 forward rate agreement (FRA) 37–8 see also futures and forwards free of payment (FoP) 98 FRNs (floating rate notes) 47 front book trading 132 front line support staff 186 front office EcoRisk project, case 235–47 market risk control 142 risks 375–6 fugit 112 fund managers 10 funding valuation adjustment (FVA) 209 futures and forwards 20–1, 35–6, 40–1, 61, 62 gold futures 311, 312 leverage 77 risks 127 FVA (funding valuation adjustment) 209 FX see foreign exchange gamma risk 130 gearing 77–8 gold futures 311, 312 governance 204 Graphical User Interface (GUI) 237–8 hedge funds 10, 168–9, 212–13 hedging strategies 133–4 hedging trades 128 help desks 247 historical market data 314 holdings 117–24 asset types 118 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 reconciliation 121 risks 124 value 120–1 human resources see people involved in trade lifecycle human risks 194–9, 359–61 hybrid trades 69–70 identification details, trades 83–4 illiquid products 140 illiquid trades 339 in person trades 92 in-the-money options 66 incentives 195 industrial metals 56 information technology (IT) architects 187 case studies 225–52 communication 259–60 dependency on 284 EcoRisk project 235–47 equity confirmation project 247–52 infrastructure 186 IT divide 253–66 business functions 255–6 business requirements 261–3 coping with change 260–1 do’s and don’ts 263 IT blockers 258 IT requirements 263–4 misuse of IT 256–7 organisational blockers 257–8 problems caused by 255 project examples 265–6 solution 259–60 language of 254 legacy systems 282 operators 188 project managers 187–8 quality control 260 and quantitative analysts 271–4 RABOND project 225–35 risks 375–6 staff 185–9, 197, 217–18, 253–66 testers 188–9 and traders 258 384 infrastructure, IT 186 instantaneous risk measures 138 insurance 30–1, 50 integration testing 300 interbank systems 158 interbank trading (LIBOR) 39 interest rates 21–3, 33–40 base rate 35 credit effects 39 deltas 175 deposits 35 discount curve 38–9 forward rate agreement 37–8 futures 35–6, 311–12 market participants 34–5 option valuation 67 products 35–8 quantitative analysts 274 swaps 23–5, 36–7 time value of money 33–4 tradeflow issues 39–40 vegas 175 interim delivery of projects 259 internal audit 191–2 International Swaps and Derivatives Association (ISDA) 50 investment banks 9–10 investments, balance sheet item 161 ISDA (International Swaps and Derivatives Association) 50 IT see information technology kappa risk 130 knock in/knock out, barrier options 68 knowledge, risks 359–60 legacy IT systems 282 legal department 189, 293, 316 legal documents 84–5 legal risks 50, 369 leverage 64–6, 76–9 LIBOR (interbank trading) 39 libraries 184–5 lifecycle of a trade see trade lifecycle limit orders 129 limits and credit worthiness 155 imposing 152–3 market risk control 141 line managers 222 INDEX linear derivatives 61, 62 liquidity 73–5, 202, 375 litigation 370 live trading 7 loans 21–3 management see also project management; risk management of changes 109–10 counterparty risk control 157 fees 169 market data usage 317 new products 292 responsibilities of 193–4 risks 374 of teams 229–31 margin payments 156 mark-to-market value 339–40 market data 180, 292, 308–17 business usage 315–17 changes as result of 107–8 curves and surfaces 310–13 sets of 314 market participants 4–5 market risk control 135–45, 190, 363–4 allocation of risk 139 balanced approach 143 controlling the risk 140–1 human factor 143 limitations 142–3 market data usage 316 methodologies 135–9 monitoring of market risk 140 need for risk 139 quantitative analyst role 268 regulatory requirements 143–4 responsibilities 141–2 market sentiment 340 matching of records 94–5 mathematical libraries 238, 241, 270 mathematical models evolution of 343 new products 293 parameters 341 prototypes 238–9 quantitative analyst role 183–5 risks 373 validation team 189–90 maturity of a trade 8, 67, 86, 112–13 MBS see mortgage backed securities 385 Index metal commodities 56, 57 middle office (product control) market data usage 316 new products 293 RABOND project, case study 225–35 role of 180–2 missing data 317 mobile phones 92 models see mathematical models Monte Carlo technique 346–7 mortgage backed securities (MBS) 47 multilateral netting 211–12 NatWest Markets, EcoRisk project 235–47 net present value (NPV) 338–9, 343–8 netting 152, 211–12 new products 289–95 checklist 292–3 evolution of 294 market data 292 market risk control 140 process development/improvement 279–88 risks 194, 294–5, 369 testing 291–2 trial basis for 290–2 new trade types 156 nonlinear derivatives 62–9 nostro accounts 99 NPV see net present value official market data 314 offsetting of risks 128 OIS (overnight indexed swap) 39 operational risks 355–8 operations department 183, 227, 316 operators, IT 188 options 27–30, 61–9 credit default swaps 65–6 exercise 110–12 exotic options 67–9, 109, 235–47, 346 leverage 64–6, 77 risks 127, 357–8 terminology 66 trade process 64–6 valuation 67, 345–6 orders 90–1, 357 OTC see over-the-counter trading OTTC equity confirmation project, case study 247–52 out-of-the-money options 66 over-the-counter (OTC) trading 6–7 clearing 210 commodities 56 price 75 overnight indexed swap (OIS) 39 overnight processes 101–5 P&L see profit and loss parallel testing 301 pay 203, 220–1 payment systems 106–7, 158–60, 357 pension funds 10 people involved in trade lifecycle 177–200 see also working in capital markets back office 183, 227, 316 compliance officers 192–3 conflicts and tensions 196–9, 360–1 control functions 189–99 counterparty risk control department 190–1 finance department 191, 316 human risks 194–9 information technology 185–9, 197, 217–18, 253–66 internal audit 191–2 legal department 189, 293, 316 line managers 222 management 193–4 market risk control department 190 middle office 180–2, 225–35, 293, 316 model validation team 189–90 personality and outlook 194–5, 244–5, 273 programmers 187, 244–5 quantitative analysts 183–5, 267–75 researchers 179–80 revenue generation 177–89 sales department 179, 227, 315, 375 senior managers 126 staffing levels 195 structurers 179 supervisors 204 testers 298–9 traders 125–6, 177–8, 218–23, 226–7, 258, 268, 315, 361 trading assistants 178 trading managers 126, 193 training of staff 193 performance reports 169 personality and outlook 194–5, 244–5, 273 PFE (potential future exposure) 151 physical assets, exercise 111 386 physical commodities, settlement 57–8, 99 planning of processes 282–3 recovery plans 203–4 risks 360 post booking processes 96–7 postal trades 92–3 potential future exposure (PFE) 151 power, abuses of 220, 221–2 pre-execution of a trade 89–91 precious metals 56, 311, 312 premiums 31 price 75–6, 138–9 pricing methods EcoRisk project, case study 235–47 short-term pricing 183 process development/improvement 279–88 coping with change 284 current processes 285–7 evolution of processes 280–1 improving the situation 284–7 inertia 287–8 inventory of current systems 282–4 planning 282–3 timing 288 producers 5 product appetite 4 product control see middle office product development see new products profit curve, commodity trading 54–5 profit and loss (P&L) accounts 164–8 accrued and incidental 165 example 165–6 individual trades 166–7 realised and unrealised 165 responsibility for producing 167 risks associated with reporting 167–8 rogue trading 168 attribution reports 171–6 benefits of 171–2 example 173–6 market movements 173, 175 process 172–3 unexplained differences 173 balance sheet item 163 end of day 182 realised and unrealised 122, 165 programmers 187, 244–5 see also quantitative analysts INDEX project management 225–47, 259, 262 project managers 187–8 proprietary (‘prop’) trading 203 prototypes, IT projects 238–9 provisional trades 89–90, 357–8 put options 62, 63 PVO1, risk measure 138 quality control, IT 260 see also testing quantitative analysts (quants) 183–5, 267–75 and IT professionals 271–4 role of 267–9, 270 seating arrangements 270–1 working methods 269–70 RABOND project, case study 225–35 management 229–31 outcome 233–5 reports 227–9 team management 229–31 traders 226–7 random market data 314 rapid application development (RAD) 260, 281 ratchet options (Cliquet) 68 ratings companies 231–2 raw data 323 raw reporting 331 real world of capital markets see working in capital markets realised P&L 122 receipts 156 reconciliation 121 recovery plans 203–4 recovery rates 52–3, 176 redundancy, processes 282 reform of banks 203 registered securities 123–4 regression testing 302 regulation 201–13, 223–4 authorities 202 Basel II and III 144, 205 credit valuation adjustment 207–13 external 192 internal 224 market risk control 143–4 new products 293 problems 204–5 requirements 202–4 387 Index risk-weighted assets 205–7 risks 369 rehypothication 212–13 remuneration 203, 220–1 reporting currency 42 reports 327–36 accuracy 330–1, 368 calculation process 342 configuration 331–2 consolidated reporting 122 content 328–9 control issues 335 dimensions 333 distribution 329–30, 335, 369 dynamic reports 332–3 end of month reports 182 enhancements 335 errors in 333–4 false reporting 375 financial reports 168–9 frame of reference 333 middle office role 180–1 OTTC equity confirmation project 250, 251 performance reports 169 presentation 329 problems 333–4 profit and loss 167, 171–6 RABOND project 227–9 raw reporting 331 readership 328, 329, 368–9 redundancy of 334–5 requirements 328–33 risks 335–6, 368–70 security issues 335, 368 timing 330 types of 330 reputation, risk to 356, 370 research 268, 375 researchers 179–80 reserve accounts 141 reset date 86 resettable strike, exotic options 68 retail banks 222 revenue generation, people involved in 177–89 rho risk 130 risk 13–16 see also counterparty risk control; market risk control advisory services 370 appetite for 4 business continuity planning 373 calculation process 352 cashflows 124, 367 changes to a trade 110 communication 371 confirmation 95–6, 355 control departments 224 correlation 363 data 324–5, 367–8 definition 13 documentation 356, 374 exercise 112 front office 375–6 human risks 194–9, 359–61 information technology 375–6 instantaneous measures 138 legal risks 369 liquidity 74–5, 375 litigation 370 management risks 374 measures 130, 138, 149–52, 155, 156 model approval 373 new products 140, 194, 294–5, 369 operational risks 355–8 orders 91 origin of risks 126–8 payment systems 357 provisional trades 90, 357–8 quantifying 14 regulation 369 reports 335–6, 368–70 reputation 356, 370 risk-weighted assets 205–7 sales 375 settlement 100, 355–7 short-term thinking 360 straight through processing 357 support activities 376 systematic 202–3, 375–6 testing 304–5, 370–1 types 130–2 unexpected charges 356 unforeseen 16, 353 valuation process 352, 373 risk management 13, 15, 125–34 in absence of trader 128–9 dreaming ahead 131–2 EcoRisk project case study 235–47 hedging strategies 133–4 hedging trades 128 388 risk management (continued) offsetting of risks 128 senior managers 126 traders 125–6, 361 trading managers 126 trading strategies 132 rogue trading 168 sales data 84 sales department 179, 227, 315, 375 SBC Warburg, equity confirmation project, case study 247–52 scenario analysis 136, 198–9, 341 scope creep 187, 264 scrutiny of trades 96 securities, custody of 123–4 security issues 181, 335, 368 semi-static data 309 senior managers 126 sensitivity analysis 138, 347–8 settlement 97–101, 147–8 breaks 101, 356–7 commodities 99 dates 101, 113 nostro accounts 99 quick settlement 101 risks 100, 355–7 shares 44–5 see also equities short selling 65 short-term pricing 183 short-term thinking 195–6, 360 silo approach 257 simple products 70–1 smoke testing 301 sovereign debt 46 speculators 5 spot prices 61, 62, 63, 67, 76–7 spot testing 301 spot trades 18–19, 40, 127 spread of bid/offer 310 spreadsheets 184, 238 staff see people involved in trade lifecycle stale data 105, 318 Standard & Poor’s (S&P) ratings 231–2 static data 309 stop-loss hedging 133–4 stop orders 129 storage of data 309 straight through processing (STP) 93–4, 357 INDEX stress, staff 222, 244–5 stress testing 302 strike price, options 67 structured trades 69–70 structurers 179 supervisors 204 support activities, risks 376 surfaces, market data 310–13 swaps credit default 30–1, 51–2, 65–6, 175, 209 fixings 107 foreign exchange 25, 41 interest rate 23–5, 36–7 yield curves 312–13 swaptions 66 synthetic equities (index) 45 systems see also information technology amalgamation 104–5 analytics 271–2 electronic systems 92 integrated 261 legacy IT systems 282 risks 375–6 testing 251–2, 300 tail behaviour, predicting 143, 364 team management 229–31 telephone transactions 91–2 tensions and conflicts 196–9, 360–1 testing 297–305 back testing 317 boundary testing 351 extreme values 352 fault logging 302–4 importance of 298 mathematical models 239 new products 291–2 risks 304–5, 370–1 stages 300–1 testers 188–9, 298–9 types of 301–2 unit testing 300 user acceptance testing 237, 239–40, 252, 264, 301 when to perform 299–300 theft 355 theta risk 130 time intervals (buckets) 148–9 time lag, commodities 57 389 Index time series analysis 320 timeline of a trade 79, 86–7 trade blotters 93 trade lifecycle 89–115 booking 93–4 business functions 11 changes during lifetime 105–10 confirmation 94–6 equity trades 45 example trade 113–15 execution 91–3 exercise 110–12 maturity 112–13 new products 293 overnight processes 101–5 post booking 96–7 pre execution 89–91 settlement 97–101 trade tickets 102 trade/trading 3–12 see also trade lifecycle anatomy 83–7 business functions 11 complicated trades 340 consequences of 7–8 definition 10–12 financial products 17–31 live trading 7 matching of records 94–5 policies 8 reasons for 3, 9–10 timeline 79, 86–7 transactions 5–7 types 132 tradeflow issues bonds 49 commodities 58 foreign exchange 43–4 interest rates 39–40 traders 177–8, 218–22, 223, 226–7, 258, 268 bonuses 220–1 market data usage 315 risk management 125–6, 361 trading assistants 178 trading desks 70–1, 256–7 trading floor 217–18, 235–6 trading managers 126, 193 training of staff 193 tranche correlation 131 treasury desk 71 trials for new products 290–2 trust 197, 222 UAT see user acceptance testing underlying 83 unexplained differences, P&L reports 173 unforeseen risk 16, 353 unit testing 300 unknown cashflows 345–6 unrealised P&L 122 unwinding a trade, cost of 76 user acceptance testing (UAT) 237, 239–40, 252, 264, 301 validation of models 189–90 valuation process see also calculation process calibration to market 351 mark-to-market value calculation 339–40 middle office role 181 NPV calculation 338–9, 343–8 options 67 problem debugging 242–3 risks 352, 364, 373 valuation systems 269 value at risk (VaR) 136–8, 341 vega (kappa) risk 130 vegas 175 vendors, data services 321 volatility 67, 130 volume of a trade, price effect 76 white box testing 301 workarounds 303 working in capital markets 217–24 see also case studies; people involved in trade lifecycle in 1990s 217–19 culture clashes 219 equal opportunities 219–20 office politics 220–2, 246 positive/negative aspects 222–3 yield curves 312–13 zero bonds 27, 29, 47 Index compiled by Indexing Specialists (UK) Ltd WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA. 

The Price of Time: The Real Story of Interest
by Edward Chancellor
Published 15 Aug 2022

After the Savings & Loan crisis at the turn of the decade, when more than a thousand US mortgage banks, ‘thrifts’, failed, the Fed funds rate was cut to below 3 per cent, its lowest level for many years and roughly half the prevailing rate of (nominal) GDP growth. Greenspan wanted to help Wall Street out: cheap short-term borrowing enabled banks and hedge funds to mint profits by ‘riding the yield curve’. A pick-up in US productivity in the mid-1990s suggested that the natural rate of interest was rising. At the same time the prices of imported goods were falling and inflation remained dormant. If the rate of interest tracks the return on capital, then American rates should have climbed in tandem.

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Just as subprime credit in the previous decade had over-egged America’s housing market, now a glut of vehicles coming to the end of their leases inundated the secondhand car market, driving down prices and saddling car owners with more debt than their vehicles were worth. In industry parlance, they were said to be ‘upside down’.fn4 DURATION RISK When the yield curve slopes upwards, bonds with longer maturities provide more income than short-dated bonds or cash. When interest rates decline, owning bonds with longer maturities – what’s known as taking ‘duration’ – also generates capital gains. During a bond bull market, owning long-dated securities with even the tiniest of yields can deliver mouthwatering profits.

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The currency pegs of the Danish and Swiss central banks provided them with an excuse to buy foreign securities with newly printed money. The Bank of Japan, which had been the first to initiate quantitative easing (in March 2001), later came up with ‘quantitative and qualitative easing’, to which it added ‘yield-curve control’.18 While interest rates in the United States and the rest of the Anglophone world never went below the ‘zero lower bound’, central banks in Europe and Japan crossed the Rubicon, venturing into the unknown territory of negative rates. THE CURSE OF NEGATIVE RATES Between the world wars a number of monetary cranks appeared, each offering his own idiosyncratic cure for economic maladies.

Solutions Manual - a Primer for the Mathematics of Financial Engineering, Second Edition
by Dan Stefanica
Published 24 Mar 2011

Find an approximate price of the bond if the yield decreases by fifty basis points. Solution: Note that , since the yield of the bond decreases , the value of the bond must increase. Recall that the percentage change in the price of the bond can be approximated by the duration of the bond multiplied by the parallel shift in the yield curve , with opposite sign , i.e. , !:1 B 万一句 - !:1 y D For B = 102 , D = 3.5 and !:1 y = -0.005 (since 1% = 100 bp) , we 五nd that !:1B 用 - !:1 y D B = 1. 785. The new value of the bond is Problem 13: If the coupon rate of a bond goes up , what can be said about the value of the bond and its duration?

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What are the payoff and the P &L at maturity of the butterfly spread? When would the butterfly spread be profitable? Assume , for simplicity, that interest rates are zero. 4. Dollar duration is defined as D电=一旦 ωθu and measures by how much the value of a bond portfolio changes for a small parallel shift in the yield curve. Similarly, dollar convexity is defined as C虫二工 θ2B eθy2· 58 CHAPTER 2. NUMERICAL INTEGRATION. BONDS. Note that , unlike classical duration and convexity, which can only be computed for individual bonds , dollar duration and dollar convexity can be estimated for any bond portfolio , assuming all bond yields change by the same amount.

The Asian Financial Crisis 1995–98: Birth of the Age of Debt
by Russell Napier
Published 19 Jul 2021

The need for institutional investors to follow benchmark indices and adapt to changes in those indices had, and still has now, economic as well as investment implications, particularly for emerging markets operating managed exchange rate regimes. Global deterioration: the markets finally look east 30 July 1996, Japan What has changed to turn global equity markets bearish? The only surprise over the past few weeks has come from Japan. In the United States, the bond market has been well behaved, the shape of yield curve unchanged and Greenspan’ s comments supportive. Earnings growth in the United States has been ahead of expectations. However, in a three-day period, the yen rallied 3.1% against the US dollar on speculation that Japanese interest rates would rise. This currency movement would appear to be the catalyst for the sell-off.

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In other words, some of the capital of the strong banks will be used to alleviate the problems of the weak banks. The capital structure of this body was not announced, but any significant equity injections from the stronger banks would clearly be another negative for their shareholders. The US authorities healed their ailing banking system via creating a steep yield curve. This was very beneficial for the banking sector as profits were boosted and low interest rates reflated asset prices. However, this remedy is not available to the BOT (due to the fixed exchange rate) and the need to reflate the economy will thus create negative repercussions for bank profitability.

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Invariably a plan will be found that works, given the consequences of a collapse of the banking system. However, it is not always the first plan that works, and the plan that works is not necessarily good for those who own bank equity in either the weak banks or the strong banks. In the 1980s, in the United States, the central bank kept short-term interest rates low and the steep yield curve that ensued allowed banks to borrow short and lend long at great profit. This was a form of surreptitious recapitalisation that met with little political backlash, required limited government capital and did not need to force strong banks to bail out weak banks. The owners of bank equity capital benefited greatly from this mechanism.

Analysis of Financial Time Series
by Ruey S. Tsay
Published 14 Oct 2001

Using the modern econometric terminology, if one assumes that the two interest rate series are unit-root nonstationary, then the behavior of the residuals of Eq. (2.40) indicates that the two interest rates are not co-integrated; see Chapter 8 for discussion of co-integration. In other words, the data fail to support the hypothesis that there exists a long-term equilibrium between the two interest rates. In some sense, this is not surprising because the pattern of “inverted yield curve” did occur during the data span. By inverted yield curve, we mean the situation under which interest rates are inversely related to their time to maturities. 1970 1980 year 1990 2000 ACF 0.0 0.2 0.4 0.6 0.8 1.0 Series : res 0 5 10 15 Lag 20 25 30 Figure 2.14. Residual series of linear regression (2.40) for two U.S. weekly interest rates: (a) time plot, and (b) sample ACF. 69 REGRESSION MODELS WITH TIME SERIES ERRORS -2 per. chg. -1 0 1 2 (a) Change in 1-year rate 1970 1980 year 1990 2000 1990 2000 -2 per. chg. -1 0 1 2 (b) Change in 3-year rate 1970 1980 year Figure 2.15.

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• Suppose that we are interested in forecasting the direction of the 1-month ahead stock movement. Fit a 6-5-1 feed-forward neural network to the return series using a Heaviside function for the output node. Compute the 1-step ahead forecasts in the forecasting subsample and compare them with the actual movements. 5. Because of the existence of inverted yield curves in the term structure of interest rates, the spread of interest rates should be nonlinear. To verify this, consider the weekly U.S. interest rates of (a) Treasury 1-year constant maturity rate, and (b) Treasury 3-year constant maturity rate. As in Chapter 2, denote the two interest rates by r1t and r3t , respectively, and the data span is from January 5, 1962 to September 10, 1999.

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ISBN: 0-471-41544-8 Index ACD model, 197 Exponential, 197 generalized Gamma, 199 threshold, 206 Weibull, 197 Activation function, see Neural network, 147 Airline model, 63 Akaike information criterion (AIC), 37, 315 Arbitrage, 332 ARCH model, 82 estimation, 88 normal, 88 t-distribution, 89 Arranged autoregression, 158 Autocorrelation function (ACF), 24 Autoregressive integrated moving-average (ARIMA) model, 59 Autoregressive model, 29 estimation, 38 forecasting, 39 order, 36 stationarity, 35 Autoregressive moving-average (ARMA) model, 48 forecasting, 53 Back propagation, neural network, 149 Back-shift operator, 33 Bartlett’s formula, 24 Bid-ask bounce, 179 Bid-ask spread, 179 Bilinear model, 128 Black–Scholes, differential equation, 234 Black–Scholes formula European call option, 79, 235 European put option, 236 Brownian motion, 224 geometric, 228 standard, 223 Business cycle, 33 Characteristic equation, 35 Characteristic root, 33, 35 CHARMA model, 107 Cholesky decomposition, 309, 351, 359 Co-integration, 68, 328 Common factor, 383 Companion matrix, 314 Compounding, 3 Conditional distribution, 7 Conditional forecast, 40 Conditional likelihood method, 46 Conjugate prior, see Distribution, 400 Correlation coefficient, 23 constant, 364 time-varying, 370 Cost-of-carry model, 332 Covariance matrix, 300 Cross-correlation matrix, 300, 301 Cross validation, 141 Data 3M stock return, 17, 51, 58, 134 Cisco stock return, 231, 377, 385 Citi-Group stock return, 17 445 446 Data (cont.) equal-weighted index, 17, 45, 46, 73, 129, 160 GE stock return, 434 Hewlett-Packard stock return, 338 Hong Kong market index, 365 IBM stock return, 17, 25, 104, 111, 115, 131, 149, 160, 230, 261, 264, 267, 268, 277, 280, 288, 303, 338, 368, 383, 426 IBM transactions, 182, 184, 188, 192, 203, 210 Intel stock return, 17, 81, 90, 268, 338, 377, 385 Japan market index, 365 Johnson and Johnson’s earning, 61 Mark/Dollar exchange rate, 83 Merrill Lynch stock return, 338 Microsoft stock return, 17 Morgan Stanley Dean Witter stock return, 338 SP 500 excess return, 95, 108 SP 500 index futures, 332, 334 SP 500 index return, 111, 113, 117, 303, 368, 377, 383, 422, 426 SP 500 spot price, 334 U.S. government bond, 19, 305, 347 U.S. interest rate, 19, 66, 408, 416 U.S. real GNP, 33, 136 U.S. unemployment rate, 164 value-weighted index, 17, 25, 37, 73, 103, 160 Data augmentation, 396 Decomposition model, 190 Descriptive statistics, 14 Dickey-Fuller test, 61 Differencing, 60 seasonal, 62 Distribution beta, 402 double exponential, 245 Frechet family, 272 Gamma, 213, 401 generalized error, 103 generalized extreme value, 271 generalized Gamma, 215 generalized Pareto, 291 INDEX inverted chi-squared, 403 multivariate normal, 353, 401 negative binomial, 402 Poisson, 402 posterior, 400 prior, 400 conjugate, 400 Weibull, 214 Diurnal pattern, 181 Donsker’s theorem, 224 Duration between trades, 182 model, 194 Durbin-Watson statistic, 72 EGARCH model, 102 forecasting, 105 Eigenvalue, 350 Eigenvector, 350 EM algorithm, 396 Error-correction model, 331 Estimation, extreme value parameter, 273 Exact likelihood method, 46 Exceedance, 284 Exceeding times, 284 Excess return, 5 Extended autocorrelation function, 51 Extreme value theory, 270 Factor analysis, 342 Factor model, estimation, 343 Factor rotation, varimax, 345 Forecast horizon, 39 origin, 39 Forecasting, MCMC method, 438 Fractional differencing, 72 GARCH model, 93 Cholesky decomposition, 374 multivariate, 363 diagonal, 367 time-varying correlation, 372 GARCH-M model, 101, 431 Geometric ergodicity, 130 Gibbs sampling, 397 Griddy Gibbs, 405 447 INDEX Hazard function, 216 Hh function, 250 Hill estimator, 275 Hyper-parameter, 406 Identifiability, 322 IGARCH model, 100, 259 Implied volatility, 80 Impulse response function, 55 Inverted yield curve, 68 Invertibility, 331 Invertible ARMA model, 55 Ito’s lemma, 228 multivariate, 242 Ito’s process, 226 Joint distribution function, 7 Jump diffusion, 244 Kernel, 139 bandwidth, 140 Epanechnikov, 140 Gaussian, 140 Kernel regression, 139 Kurtosis, 8 excess, 9 Lag operator, 33 Lead-lag relationship, 301 Likelihood function, 14 Linear time series, 27 Liquidity, 179 Ljung–Box statistic, 25, 87 multivariate, 308 Local linear regression, 143 Log return, 4 Logit model, 209 Long-memory stochastic volatility, 111 time series, 72 Long position, 5 Marginal distribution, 7 Markov process, 395 Markov property, 29 Markov switching model, 135, 429 Martingale difference, 93 Maximum likelihood estimate, exact, 320 MCMC method, 146 Mean equation, 82 Mean reversion, 41, 56 Metropolis algorithm, 404 Metropolis–Hasting algorithm, 405 Missing value, 410 Model checking, 39 Moment, of a random variable, 8 Moving-average model, 42 Nadaraya–Watson estimator, 139 Neural network, 146 activation function, 147 feed-forward, 146 skip layer, 148 Neuron, see neural network, 146 Node, see neural network, 146 Nonlinearity test, 152 BDS, 154 bispectral, 153 F-test, 157 Kennan, 156 RESET, 155 Tar-F, 159 Nonstationarity, unit-root, 56 Nonsynchronous trading, 176 Nuisance parameter, 158 Options American, 222 at-the-money, 222 European call, 79 in-the-money, 222 out-of-the-money, 222 stock, 222 strike price, 79, 222 Order statistics, 267 Ordered probit model, 187 Orthogonal factor model, 342 Outlier additive, 410 detection, 413 Parametric bootstrap, 161 Partial autoregressive function (PACF), 36 PCD model, 207 π -weight, 55 Pickands estimator, 275 448 Poisson process, 244 inhomogeneous, 290 intensity function, 286 Portmanteau test, 25.

Not Working: Where Have All the Good Jobs Gone?
by David G. Blanchflower
Published 12 Apr 2021

If that is the case, it’s no surprise that inflation has not kicked in.39 Sabine Lautenschläger at least has got it. There are one or two EWA indicators that were flashing amber in the United States in mid-2018. The U.S. yield curve plots Treasuries with maturities ranging from four weeks to thirty years. The gap between long and short yields turning negative has been a reliable indicator of recession. The yield curve was flattening during the first few months of 2018. Ed Yardeni’s Boom-Bust Barometer, which measures spot prices of industrial inputs like copper, steel, and lead scrap divided by initial unemployment claims, fell before or during the last two recessions.

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See also Brexit UK Independence Party (UKIP), 238, 275 UK Labor Force Survey (UKLFS), 124–25, 128 Ukraine, 254 United States: anti-intellectualism in, 286; austerity in, 329; consumer confidence in, 194–95, 210, 321; cyclicality in, 64, 96, 303; crime fears in, 257; deskilling in, 101–2; disability in, 95; drug and alcohol use in, 36, 214, 216–18, 220, 221, 225, 229, 230–31, 236; economic indicators in, 198; employment measurement in, 20, 118, 136; financial sector in, 84; Great Recession in, 3, 9, 23, 41, 78–79, 81, 100, 111–12, 129, 154, 168, 195–96, 199–201, 204; happiness and life satisfaction in, 28, 36, 73, 116, 215–16, 226, 333–34; housing market in, 84, 192, 193, 202, 208, 302, 345; immigration to, 24, 84, 93, 238–39, 241–44, 246–47, 250–52, 254, 258–62, 283; incarceration rates in, 102; income maintenance in, 183; inequality in, 105, 106, 108–12, 114, 116–17; inequality viewed in, 107, 116; inflation in, 71, 315; infrastructure in, 23, 339–40, 347; job insecurity in, 28–29; labor market concentration in, 125; long-term unemployment in, 40–42, 69–71; manufacturing employment in, 93, 173, 201, 214; mobility in, 39, 86–87, 116, 342; monetary policy in, 7, 67, 68–69, 83, 299, 313; mortality in, 229, 233, 236–37; multiple job holding in, 140; obesity in, 224; out of labor force cohort in, 26; overoptimistic forecasts in, 152, 154–55, 205; participation rate in, 25, 39, 94, 97, 100, 102, 104; physical pain in, 218–20; populism in, 7, 264, 279–80, 324, 325–26, 347; post–Great Recession expansion in, 83, 322; productivity in, 63, 65; protectionism in, 207, 317, 319; riots in, 270; self-employment in, 103–4, 140–41; social fragmentation in, 330–31; stock market crashes in, 3, 4, 79, 185, 212; suicide in, 7, 214, 225, 233; terrorism fears in, 249; underemployment in, 25, 32, 49, 54–55, 118–19, 126–30, 132, 134, 136–37, 141–42, 145, 231, 310; unemployment in, 4–5, 6, 18, 19, 23, 43, 49, 84, 134, 141, 144, 145, 184, 195, 201, 214, 290, 297, 298, 305, 306; unionization in, 113–14; wage stagnation in, 6, 48, 51, 54–55, 58, 61–62, 71, 214, 301, 308; work-life balance in, 73; yield curve in, 208; young people’s living arrangements in, 37, 39, 85 United States Conference of Mayors, 23 U.S. General Social Survey (GSS), 227, 330 United States–Mexico–Canada Trade Agreement (USMCA), 317 U.S. Steel, 290 Universal Basic Income (UBI), 343 universal credit, 34 University of Michigan, 194 unsecured debt, 74 U7 measure, 118, 119, 129, 136–37, 138, 143–44, 308, 310, 311 vacation allowances, 54 Valletta, Robert G., 126, 128 van Baardwijk, Marjolein, 185 Vance, J.

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See also inflation “wage ratchet,” 28 Wales, 188, 272, 273, 275, 291 Wallop, Henry, 159 Walmart, 18 Wardle, Jane, 223 Wascher, Bill, 97 Washington State, 193 Watson, Mark W., 305 Webb, Beatrice, 182 Weidmann, Jens, 207 Weismann, Jens, 84 Weiss, Yoram, 252 Welch, Jack, 16 Wells, Claudia, 113 Wessel, David, 315 West Virginia, 224, 227, 231, 236, 243, 265, 289 Whirlpool, 319 White, Nicola, 342 Whittaker, Matthew, 276 Wilkins, Roger, 125 Willsher, Kim, 271 Winters, John V., 140 Wisconsin, 193, 326 Wolf, Martin, 160, 174 Wolfe, Richard, 334 Wolfers, Justin, 86 Wooden, Mark, 125 work-life balance, 71–77 World Bank, 205 World Database of Happiness, 116 World Economic Outlook (IMF), 120, 345 World War I, 328, 344 World War II, 5, 22 Worswick, G. D. N., 22 Wren-Lewis, Simon, 175–77, 214 Xi Jingping, 317 XpertHR, 308 Yagan, Danny, 96 Yamarone, Richard, 185–86 Yardeni, Edward, 208 Yellen, Janet, 165, 304 Yemen, 244 yield curve, 208 Zaninotto, Paola, 223 zero-hours contracts, 35, 104, 270 zero lower bound (ZLB), 160, 161 Ziblatt, Daniel, 347 Zimmermann, Klaus F., 57 Znojmo, Moravia, 189–90 Zuckerberg, Mark, 337 Zucman, Gabriel, 108, 109–10, 337 Zweimüller, Josef, 45

Safe Haven: Investing for Financial Storms
by Mark Spitznagel
Published 9 Aug 2021

Thus, our null hypothesis that the three‐month Treasury bill is a cost‐effective safe haven must be rejected, as we deny its consequent: that adding the three‐month Treasury bill to our SPX portfolio raises that portfolio's CAGR over time (and which we've just seen, it doesn't). As a next step, we can move further out along the yield curve, from 3 months to 10 and 20 years. This becomes more representative of the bonds in the “stocks/bonds” portfolio that is the “balanced portfolio” in investing. We might even think of it as the standard in diversified portfolios. As we move out along the yield curve, we also move out along the safe haven spectrum as defined by our three cartoons. And as we move from the three‐month to the 10‐ and 20‐year Treasury maturity, we move from the store‐of‐value toward a more presumably negatively correlated payoff—a hybrid between the two.

Trading and Exchanges: Market Microstructure for Practitioners
by Larry Harris
Published 2 Jan 2003

Since such valuation factors make the basis nonstationary, maturity spreads are speculative arbitrages. In practice, the mean-reverting component of the basis usually dominates. The most common maturity spreads are calendar spreads and yield curve spreads. Calendar spreads involve futures contracts or option contracts that mature on different dates. Yield curve spreads involve bonds that mature on different dates. 17.3.2.2 Pairs Trading Pairs traders try to identify pairs of instruments that they believe are mispriced relative to each other. They then buy the one that appears cheap and sell the one that appears expensive.

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This is a cash-settled futures contract that prices the expiration day value of a standard bond-pricing formula for a hypothetical fixed-rate bond. The hypothetical bond consists of a series of notional fixed 6 percent interest payments followed by the return of the notional principal at the maturity of the hypothetical bond. The pricing formula uses discount rates that are derived from the swaps yield curve, which is computed from ISDA Benchmark Euribor Swap Rate fixings. The Swapnote futures contracts thus derive their values from prices in the swaps market. LIFFE also trades options on Swapnote futures. The Swapnote futures option is a derivative on a derivative on a derivative. (It is an option contract on a futures contract based on swaps contract prices.) ◀ Source: www.liffe.com * * * Swaptions are options on a swap contract.

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The most successful recent contract introductions have involved energy and financial products. Some interesting failures have included contracts in sunflower seeds, wool, butter, eggs, high fructose corn syrup, boneless beef trimmings, frozen turkeys, crop yields, barge freight rates, anhydrous ammonia fertilizer, diammonium phosphate fertilizer, various Brady bonds, various yield curve spreads, the U.S. inflation rate, various catastrophe insurance indexes, aluminum, and U.S. silver coins. Table 8-2 lists some recent successful futures contract introductions. TABLE 8-1. Examples of Successful Hedging Markets 8.1.4 Gamblers Gamblers bet on future events. Their bets are contracts whose values depend on the uncertain outcomes of future events.

Financial Market Meltdown: Everything You Need to Know to Understand and Survive the Global Credit Crisis
by Kevin Mellyn
Published 30 Sep 2009

How much more depends on their specific credit rating but most critically on current market sentiment about risk in general. The effective rate that the government has to pay to borrow money for any given tenor can be plotted as a line called the ‘‘yield curve.’’ Normally, the curve should run from left to right, with rates going up with tenor. However, at times, we can have what is called an ‘‘inverted’’ yield curve, where shorter rates are higher than longer rates. This is because bond rates are set by the market, which is to say by you and me. Although you can buy government debt directly from the treasury, very few people do so.

Limitless: The Federal Reserve Takes on a New Age of Crisis
by Jeanna Smialek
Published 27 Feb 2023

Rates on Treasury securities continued to climb, when they should have been falling as investors rushed toward safety. Money market funds were dumping short-term corporate and municipal debt frantically. Fed vice-chair Clarida and Powell briefly discussed that evening whether they should roll out a yield curve control program, a drastic monetary policy tool in which a central bank promises to buy as much debt as is needed to keep key interest rates below a given level—essentially the “pegging” policy that had been used in Eccles’s time, though not as explicitly coordinated with elected officials. The policy would have been an extreme resort, opening the possibility that the Fed would be left holding a large chunk of the entire debt market.

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Central bankers had not come to a concrete enough agreement to release an outline of what Main Street would look like that Monday, so they simply announced that a rescue was coming. In its release, the Fed also promised to buy as much government-backed debt as was needed to restore function to the disrupted Treasury and mortgage-backed bond markets. It wasn’t the yield curve control Powell and Clarida had discussed, but the amped-up version of quantitative easing wasn’t a million miles away, either. The media immediately took the Fed’s series of market supports as the huge deal that they were. “Fed Signals Unlimited QE, Adds Company Aid,” the Bloomberg chyron read as economics reporter Mike McKee read the news live on air.

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See also public/civil society V vaccines, 138, 164, 218, 219, 245, 255–6, 263 Van Buren, Martin, 47, 48 Vanderlip, Frank, 54 Van Der Weide, Mark, 180, 212 Volcker, Paul: chairmanship of, 23n, 79–82, 81n, 83–4, 86, 94, 96; New York Fed as holy of holies, 33; “only game in town” phrase of, 113, 113n; secretive Fed under, 23n, 81, 84, 86; staff economists, use of by, 108 W war bonds and credit, 60, 159, 344n42 Warburg, Paul, 54 Warner, Mark, 179–80, 191, 199, 344–5n11 Warren, Elizabeth, 121, 139, 184, 195, 199, 208, 248, 258, 296, 297 Warsh, Kevin, 118–19 wealth inequality, 5, 113, 113n, 223–9, 227n, 348nn13–14, 348nn21–22 Wells Fargo, 64n, 156 Willard Hotel, 118, 153 Williams, John, 91, 115, 128, 129–31, 130n, 142, 149, 212 Wilson, Woodrow, 55–8, 60, 62 World Health Organization (WHO), 145 World War I, 61, 344n42 World War II, 63, 70, 71, 75, 189 X Xi Jinping, 108 Y Yellen, Janet: background and expertise of, 18, 99–100; career in private sector of, 200; chairmanship of, 18–20, 99–103; character of, 18; corporate bond market, opinion piece on, 174–5, 176; economy during chairmanship of, 101–2, 114; employment, labor market, and inflation policy of, 96–7, 97n, 100–2; governor role of, 96–7, 97n, 100; gradualist approach of, 19, 26, 100–2; housing bubble, awareness of, 132–3n; opinion about Powell, 17; post-chairmanship career of, 129n, 200, 200n; Powell as successor to, 20, 103, 299; staff economists, use of by, 109; statement on inequality by, 222; suspension of bank payments, opinion about, 215; Treasury secretary role of, 271, 271n; Trump meeting with, 20; vice-chair position of, 100 yield curve control program, 182, 187 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A NOTE ABOUT THE AUTHOR Jeanna Smialek has been the Federal Reserve reporter at The New York Times since April 2019, having previously covered economics for Bloomberg since 2013 from Washington, D.C., New York, and, briefly, Frankfurt.

Birth of the Euro
by Otmar Issing
Published 20 Oct 2008

In the short to medium term, prices are determined by non-monetary factors such as wages (unit labour costs), the exchange rate, energy and import prices, indirect taxes, etc. Indicators of developments in the real economy include data on employment and unemployment, data from surveys (such as the Ifo Business Climate Index), incoming orders, and so on. This economic analysis also encompasses financial sector data such as the yield curve, stock prices and real estate prices. Asset price trends can yield information, for example, on how the wealth effect is expected to influence the growth of demand of private households. As part of its economic analysis, the ECB takes a broad look at developments in macroeconomic demand and its structure, in costs and in the labour market.

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Meltzer, ‘A theory of ambiguity, credibility, and inflation under discretion and asymmetric information’, Econometrica, 54:5 (1986). 166 • The ECB – monetary policy for a stable euro only control the (very) short end of the interest rate spectrum. The influence of monetary policy on the long end depends very largely on the markets’ expectations of the central bank’s policy actions in the future and of future inflation. If the mandate is price stability or low inflation, the evolution of interest rates all along the yield curve, and in addition the decisions of agents in virtually all markets, will hinge on how far the latter expect the central bank to fulfil its mandate. Efficient and effective communication can play a major part in influencing expectations in line with the central bank’s policy. In guiding expectations in the financial markets, two dimensions need to be distinguished.

Investment Banking: Valuation, Leveraged Buyouts, and Mergers and Acquisitions
by Joshua Rosenbaum , Joshua Pearl and Joseph R. Perella
Published 18 May 2009

T-notes are issued with maturities of between one and ten years, while T-bonds are issued with maturities of more than ten years. 89 Yields on nominal Treasury securities at “constant maturity” are interpolated by the U.S. Treasury from the daily yield curve for non-inflation-indexed Treasury securities. This curve, which relates the yield on a security to its time-to-maturity, is based on the closing market bid yields on actively traded Treasury securities in the over-the-counter market. 90 Bloomberg function: “ICUR {# years} <GO>.” For example, the interpolated yield for a 10-year Treasury note can be obtained from Bloomberg by typing “ICUR10,” then pressing <GO>. 91 Located under “Daily Treasury Yield Curve Rates.” 92 The 30-year Treasury bond was discontinued on February 18, 2002, and reintroduced on February 9, 2006. 93 Morningstar acquired Ibbotson Associates in March 2006.

Mastering the Market Cycle: Getting the Odds on Your Side
by Howard Marks
Published 30 Sep 2018

Here’s how I described the creation of the investment environment in “Risk and Return Today” in October 2004: I’ll use a “typical” market of a few years back to illustrate how this works in real life: The interest rate on the 30-day T-bill might have been 4%. So an investor says, “If I’m going to go out five years, I want 5%. And to buy the 10-year note I have to get 6%.” He demands a higher rate to extend maturity because he’s concerned about the risk to purchasing power, a risk that is assumed to increase with time to maturity. That’s why the yield curve, which in reality is a portion of the capital market line, normally slopes upward with the increase in asset life. Now let’s factor in credit risk. “If the 10-year Treasury pays 6%, I’m not going to buy a 10-year single-A corporate unless I’m promised 7%.” This introduces the concept of credit spreads.

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In order to expand the volume of mortgages they issued, lenders hit on novel ways to increase their appeal to borrowers: interest-only mortgages that minimized monthly payments by eliminating the traditional requirement that the principal balance be paid down; adjustable-rate mortgages that allowed borrowers to benefit from the ultra-low interest rates at the short end of the yield curve; and, most importantly, “sub-prime” mortgages (sometimes called “liar loans”) that didn’t require applicants to document income and employment. With sub-prime mortgages being packaged into securities and sold onward, as opposed to being retained as in the past, lenders’ emphasis shifted from borrowers’ creditworthiness to loan volume.

The Greed Merchants: How the Investment Banks Exploited the System
by Philip Augar
Published 20 Apr 2005

Specialists exploit that advantage too: in late 2001, they were accounting for about 32 per cent of all the shares traded.’17 When market makers pre-position their books, the boundaries between customer facilitation, hedging and proprietary trading are fluid and difficult to define. At what point does loading up ahead of expected demand move from being client facilitation to taking a view on the firm’s own account? When does leveraging up to play the yield curve because you know that’s what your customers will do become a proprietary trade? No outsider, and perhaps no insider either, can really tell, making it very difficult to divide trading profits into customer and proprietary. A survey of a group of banks operating in London in 2003 found that several made no distinction in their management accounts between client and proprietary trading.18 It was either an unimportant distinction or, more likely, it was just too difficult to separate out.

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They were helped by favourable market conditions. As interest rates fell to their lowest levels since the 1960s, corporate treasurers rushed to borrow money and to refinance debt at low interest rates. The investment banks were there in a flash, pitching new bond and bond derivatives issues and selling them to fund managers. The yield curve was steep and the proprietary trading departments were able to borrow short, invest long and pick up a huge interest carry. Fixed income people, out of the limelight during the equities bull market, suddenly found themselves the flavour of the month and gained in power, influence and compensation: ‘Bond traders who not long ago were considered second class citizens by their colleagues in investment banking and equities were now back on top of the social pile.’18 The growth of the hedge fund industry also illustrates the investment banks’ ability to latch on to new trends and work up a business around them.

Market Wizards: Interviews With Top Traders
by Jack D. Schwager
Published 7 Feb 2012

For about a year, Kovner immersed himself in studying markets and the related economic theory. He read everything he could get his hands on. One subject he studied intensively was interest rate theory. “I fell in love with the yield curve.” [The yield curve is the relationship between the yield on government securities and their time to maturity. For example, if each successively longer-term maturity provided a higher yield than a shorter-term maturity—for example, five-year T-notes at a higher yield than one-year T-bills—the yield curve would reflect a continually rising slope on a graph.] Kovner’s study of the interest rate markets coincided with the initial years of trading in interest rate futures.

Market Sense and Nonsense
by Jack D. Schwager
Published 5 Oct 2012

Positions are balanced to maintain neutrality to changes in the broad interest rate level, but may express directional biases in terms of the yield curve—anticipated changes in the yield relationship between short-term, medium-term, and long-term interest rates. As an example of a fixed income arbitrage trade, if five-year rates were viewed as being relatively low versus both shorter- and longer-term rates, the portfolio manager might initiate a three-legged trade of long two-year Treasury notes, short five-year T-notes, and long 10-year T-notes, with the position balanced so that it was neutral to parallel shifts in the yield curve. Fixed income arbitrage normally requires the use of substantial leverage because the relative price aberrations it seeks to exploit tend to be small.

Design Patterns: Elements of Reusable Object-Oriented Software (Joanne Romanovich's Library)
by Erich Gamma , Richard Helm , Ralph Johnson and John Vlissides
Published 18 Jul 1995

In the RTL System for compiler code optimization [JML92], strategies define different register allocation schemes (RegisterAllocator) and instruction set scheduling policies (RISCscheduler, CISCscheduler). This provides flexibility in targeting the optimizer for different machine architectures. The ET++SwapsManager calculation engine framework computes prices for different financial instruments [EG92]. Its key abstractions are Instrument and Yield-Curve. Different instruments are implemented as subclasses of Instrument. Yield-Curve calculates discount factors, which determine the present value of future cash flows. Both of these classes delegate some behavior to Strategy objects. The framework provides a family of ConcreteStrategy classes for generating cash flows, valuing swaps, and calculating discount factors.

Understanding Asset Allocation: An Intuitive Approach to Maximizing Your Portfolio
by Victor A. Canto
Published 2 Jan 2005

At the very top are those that directly arise from government policy, such as taxes, money supply, and regulations. Moving down a notch, there’s the value of the dollar, foreign exchange rates, and trade balances. As noted, there’s inflation and the inflation indicators, such as gold prices and Treasury yield curves that speak to the phenomenon of the way money and goods interact. On the corporate level, there’s inventory, shipments, and retained earnings. After that, there’s employment, productivity, and wage levels. Then there’s the abstract, such as supply and demand curves, or the elasticities inherent in different industries and businesses.

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These conditions created what some called a liquidity trap. As the Japan central bank printed money to stimulate the economy, the commercial banks did not lend the extra money. Instead, the money was held as excess reserves. The abundance of bank reserves reduced short-term interest rates, while stagnation lowered long-term rates. Worse, the yield curve flattened to near zero levels, hence the liquidity trap. The Japanese economy remained stagnant for several years following this turn of events. Eventually, most of the bad loans were worked out and the banks began lending again, once their capital had increased. Rising asset prices started to generate a virtuous cycle, and climbing net worth in the Japanese private sector made the sector’s credit worthy once more.

The Curse of Cash
by Kenneth S Rogoff
Published 29 Aug 2016

Clearly, it would be helpful to have legal and financial experts examine every aspect of negative rates to make a transition as smooth as possible. Finally, when thinking about these hurdles, it is again important to bear in mind that part of the idea of employing negative short-term policy rates is to raise current and future expected inflation, thereby raising long-term rates and tilting the yield curve up. Even if short rates were expected to remain negative for a year or even two, one would not expect long-term nominal rates to be negative if the central bank seems determined to create inflation. Admittedly, it is difficult to know how aggressively the central bank will need to move to dislodge deflationary expectations.

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They also find, however, that most of this came from QE during the height of the crisis and not later rounds. Wu and Xia (2016) suggest that the effects found in studies such as Chung et al. (2012) may overstate the effect of QE, because it is implicitly assumed that there is a large effect across the yield curve. 29. Krishnamurthy and Vissing-Jorgensen (2011, 2013). 30. Professor James Hamilton of the University of San Diego, whose work spans both macroeconomics and econometrics, gives an extremely insightful discussion on the difficulty of discerning any long-term effect of QE in his Econbrowser column “Evaluation of Quantitative Easing,” November 2, 2014, available at http://econbrowser.com/archives/2014/11/evaluation-of-quantitative-easing. 31.

How the City Really Works: The Definitive Guide to Money and Investing in London's Square Mile
by Alexander Davidson
Published 1 Apr 2008

The T-bill is issued in sterling at a discount to face value, and the face value is later repaid, the difference being interest equivalent. The T-bill is traded less than it was because developed countries such as the UK and United States are able to borrow for longer periods, which is cheaper based on the inverted yield curve that reflects a decline in bond yields as the maturity extends into the future. Issuance is consequently more likely in bonds than in T-bills. The euro bill is similar to the T-bill but is issued in euros. The Bank of England issues £900 million a month in three and six-month euro bills, which helps it to fund euro liabilities. ______________________________________ INTEREST RATE PRODUCTS 83  The certificate of deposit (CD) is a money market instrument distinguished by its maturity date and its fixed interest rate.

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On this basis, long-term bonds, particularly if undated, are more exposed to interest rates because redemption is further off. If you think interest rates will go down, you should buy long-term bonds. The yields are generally higher to compensate for a perceived greater risk, despite the inverted yield curve discussed earlier. A bond may often be callable, which means that the issuer, usually a company, may redeem it before maturity. If interest rates should decline, the issuer is likely to call the bond and reissue it at a lower rate of interest. The investor would then be left with money to reinvest in a world where interest rates are low.

High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems
by Irene Aldridge
Published 1 Dec 2009

Treasury. 182 HIGH-FREQUENCY TRADING High-frequency studies of the bond market responses to macroeconomic announcements include those by Ederington and Lee (1993); Fleming and Remolona (1997, 1999); and Balduzzi, Elton and Green (2001). Ederington and Lee (1993) and Fleming and Remolona (1999) show that new information is fully incorporated in bond prices just two minutes following its announcement. Fleming and Remolona (1999) estimate the high-frequency impact of macroeconomic announcements on the entire U.S. Treasury yield curve. Fleming and Remolona (1999) measure the impact of 10 distinct announcement classes: consumer price index (CPI), durable goods orders, gross domestic product (GDP), housing starts, jobless rate, leading indicators, non-farm payrolls, producer price index (PPI), retail sales, and trade balance. Fleming and Remolona (1999) define the macroeconomic surprise to be the actual number released less the Thomson Reuters consensus forecast for the same news release.

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Fleming and Remolona (1999) define the macroeconomic surprise to be the actual number released less the Thomson Reuters consensus forecast for the same news release. All of the 10 macroeconomic news announcements studied by Fleming and Remolona (1999) were released at 8:30 A . M. The authors then measure the significance of the impact of the news releases on the entire yield curve from 8:30 A . M. to 8:35 A . M., and document statistically significant average changes in yields in response to a 1 percent positive surprise change in the macro variable. The results are reproduced in Table 12.4. As Table 12.4 shows, a 1 percent “surprise” increase in the jobless rate led on average to a 0.9 percent drop in the yield of the 3-month bill with 95 percent TABLE 12.4 Effects of Macroeconomic News Announcements Documented by Fleming and Remolona (1999) Announcement 3-Month Bill 2-Year Note 30-Year Bond CPI Durable Goods Orders GDP Housing Starts Jobless Rate Leading Indicators Non-Farm Payrolls PPI Retail Sales Trade Balance 0.593* 1.275† 0.277 0.670† −0.939* 0.411† 3.831† 0.768† 0.582* −0.138 1.472† 2.180† 0.379 1.406† −1.318† 0.525* 6.124† 1.879† 1.428† 0.027 1.296† 1.170† 0.167 0.731† −0.158 0.271* 2.679* 1.738 0.766† −0.062 The table shows the average change in percent in the yields of the 3-month U.S.

The Bond King: How One Man Made a Market, Built an Empire, and Lost It All
by Mary Childs
Published 15 Mar 2022

In the press, Gross was eternally the yogi; his practice was mentioned in nearly every profile since a 2002 story in Fortune, for which he was photographed in Tree Pose, youngish and mustachioed, staring off into the distance. Back on the trade floor, he shook off his annoyance over the cake and settled in for the day. In bonds, trading the “new normal” was humming along. The firm’s muted optimism served to highlight an obvious trade in the Treasury yield curve. Before the crisis, the yield on short-term Treasuries had become basically the same as long-dated ones, which is an aberration: the more time in a promise, the more opportunity for things to go wrong, more risk. This should have meant more yield for long bonds. But then it got worse: The curve—more like a straight, flat line by then—flipped upside down.

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He’d said then that it was a “big mistake,” and later on clients had been richly rewarded when he bounced back. They knew this; they’d remember. In the meantime, he made an aggressive U-turn. In September, the Fed announced it would buy longer-term U.S. Treasuries and sell the same amount of shorter-term securities, a move everyone called “Operation Twist,” for how it twisted the yield curve. Gross flipped from bear to bull, guiding the Total Return supertanker toward a huge bet that the program would work and that long-term rates would fall. It helped, a little. By the end of the year, Total Return had managed to generate 4.2 percent. But it still lagged 87 percent of peers, who returned an average 6.3 percent.

Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals
by David Aronson
Published 1 Nov 2006

This transformation was used in the case study and was performed on four interest rate series: three-month treasury bills, 10-year treasury bonds, Moody’s AAA corporate bonds, and Moody’s BAA corporate bonds. Interest Rate Spreads. An interest-rate spread is the difference between two comparable interest rates. Two types of interest-rate spreads were constructed for the case study; the duration spread and the quality spread. The duration spread, also known as the slope of the yield curve, is the difference between yields on debt instruments having the same credit quality but having different durations (i.e., time to maturity). The duration spread used in the case study was defined as the yield on the 10-year treasury note minus the yield on the three-month treasury bills (10-year yield minus 3-month yield).

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APT says a linear Notes 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 503 model relates a stock’s returns to a number of factors, and this relationship is the result of arbitrageurs hunting for riskless, zero-investment opportunities. APT specifies factors, including the rate of inflation, the spread between low and high quality bonds, the slope of the yield curve, and so on. In other words, the current price change is correlated with the prior change (i.e., a lag interval of 1), then with the change prior to that (lag interval = 2), and so forth. A correlation coefficient is computed for each of these lags. Typically, in a random data series, the correlations drop off very quickly as a function of the lag interval.

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See also Nonrandom price motion theories Random variables, defined, 175 Random walks, see Efficient Markets Hypothesis Rational investor assumption, of Efficient Markets Hypothesis, 343–346 Rationality, limits of, 356–357 Reasoning by representativeness, 87–88 Reinforcement schedule, illusory correlations and, 81–82 Relative frequency distribution, 181–186, 197–202 Relative Strength Index (RSI), 460 Representativeness heuristic, 88–93, 93–101 525 Reversal rules, defined, 17 Risk, defining and quantifying, 340–341 Risk transfer premiums, 378–385 Roberts, Henry, 83 Roll, R., 349 Romano, J.P., 330 Rule data mining case study: critique of, 448–451 indicators used in, 405–417 interest rate spreads, 417 market breadth indicators, 413–416 price and volume functions, 406–413 prices-of-debt instruments from interest rates, 416–417 parameters of, 389–392 possible extensions of, 451–461 raw time series used in, 405–406, 417–418 results of, 441–448 rules tested in: divergence, 430–440 extremes and transitions, 420–430 trend rules, 419–420 in statistical terms, 392–394 time-series operators in, 396–405 channel breakout operator, 397–398 channel-normalization operator, 401–403 indicator scripting language, 403–405 moving-average operator, 398–401 transforming data series into market positions, 394–396 Rules, see Binary rules; Rule data mining case study Russell, Bertrand, 59, 166 Russo, J.E., 467 526 S&P 500, see Rule data mining case study Sagan, Carl, 40–41 Sample mean, 191, 243–245 Sample size neglect, 361–362, 372–374 Sampling, see also Sampling distribution beads in a box example of, 172–186 frequency distribution and, 179–181 relative frequency distribution, 181–186 sample statistics, 175–177, 188–189, 202, 393 sampling variability, 177–179 Sampling distribution, 201–202 classical derivation approach, 209–215 computer-intensive methods of generating, 215, 234–243, 464–465, 471–473 confidence intervals and, 247–248 data mining and, 276–278 defined, 203 mechanics of hypothesis testing and, 227–234 sampling distribution of the mean, 209–213 trading performance and, 206 uncertainty qualified by, 203–206 Samuelson, Paul, 335–336 Sawyer, J., 466 Schoemaker, P.J.H., 467 Scientific method: defined, 103, 332 history of, 103–108 hypothetic-deductive method, 144–147 key aspects of, 147–148 logic and, 111–124 INDEX nature of scientific knowledge and, 108–110 objectification of subjective technical analysis, 148–151 example, 151–161 openness and skepticism in, 143, 225 philosophy of, 124–143 search bias and, 64 Secondhand information bias, 58–61 anchoring and, 360–361 information diffusion and, 365–366 Self-attribution bias, 48–49 DHS hypothesis and, 375–376 Self-interest, secondhand accounts and, 61 Shermer, Michael, 38 Shiller, Robert, 333–334, 365, 366 Shleifer, Andre, 347 Siegel, Jeremy, 84 Signals, 16–18 Simon, Barry, 259 Simon, Herbert, 42 Simplicity, principle of, 107–108, 225–227 Single-rule back-testing, versus data mining, 268–271 Skepticism, 143, 225 Slope of yield curve, 417 Slovic, Paul, 41, 470 Snelson, Jay Stuart, 71 Socioeconomics, 151 Spatial clustering, 100–101 Stale information, 340, 349, 351–354 Standard deviation, 192 Standard error of the mean, 213–215 Statement about reliability of inference, 190 Index Stationary statistical problems, 174, 188 Stationary time series, 19 Statistical analysis: descriptive statistics tools: central tendency measurements, 191 frequency distribution, 190–191 variability (dispersion) measurements, 192–193 inferential statistics: elements of statistical inference problem, 186–190 sampling example, 172–186 three distributions of, 206–207 probability, 193 Law of Large Numbers, 194–195 probability distribution, 200–202 probability distribution of random variables, 197–199 theoretical versus empirical, 196 sampling distribution and, 201–206 classical derivation approach, 209–215 computer-intensive approach, 215 used to counter uncertainty, 165–172 Statistical hypothesis, defined, 220 Statistical inference: data mining and, 272–278 defined, 189 hypothesis tests: computer-intensive methods of sampling distribution generation, 234–243 confidence intervals contrasted to, 250–252 527 defined, 217–218 informal inference contrasted, 218–223 mechanics of, 227–234 rationale of, 223–227 parameter estimation: defined, 217–218 interval estimates, 218, 243, 245–253 point estimates, 218, 243–245 Statistical significance, 23 in case study, 394 statistical significance of observation, 171 statistical significance of test (p-value), 232–234 Stiglitz, J.E., 343, 378 Stochastics, 401–403 Stories, see Secondhand information bias Subjective technical analysis, 5–8, 15–16, 161–163 adoption of scientific method and, 148–151 example, 151–161 chart analysis and, 82–86 confirmation bias and, 62–71 erroneous beliefs and, 33–35 futility of forecasting and, 465–471 heuristic bias and, 86–93 illusion trends and chart patterns, 93–101 human pattern finding and information processing, 39–45 illusory correlations and, 72–82 overconfidence bias and, 45–58 secondhand information bias and, 58–61 as untestable and not legitimate knowledge, 35–38 528 Syllogisms: categorical, 112–115 conditional, 115–116 invalid forms, 118–121 valid forms, 117–118 Taleb, Nassim, 337 Technical analysis (TA), 9–11.

Money and Government: The Past and Future of Economics
by Robert Skidelsky
Published 13 Nov 2018

He now doubted the ability of the monetary authority to get interest rates low enough and prices high enough to offset a marked rise in liquidity preference. However, there was a role for monetary policy in ‘normal’ times, which was to maintain continuously low long-term interest rates. For this reason, Keynes opposed the use of ‘dear money’ to check a boom. The effect of a rise in the interest rate on the yield curve would be very difficult to reverse. A low enough long-term rate of interest cannot be achieved if we allow it to be believed that better terms will be obtainable from time to time by those who keep their resources liquid. The long-term rate of interest must be kept continuously as near as possible to what we believe 124 k e y n e s’s i n t e rv e n t ion to be the long-term optimum.

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In addition, the Bank retained its traditional role as lender of last resort, a role denied to the European Central Bank. 249 M ac roe c onom ic s i n t h e C r a s h a n d A f t e r , 2 0 0 7 – Bank Rate, less familiarly the ‘base rate’, is the interest rate or ‘price’ that the central bank charges for lending money to member banks. The theory is that a change in the base rate pushes the yield curve upwards or downwards. It is immediately transmitted to the interbank lending rate. Banks will then adjust their own lending rates, both short-term and long-term. This will affect how much income is saved and invested. In 1930 the Bank of England had denied that it had such power over commercial lending rates, and uncertainty remained about the impact of the short-rate on the long-rate.9 The supposed transmission mechanism from the base rate to the level of spending and prices in the economy can be summarized by Figure 38.

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However, central banks played the strategic game. By announcing changes in the composition of purchases, like the Fed’s ‘Operation Twist’ and the Bank of England’s decision to ‘increase the amount of shorter dated securities’, they were able to surprise investors and continue, at least in their own view, to make impacts on yield curves.61 Through the four channels above, the injection of narrow money (M1) was supposed to influence the movement of broad money and, through broad money, growth in nominal GDP. Broad Money Broad money is largely synonymous with bank lending. As we have seen, bank reserves went up while bank lending fell.

Dark Towers: Deutsche Bank, Donald Trump, and an Epic Trail of Destruction
by David Enrich
Published 18 Feb 2020

Bill and Edson expanded the menu. Bill started dreaming up new types of a popular derivative known as swaps that were designed to help institutions protect themselves from changes in things like interest rates. He combined different types of swaps into mutant instruments with names like callable interest rate swaps and yield curve swaps and swaptions. This was good news for clients and great news for Merrill. Each time Merrill sold a swap to a client, it pocketed a fee. What’s more, Broeksmit devised clever new ways for Merrill to protect itself by using derivatives when it bought assets from customers. Because the derivatives were reducing the risks Merrill faced on various transactions, the firm now had a greater capacity to do more of those transactions—which meant more revenue for Merrill.

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See Trump, Donald, presidential campaign of 2016 United States elections of 2018, 353 United States Football League (USFL), 270 United States housing bubble, 134, 137–40, 157–58 University Club, 242, 284–86 University of Massachusetts (UMass), 46, 47, 57 University of Pennsylvania, 126 Ursuline School, 166, 168–69 US Open, 113 Vaccaro, Jon, 78 Vekselberg, Viktor, 338 Venmo, 351 Villard, Henry, 13–15, 16–18, 310 Northern Pacific Railway loan, 13, 14–15, 17–18 Virgin Atlantic, 229 Virgin Gorda, 207–208 Volcker Rule, 343 Vonnegut, Kurt, 68 Vrablic, Rosemary background of, 166–67 at Bank of America, 168–69 at Citicorp, 167–68 Trump presidency and, 320 Vrablic, Rosemary, at Deutsche Bank Kushners and, 169, 172, 275–77, 306–307, 312 Trump Jr. loan, 275 Vrablic, Rosemary, at Deutsche Bank, and Trump loans, 6–7, 172–74, 270–71, 306–308, 354 Doral property, 175–77, 270, 278 McFadden review, 310–11 Washington, D.C. property, 273–75 VTB Bank, 109–10, 197, 317–18, 327, 328–29 Walker, Dick, 93, 93n, 264, 344–45 Wall Street Journal, 41, 49, 64, 255, 323, 329 DBTCA and Federal Reserve story, 241–42, 249–50 Val’s contact with author, 247–48, 252, 257, 279 Washington Monument, 271 Waters, Maxine, 353 Waugh, Seth, 113–14, 116, 119, 187 Wauthier, Pierre, 203–204, 227, 244 Weber, Axel, 180 Weinstein, Boaz, 128, 137 West, Kanye, 178 Wilcox, Fiona, 287–89 Wilhelm, German Emperor, 15, 178 Wimbledon, 220 Wisley Golf Club, 60, 61, 83 Wiswell, Tim, 198–99, 202, 232–33, 236, 329, 358 Wolfe, Tom, 172 World Economic Forum (Davos), 209–10, 261 World War I reparations, 21 World War II, 19–21. See also Nazi Party Xanax, 226, 285, 287 Yale Club (New York City), 334–35 Yallop, Mark, 81 Yield curve swaps, 34 Young, Neil, 245 Young, Pegi, 244–45, 248, 279, 353, 354–55 Zurich Insurance Group, 203–204, 204n, 210, 227, 338 Zyklon B, 20 About the Author DAVID ENRICH is the finance editor at the New York Times. He previously was an editor and reporter at the Wall Street Journal in New York and London.

Anatomy of the Bear: Lessons From Wall Street's Four Great Bottoms
by Russell Napier
Published 18 Jan 2016

Although only the commitment to intervene in the Treasury bill market was explicit, in practice the actions of the Federal Reserve created a capped federal debt yield curve. The rationale behind these actions was that it would encourage investors, who would not be speculating on higher future interest rates, to buy War Bonds and thus reduce the cost of financing the war. The de facto maximum permitted yield on the longest-term government bonds was 2.5%. The capped rates effectively enshrined the positively sloping yield curve, which the market was dictating prior to April 1942, for the duration of the war and beyond. Not surprisingly the investing public and the commercial banks flocked to the long end of the market, where the risk of capital loss had been eliminated for the duration of the war, and ownership of the T-bill market passed increasingly to the Federal Reserve.

DeFi and the Future of Finance
by Campbell R. Harvey , Ashwin Ramachandran , Joey Santoro , Vitalik Buterin and Fred Ehrsam
Published 23 Aug 2021

For example, the portfolio may include three-, six-, and nine-month plus one-year maturity yTokens; once the three-month tokens mature, the smart contract can reinvest the balance into one-year maturity yTokens. Token holders in this fund would essentially be experiencing a floating rate yield on the underlying asset with rate updates every three months. The yTokens also allow for the construction of yield curves by analyzing the implied yields of short and longer term contracts. This allows observers to quantify investor sentiment among the various supported target assets. The Yield Protocol can even be directly used to speculate on interest rates. Several DAI derivative assets – Compound cDAI, Aave aDAI, and Chai25 – represent a variable interest rate.

House of Cards: A Tale of Hubris and Wretched Excess on Wall Street
by William D. Cohan
Published 15 Nov 2009

“This man would be gone for two weeks at a time in every single city and every single bank to get control of their portfolios and move the bonds around,” Sandy Lewis said. “He was known throughout the United States. If he could do this, he could support the rail bonds. This was all about ‘I'll help you. I'll rearrange your portfolio.' He could run a yield curve in his sleep. All so that he could earn enough revenue to support this huge bet that he had made.” Bear Stearns would have been bankrupt if Lewis's bet had failed. “Gone,” Sandy said. “Out of business. No question about it. They weren't an underwriting firm. They weren't a mergers firm. They didn't have any other business.”

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Particularly important was the exponential growth of the fixed-income business, which was without question Spector's fiefdom. Fixed-income revenue in 2004 was $3.1 billion—nearly 45 percent of the firm's overall revenue of $6.8 billion—and had increased some 63 percent, from $1.9 billion in revenues, since 2002. “These businesses benefited from the low level of interest rates, a steep yield curve and narrowing of corporate credit spreads,” the firm reported in its SEC filings. “Mortgage-backed securities revenues increased significantly as residential mortgage refinancing activity reached record levels during the year, driving record new issue activity, and demand for high-quality fixed income investments continued.”

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While Bear Stearns's fixed-income revenue for the year ended November 30, 2005, declined 12 percent, to $2.3 billion, from $2.6 billion in 2004, the business was still humming along quite profitably. The firm's SEC filing stated that “mortgage-backed securities origination revenues declined from the robust levels of fiscal 2004 due to a flattening yield curve, shifting market conditions and changes in product mix. A decline in agency CMO volumes was offset by an increase in non-agency mortgage originations.” Regardless of the stumble in fixed income, the firm posted a record profit of $1.5 billion in fiscal 2005, up 9 percent from the $1.3 billion of net income the year before.

Red-Blooded Risk: The Secret History of Wall Street
by Aaron Brown and Eric Kim
Published 10 Oct 2011

The reason people solve for the yield to maturity of bonds is that two bonds with similar terms and credit qualities will have similar yields, but not necessarily similar prices. Thus we can take the price of a bond we do know, convert it to a yield, and apply the yield to get the price of a similar bond whose price we do not know. We can graph bond yield versus time to maturity to get a reasonably smooth yield curve. This is both a useful economic indicator and a way to interpolate yields of other bonds. We can also graph bond yield versus credit quality with similar results. And we can take the derivative of bond price with respect to yield to get a first order idea of the volatility of a bond. The Black-Scholes-Merton model works the same way.

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So we can use implied volatilities of options we know the prices of to estimate the implied volatilities, and hence the prices, of options whose prices we do not know. We can graph option implied volatility versus time or moneyness (the ratio of the strike price of an option to the underlying price) and get the same kind of insights we get from yield curves and credit curves. We can take the derivative of option price with respect to implied volatility, known as vega, which some forgotten trader thought was a Greek letter. All of this is pure mathematics; it does not require any economic assumptions. Anyway, the derivative concept in the old sense led to a fresh conflation of frequency and degree of belief.

Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor
by John Kay
Published 24 May 2004

Places The American Business Model The Future of Economics The Future of Capitalism 277 289 302 311 323 340 Appendix: Nobel Prizes in Economics Glossary Notes Bibliography Index 356 361 365 390 411 17 18 19 20 21 22 23 {part V} 24 25 26 27 28 29 {List of Figures, Tables, and Boxes} Figures 4.1 4.2 5.1 5.2 14.1 The Distribution of World Income The Dimensions of Economic Lives Rich States in Europe Rich Stares in Asia U.S. Treasury Yield Curve 34 38 65 66 167 Tables Resources per Head, U.S. The World's Richest Countries Intermediate Economies What America Spends, 2001 What America Earns, 2001 Redistribution of Income Among Households, America, 2001 4.6 What America Produces, 2001 4.7 Living Standards and Productivity, 2001 4.8 Why Material Living Standards Differ, 2001 5.1 Rich and Poor States, 1820 16.1 Lighting Efficiency 16.2 Refrigerator Features 3.1 4.1 4.2 4.3 4.4 4.5 27 32 33 39 39 40 41 46 48 68 185 186 {viii} Figures, Tables and Boxes Boxes 4.1 4.2 4.3 Inequality in World Income Distribution What GDP Is, and Isn't Work and Living Standards, United States and France, 2001 12.1 Economic Rent 18.1 Happiness and Welfare 36 42 50 145 211 {Acknowledgments} • • • • • • • • • • • • • • The background research took us from the Cro-Magnon cave paintings at Lascaux to the dot.com bubble of 1999-2000, from Auckland to Zanzibar.

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Banks match borrowers and lenders and allow lenders to get their money back before the borrowers repay. Bonds are another means of handling the same problem. The bond market is a secondary market, in which the right to receive repayment of a loan can be sold to someone else. Figure 14.1 U.S. Treasury Yield Curve (September 30, 2003) 0 9 10 15 Length ofbond (years) SOURCE: U.S. Treasury (Web site) 20 25 { 168} John Kay The price of a bond in this secondary market will not necessarily be the same as the original amount of the loan. The credit risk may have changed. You can today buy the debt of many telecom companies for less than half its repayment value: these companies borrowed extravagantly and many people are now skeptical of their ability to repay.

The End of Alchemy: Money, Banking and the Future of the Global Economy
by Mervyn King
Published 3 Mar 2016

But over longer horizons still, such as a decade or more, interest rates are determined by the balance between spending and saving in the world as a whole, and central banks react to these developments when setting short-term official interest rates. Governments borrow by selling securities or bonds to the market with different periods of maturity, ranging from one month to thirty years or sometimes more. The interest rate at different maturities for such borrowing is known as the yield curve. Another important distinction is between ‘money’ and ‘real’ interest rates. Money interest rates are the usual quoted rate – if you lend $100 and after one year receive $105, the money interest rate is 5 per cent. If over the course of that year the price of the things that you like to buy is expected to rise by 5 per cent, then the ‘real’ rate of interest you earn is the money rate less the anticipated rate of inflation (in this example the real rate is zero).

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In late 2015, bond yields were around 2 per cent in the United States and most other advanced economies, apart from Germany and Japan, where rates were around 1 per cent and 0.5 per cent respectively. Only in Switzerland, of the major economies, were ten-year bond yields slightly negative. When the yield curve is completely flat, central banks may still create money by purchasing assets other than government bonds – either private sector assets, such as corporate bonds, or overseas currencies (the latter was the main strategy pursued by the Swiss National Bank in a vain attempt to prevent a sharp appreciation of the Swiss franc against the euro).

The Tyranny of Nostalgia: Half a Century of British Economic Decline
by Russell Jones
Published 15 Jan 2023

Annual RPIX inflation averaged 2.4% between 1997 and 2001, so the Bank can be said to have met its inflation target, but there was a tendency for it to undershoot the mark from the spring of 1999. Eddie George never had to write an explanatory letter about a significant inflation ‘miss’ to the chancellor. Indeed, it took ten years of Bank independence until such a missive proved necessary. Most pertinently, continually benign inflation encouraged lower nominal interest rates across the yield curve, as both inflation expectations and the inflation risk premium declined. At the same time, sterling moved sharply higher in trade-weighted terms and remained elevated for the next decade, and the spread of UK long-term bond yields over their German equivalents narrowed sharply. There was a clear credibility windfall from UK central bank independence.

…

Forward guidance was grounded in finance theory, and the notion that longer-term interest rates are determined by the expected path of short-rates plus a term premium influenced by a range of considerations, including uncertainty, risk aversion, market liquidity and preferred investor habitats.11 The idea behind such ‘state-contingent’ guidance was to provide greater clarity about the Bank’s reaction function, to reduce ambiguity about the monetary policy outlook, and to thereby encourage the entire gilt market yield curve – and related borrowing costs – to shift lower. The decision to go down this road certainly made Carney a hostage to fortune, and it was greeted with a degree of scepticism both within the Bank and beyond. Some argued that to maximize the effect, the Bank should have backed up its words with more asset purchases, i.e. it should have put its money where its mouth was.

Principles of Corporate Finance
by Richard A. Brealey , Stewart C. Myers and Franklin Allen
Published 15 Feb 2014

The term is commonly used as synonymous with net working capital. Workout Informal arrangement between a borrower and creditors. Writer Option seller. X xd Ex dividend. xr Ex rights. Y Yankee bond A dollar bond issued in the United States by a non-U.S. borrower (cf. bulldog bond, Samurai bond). Yield curve Term structure of interest rates. Yield curve note Reverse FRN. Yield to call Yield on a bond assuming that it will be called. Yield to maturity Internal rate of return on a bond. Z Zero-coupon bond Discount bond making no coupon payments. Z-score Measure of the likelihood of bankruptcy. Index Note: Page numbers followed by n indicate material in source notes and footnotes.

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For example, you can see that the yield on the four-year bond (5.81%) lies between the one- and four-year spot rates (3% and 6%). Financial managers who want a quick, summary measure of interest rates bypass spot interest rates and look in the financial press at yields to maturity. They may refer to the yield curve, which plots yields to maturity, instead of referring to the term structure, which plots spot rates. They may use the yield to maturity on one bond to value another bond with roughly the same coupon and maturity. They may speak with a broad brush and say, “Ampersand Bank will charge us 6% on a three-year loan,” referring to a 6% yield to maturity.

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Return on capital (ROC) After-tax operating income as a percentage of long-term capital. Return on equity (ROE) Usually, equity earnings as a proportion of the book value of equity. Return on investment (ROI) Generally, book income as a proportion of net book value. Revenue bond Municipal bond that is serviced out of the revenues from a particular project. Reverse FRN (yield curve note) Floating-rate note whose payments rise as the general level of interest rates falls and vice versa. Reverse split Action by the company to reduce the number of outstanding shares by replacing two or more of its shares with a single, more valuable share. Revolving credit Legally assured line of credit with a bank.

Unelected Power: The Quest for Legitimacy in Central Banking and the Regulatory State
by Paul Tucker
Published 21 Apr 2018

If inflation in the short term is powerfully influenced by expectations of inflation over the medium term, then households and firms need information to help them form those expectations. If the traction of policy comes through expectations of the path of the central bank’s month-by-month decisions, as reflected in the bond-market yield curve, then the markets need information on the central bank’s approach to policy (in the jargon, its reaction function). If, then, the central bank is to be incentivized to stick to its mandate, its target and actions and the results all have to be visible. That way, it is hoist on its own reputation for competence and reliability.

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I have no sense that Ben Friedman opposes CBI. 10 Similar points, without the constitutionalist framing, are made in Bernanke, “Monetary Policy.” 11 For similar sentiments, see Granville, Remembering Inflation. 12 Stein and Hanson, “Monetary Policy.” First published as a Federal Reserve research paper in 2012, this revealed that persistently easy conventional monetary policy can lead to a reduction in term premia, the compensation investors demand for taking longer-term exposures. The result was replicated for the sterling yield curve, as reported in Tucker, “National Balance Sheets.” Although not proven, this phenomenon might be driven by a search for yield by asset managers and intermediaries that are subject to nominal yield targets and/or relative performance objectives. 13 Respectively, Turner, Between Debt, and King, End of Alchemy. 14 Tucker, Financial Stability Regimes. 15 Rajan, “Step in the Dark,” p. 12.

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Conflict Resolution 1, no. 1 (1957): 9–18. ________. The Professional Soldier: A Social and Political Portrait. Glencoe, IL: Free Press, 1960. Joyce, Michael A. S., Peter Lilholdt, and Steffan Sorensen. “Extracting Inflation Expectations and Inflation Risk Premia from the Term Structure: A Joint Model of the UK Nominal and Real Yield Curves.” Journal of Banking & Finance 34, no. 2 (2010): 281–94. Judge, Igor. The Safest Shield: Lectures, Speeches and Essays. Oxford: Hart Publishing, 2015. ________. “Ceding Power to the Executive: The Resurrection of Henry VIII.” Paper delivered at King’s College London, April 12, 2016. Judiciary of England and Wales.

The Scandal of Money
by George Gilder
Published 23 Feb 2016

But these quantitative changes also lavishly benefit any early borrowers or lenders of the government money who can act before related price changes propagate through the economy. Central banks currently change the money supply through a Rube Goldberg contrivance of open-market operations buying and selling Treasury notes, “quantitative easing” through purchase of private bonds and other assets, adaptive “twists” of yield curves and maturities, reserve requirements regulating bank leverage, and interest-rate manipulations that change the cost of money. These measures deny most of the users of the money any pro rata increase in their quantities during inflations and inflict borrowers with the full brunt of contractionary policy (they have to pay back their loans with more valuable units than they received).

In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest
by Andrew W. Lo and Stephen R. Foerster
Published 16 Aug 2021

Rational expectations are a consistency condition that expectations in the model should be expectations of the model, while market efficiency is closer to a descriptive statement about the world. Shiller’s completed dissertation in 1972 was titled “Rational Expectations and the Structure of Interest Rates.”13 Samuelson was a member of his dissertation committee, along with Robert Merton. Shiller’s 182-page dissertation developed a model of the term structure of interest rates, or the yield curve, a series of rates at which businesses or the government can borrow money, depending on the maturity rate of the debt that was issued. His model was based on expectations of future interest rates. He found that the model, tested using corporate bond yields, worked quite well. By the time his dissertation was complete, Shiller had three publications in print or forthcoming, including one study for the Federal Reserve, one at the prestigious economics journal Econometrica, and a joint publication with Modigliani.

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“The dentist was drilling away, and by the time it was finished I almost said, ‘Can you take a few more minutes?’ And I borrowed a pencil from him and some paper. And I wrote down these thoughts, and that turned out to be the basis for what I thought was, at that time, a pretty important chapter [of our book].” 30. Leibowitz noted that newer readers often mistakenly refer to the book as “Inside the Yield Curve” given their unfamiliarity with the Yield Book. 31. See Homer and Leibowitz (2013). 32. CFA Institute (2015). 33. See Fabozzi (1992), “Biographical Sketch” section. 34. See Leibowitz (1986). 35. See Leibowitz (1987). 36. CFA Institute (2015). 37. See Langetieg, Leibowitz, and Kogelman (1990). 38.

The Gone Fishin' Portfolio: Get Wise, Get Wealthy...and Get on With Your Life
by Alexander Green
Published 15 Sep 2008

REITs avoid corporate income taxes by distributing more than 90% of their net cash flow to shareholders each year. 8. Short-term corporate bonds. A corporate bond is a company’s IOU, a debt security that represents a promise to repay a sum of money at a fixed interest rate over a certain period of time. Short-term bonds generally yield somewhat less than long-term bonds. (Although when the yield curve is inverted, they may yield more.) Their shorter maturities make them less volatile than long-term bonds. 9. High-yield bonds. High yield or “junk bonds” are corporate bonds that do not qualify for investment-grade ratings. These bonds pay higher rates of interest because the issuers are less creditworthy.

Crashed: How a Decade of Financial Crises Changed the World
by Adam Tooze
Published 31 Jul 2018

The mortgage boom continued undeterred, as did global demand for American safe assets and the expansion of the shadow banking sector. By the spring of 2006, to the alarm of many commentators, the result was that the yield curve was inverted. Long-term rates were below the short-term interest rates set by the Fed. This was usually a signal for trouble. It meant that the normal bank-funding model of borrowing short to lend long no longer made any sense. In due course, the inversion of the yield curve might by itself have produced a recession. But it wasn’t Greenspan or Bernanke who killed the mortgage boom. It killed itself. By 2005 at the latest it was clear that low-quality mortgage debt was a ticking bomb.

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See International Monetary Fund (IMF) India, 477, 483 Indonesia, 477, 483 Asian financial crisis and, 7, 32, 255–56, 261 capital controls adopted by, 475 financial crisis of 2008 and, 258–59 stimulus program, 258–59 Industrial and Commercial Bank of China, 249 inequality, 455–63 inflation, 11, 44–45 ING, 124 interest rates ECB rate increase 2011, 378–79 Fed’s rate hikes, 2015–2018, 590 Greenspan cuts, after dot-com bust and 9/11, 37–38, 55–56, 69–70 inverted yield curve, 2006, 70 taper tantrum of 2013, 472–82 Volcker’s raising of, 43–44 intergovernmentalism, 113, 114–15 International Monetary Fund (IMF), 17–18, 89, 127 acceptance of exchange controls, 475 Asian financial crisis, 261 banking crisis, 206, 401-2 Eastern European crisis, 127, 230–32, 235, 237, 491–93 eurozone crisis, 2010–12, Greece and, 323, 325, 332–34, 336, 340, 343, 344–45, 357, 377, 382–85, 388–89, 405, 413, 422, 424 eurozone crisis, 2015, Greece and 516–517, 520, 523, 527, 528–30 eurozone crisis Ireland and, 360, 364–65, 368, 398 eurozone crisis Italy and, 410–11 fiscal multiplier underestimated by, 423, 429–30 global imbalances, 40, 370 G20 agreement for expanded funding of, 270, 272 quota reallocation, 270, 272, 469, 479, 488 Ukraine and 2013–15, 493–94, 495–98, 500–1, 507–8 warns against Brexit, 550 investment banks, 51–54 Brexit and, 550–51 compensation at, 65 crises faced by, in 1990s and early 2000s, 53–54 funding of, 52–53 growth from 1970s, 51–53 products engineered by, 52 profits made by, 64–65 See also specific investment banks Iraq War, 3, 28, 115–16 Ireland, 83–84, 167, 337, 338 bank bailouts in, 185–86, 193 debt crisis in, 322, 323, 359–66 ECB forces austerity plan on, 362–65 household wealth lost in, 156 IMF and, 360, 364–65, 368, 398 real estate boom in, 105, 106, 107, 109 Irish Times, 363 Irwin, Neil, 215–17, 350 Italy, 322, 385 austerity program adopted in, 387 Cannes G20 and, 410–12 debt of, 386–87, 389 ECB’s bond buying program, 2011, 398–99 euro entry of, 94 eurozone crisis resolution, 2012 and, 431–37 Japan, 30, 158–59 Jay Z, 40 Johnson, Boris, 548, 552 J.P.

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life
by Emanuel Derman
Published 13 Oct 2011

There are sweetness and tartness, spiciness and blandness, smoothness and lumpiness, all of them different types of gustatory pleasure. And I have ignored other kinds of mentionable and unmentionable bodily pleasures, which have their pleasure premiums too. Similarly, there is more than one kind of risk and more than one kind of risk premium: stock risk and bond risk and currency risk and commodity risk and slope-of-the-yield-curve risk; and within the universe of stocks there is sector risk—health risk, technology risk, consumer durables risk, et cetera. In physics the values of the fundamental constants (the gravitational constant G, the electric charge e, Planck’s constant h, the speed of light c) are apparently timeless and universal.

Millionaire Teacher: The Nine Rules of Wealth You Should Have Learned in School
by Andrew Hallam
Published 1 Nov 2011

They read something like this: Stocks fell this month because retail sales were off 2.5 percent, creating a surplus of gold buyers over denim, which will likely raise Chinese futures on the backs of the growing federal deficit, which caused two Wall Street Bankers to streak through Central Park because of the narrowing bond yield curve. Saying stock markets rose this year because more polar bears were able to find suitable mates before November has as much merit as the confusing economic drivel that financial planners write and distribute, assuming that nobody will read it anyway. If you ask her, she will tell you that actively managed mutual funds are the way to go—but curiously doesn’t mention she has killer mortgage payments on her $17 million, Hawaiian beachside summer home and you need to help her pay it.

Just Keep Buying: Proven Ways to Save Money and Build Your Wealth
by Nick Maggiulli
Published 15 May 2022

* * * 63 Colberg, Fran, “The Making of a Champion,” Black Belt (April 1975). 64 Seigel, Jeremy J., Stocks for the Long Run (New York, NY: McGraw-Hill, 2020). 65 Dimson, Elroy, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2009). 66 Biggs, Barton, Wealth, War and Wisdom (Oxford: John Wiley & Sons, 2009). 67 U.S. Department of the Treasury, Daily Treasury Yield Curve Rates (February 12, 2021). 68 Asness, Clifford S., “My Top 10 Peeves,” Financial Analysts Journal 70:1 (2014), 22–30. 69 Jay Girotto, interview with Ted Seides, Capital Allocators, podcast audio (October 13, 2019). 70 Beshore, Brent (@brentbeshore). 12 Dec 2018, 3:52 PM.

Addiction by Design: Machine Gambling in Las Vegas
by Natasha Dow Schüll
Published 15 Jan 2012

Mariposa’s “player contact” component has incorporated a similar feature that color codes player’s floor icons to indicate whether they are expected to increase in value (green), decline in value (red), or remain the same (yellow). 48. Wilson 2007. Despite the argument for the emotion-removing capacities of visual analytic tools, it should be noted that such tools can also be a source of anxiety and other forms of affect on the part of analysts, as the anthropologist Zaloom (2009) has pointed out in the case of the “yield curve.” For more work on how financial professionals have used visual tools to model the market and thus better intervene in it, see Knorr Cetina and Breugger 2002; Mackenzie 2006; Preda 2006; Zaloom 2006. Tools for visualizing the market are part of a more general contemporary trend in which “narrative, models, and scenarios [are devised to] capture in useful ways the uncertainties, contingencies, and calculations of risk that complex technologies and interactions inherently generate” (Fischer 2003, 2). 49.

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Tyler. 2006. Northern Territory Gambling Prevalence Survey 2005. School for Social and Policy Research, Charles Darwin University. Zaloom, Caitlin. 2006. Out of the Pits: Traders and Technology from Chicago to London. Chicago: University of Chicago Press. ———. 2009. “How to Read the Future: The Yield Curve, Affect, and Financial Prediction.” Public Culture 21: 2. ———. 2010. “The Derivative World.” The Hedgehog Review (Summer). Zangeneh, Masood, and T. Hason. 2006. “Suicide and Gambling.” International Journal of Mental Health and Addiction 4 (3): 191–93. Zangeneh, Masood, and E. Haydon. 2004. “Psycho-Structural Cybernetic Model, Feedback and Problem Gambling: A New Theoretical Approach.”

The Alchemists: Three Central Bankers and a World on Fire
by Neil Irwin
Published 4 Apr 2013

The success of the approach suggested an interesting possibility: If the Fed were to shift its portfolio into longer-term bonds and away from shorter-term debt, it might be able to lower long-term interest rates across the economy, encouraging business investment and mortgage borrowing. The action would have the effect of simultaneously raising short-term interest rates, but only negligibly, because the Fed had already committed to keeping them near zero. Theoretically, borrowing would be inexpensive in both the short and the long term. It’s called twisting the yield curve, and a variation had been tried at the central bank in 1961, when it was called Operation Twist, a not terribly sly reference to the dance craze of the time. The Bernanke Fed, with its culture of seriousness, called the strategy a Maturity Extension Program. But to the media, Operation Twist, with its attendant possibility of Chubby Checker–based headline puns, was an irresistible way to describe the policy.

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See also European Central Bank (ECB) remedies background information, 12, 112–15 beginning crisis, view of, 7, 128, 135, 137 BNP Paribas crisis as first, 1–3 on coordination of remedies, 159–61 economic orientation of, 115, 287 Eurogroup meeting protest, 306–7 Franco-German Declaration criticism by, 290–92 -Geithner relationship, 219, 317 Governing Council meetings, role at, 136–37 on Greek financial crisis, 204, 206–8, 211–12, 218–19, 222–23, 287 on Italy/Spain crises, 317–23 at Jackson Hole conference, 97 on Lehman failure, 143 at Maastricht negotiations, 77, 114 nomination as ECB president, 81–82 personal traits, 114–15 poor decisions of, 135–37, 212–13, 303–5 as “president” of Europe, 322 retirement gala, 324–26 -Sarkozy dispute, 324 successor to. See Draghi, Mario on Term Auction Facility (TAF), 131–32 True Finns, 297 Trust Company of America, 41 Tucker, Paul, 241, 388 Twisting the yield curve, 331–32 Tyrie, Andrew, 250 Ueda, Kazuo, 89, 91–92 Ullstein, Leopold, 52 Unemployment Great Britain (2009–2011), 236, 248, 251, 334 Great Depression era, 57, 58, 60 during Greenspan tenure, 94, 99 during inflation of 1970s, 65 Ireland (2010), 284 level in 2009, 188 U.S. weak jobs growth, 259, 268–69, 328, 378 United Copper, 40–41 United States annual growth needs, 267 central bank.

Rentier Capitalism: Who Owns the Economy, and Who Pays for It?
by Brett Christophers
Published 17 Nov 2020

But capital is not just capital; it comes in different forms, and banks tend to borrow and lend capital of different types. In particular, they typically borrow short-term (capital with a short ‘tenor’) and lend long-term – this is their so-called ‘maturity transformation’ function – and in ‘normal’ times interest rates are lower for short-term than for long-term borrowing. The ‘yield curve’ slopes upwards. Indeed, what ultimately matters to banks’ bottom line, at least where they fulfil the classic rentier role described by Keynes, is not the rate they are able to charge borrowers, but the differential, or ‘spread’, between their own borrowing and lending rates. Healthy lending rates of 5, 10, 15 or even 20 per cent are for nothing if banks must pay the same or more to borrow.

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Thus, ‘it is precisely the liquidity-premium on cash ruling in the market which determines the rate of interest at which finance is obtainable’ (248). So, supply and demand – but, to be sure, not supply and demand in any simplistic sense. 50. Keynes, General Theory, p. 375. 51. P. Alessandri and B. D. Nelson, ‘Simple Banking: Profitability and the Yield Curve’, Journal of Money, Credit and Banking 47: 1 (2015), pp. 143–75, at p. 146. Interest-rate volatility also positively impacts bank profitability: A. Saunders and L. Schumacher, ‘The determinants of bank interest rate margins: an international study’, Journal of International Money and Finance 19 (2000), pp. 813–32. 52.

Addiction by Design: Machine Gambling in Las Vegas
by Natasha Dow Schüll
Published 19 Aug 2012

Mariposa’s “player contact” component has incorporated a similar feature that color codes player’s floor icons to indicate whether they are expected to increase in value (green), decline in value (red), or remain the same (yellow). 48. Wilson 2007. Despite the argument for the emotion-removing capacities of visual analytic tools, it should be noted that such tools can also be a source of anxiety and other forms of affect on the part of analysts, as the anthropologist Zaloom (2009) has pointed out in the case of the “yield curve.” For more work on how financial professionals have used visual tools to model the market and thus better intervene in it, see Knorr Cetina and Breugger 2002; Mackenzie 2006; Preda 2006; Zaloom 2006. Tools for visualizing the market are part of a more general contemporary trend in which “narrative, models, and scenarios [are devised to] capture in useful ways the uncertainties, contingencies, and calculations of risk that complex technologies and interactions inherently generate” (Fischer 2003, 2). 49.

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Tyler. 2006. Northern Territory Gambling Prevalence Survey 2005. School for Social and Policy Research, Charles Darwin University. Zaloom, Caitlin. 2006. Out of the Pits: Traders and Technology from Chicago to London. Chicago: University of Chicago Press. ———. 2009. “How to Read the Future: The Yield Curve, Affect, and Financial Prediction.” Public Culture 21: 2. ———. 2010. “The Derivative World.” The Hedgehog Review (Summer). Zangeneh, Masood, and T. Hason. 2006. “Suicide and Gambling.” International Journal of Mental Health and Addiction 4 (3): 191–93. Zangeneh, Masood, and E. Haydon. 2004. “Psycho-Structural Cybernetic Model, Feedback and Problem Gambling: A New Theoretical Approach.”

Electronic and Algorithmic Trading Technology: The Complete Guide
by Kendall Kim
Published 31 May 2007

The pilot program was implemented to assess the impact on trading profiles and behavior; to identify the demographics of participants pre- and post-pilot implementation; to determine whether the change in algorithm impacts the number of participants in a contract; and to assess the growth rate of the five-year Treasury Note contracts benchmarked against relevant instruments along the yield curve. The program was designed to monitor a straight First In First Out (FIFO) algorithm, which matches trades on a strict time and price priority, versus a pro rata algorithm, which matches trades based on a distributed proportionate approach. The exchange will continue to change in contract volume, participation levels, and order management behavior.7 6.8 Conclusion Algorithms are designed to balance a juggling act.

The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton
by Colin Read
Published 16 Jul 2012

Black saw the description and prediction of interest rates to be a multi-faceted and challenging problem. While he had demonstrated that an options price depends on the underlying stock price mean and volatility, and the risk-free interest rate, the overall market for interest rates is much more multi-dimensional. The interest rate yield curve, which graphs rates against maturities, depends on many markets and instruments, each of which is subject to stochastic processes. His interest and collaboration with Emanuel Derman and Bill Toy resulted in a model of interest rates that was first used profitably by Goldman Sachs through the 1980s, but eventually entered the public domain when they published their work in the Financial Analysts Journal in 1990.2 Their model provided reasonable estimates for both the prices and volatilities of treasury bonds, and is still used today.

Notes From an Apocalypse: A Personal Journey to the End of the World and Back
by Mark O'Connell
Published 13 Apr 2020

The UN had announced sanctions against North Korea, and North Korea had vowed to take physical action against such sanctions, and America, in the person of a president who was at that point vacationing at one of his many eponymous luxury golf resorts, advised that if they so much as lifted a finger they would be met with “fire and fury like the world has never seen.” According to The Wall Street Journal, analysts were trying to guess what would happen to the markets in the event of all-out nuclear war between the United States and North Korea. (The answer seemed to be that you would likely see some flattening of yield curves due to lower risk appetites, but that from a financial perspective a nuclear apocalypse wouldn’t exactly be the end of the world.) The apocalypse was trending. The memes were dank with foreboding, and the presiding mood was one of half-ironic Cold War nostalgia mixed with sincere eschatological unease.

Strong Towns: A Bottom-Up Revolution to Rebuild American Prosperity
by Charles L. Marohn, Jr.
Published 24 Sep 2019

What is lost in all the centralization and efficiency is local nuance, or what most people would consider real meaning. The Difference Between Growth and Wealth Going into the summer of 2005, there was general concern among economists and money managers that a recession was imminent. The yield curve was flattening as investors bought longer-term notes to lock in higher rates ahead of possible interest rate declines.9 The Dow Jones average was down 7% from the start of the year.10 The Federal Reserve was raising rates to get some wiggle room should the anticipated rate-cutting stimulus be needed.11 Indicators were moving in the wrong direction, and then at the end of August came Hurricane Katrina, which destroyed large portions of New Orleans and the Mississippi Gulf Coast.

Leave the World Behind
by Rumaan Alam
Published 15 Dec 2020

H. had driven fast, but there were some things that couldn’t be outrun. His reticence was because of a very particular burden: he knew that something was wrong, truly wrong. “I can’t exactly throw them out.” G. H. didn’t want to say that he had known something was coming. His business was clairvoyance. You looked at the yield curve arching and slumping like an inchworm making its inefficient progress, and it told you everything you needed to know. He had known not to trust that particular parabola. It was more than portent, it was a promise. Something was upon them. It had been decreed. “You saw how dirty they had the kitchen.”

The Handbook of Personal Wealth Management
by Reuvid, Jonathan.
Published 30 Oct 2011

As distressed sellers are unloading cheap assets to unwind their over-leverage, it presents opportunities for relative value traders, who may be able to hedge out various market risks. In the commodities sector, dislocations between cash and futures prices are increasing. Macro managers may also be able to benefit from steepening yield curves following the sharp interest rate cuts of 1.5 per cent on 6 November 2008 in the UK (with other countries following suit), the further rate cut of 1 per cent in December and the possibility of further cuts to follow. Distressed managers are beginning to see a huge number of potential opportunities emerging.

Broken Markets: A User's Guide to the Post-Finance Economy
by Kevin Mellyn
Published 18 Jun 2012

The Fed policy is literally forcing institutional investors to take on more and more risk in search of returns, and certain exotic structured products such as collateralized debt obligations are creeping back into the market. With the central banks flooding the market with liquidity, the market is too distorted and the yield curves too flat (long-term and short-term rates are about the same) for ordinary investors to navigate. Also, don’t take for granted that money market funds are risk free in today’s world. Stay Debt Free Fifth, not spending money is as good as earning more money in a repressed economy. For starters, if your portfolio is doing a bit better than the market, but you are paying substantial management or advisor fees, it can cancel out.

Who Needs the Fed?: What Taylor Swift, Uber, and Robots Tell Us About Money, Credit, and Why We Should Abolish America's Central Bank
by John Tamny
Published 30 Apr 2016

But to believe this, one would have to believe that central bankers suddenly figured out how to engineer bull markets. The problem with such an assertion, particularly one that says low rates push investors into stocks, is that the latter has been policy from the Bank of Japan since the 1990s. Low interest rates across the yield curve have long been the norm for Japan’s central bank, as has quantitative easing (Japan’s economy has suffered 10 doses of QE from the Bank of Japan10). Yet, the Nikkei 225 is still half of what it was in the late 1980s. Moving to China, its stock markets started to buckle in August 2015. Worried about stocks falling further, the Chinese government spent tens of billions of yuan trying to prop the market up.11 It failed.

The Social Life of Money
by Nigel Dodd
Published 14 May 2014

Eurozone member states were able to borrow at lower interest rates because creditors (mostly bondholders) were treating them as part of a homogeneous financial space. That is to say, the introduction of the euro appeared to coincide with the unification of government bond yields across the Eurozone. Member states were borrowing at similar rates, reflecting that their debt carried a similar underlying degree of risk. It was as if a single yield curve had been established for the bonds issued by all Eurozone member states (Aglietta and Scialom 2003: 52). The effect of those lower borrowing costs on Greece was especially striking: starting with a yield of more than 11 percent in the beginning of 1998, Greek borrowing costs declined constantly to about 6 percent in mid-2000 and even further to a low at 3.3 percent in September 2005.36 Similar examples can be seen among more recent entrants to Euroland, Slovenia and Slovakia.

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On joining the euro, both experienced a rapid lowering of bond rates. Indeed, almost all newly joining countries have experienced a boom upon joining the Eurozone. If the Eurozone resembled a monetary and financial union during its first few years, it turned out to be an illusion. That single yield curve for sovereign bonds splintered midway through 2008, and spreads have been widening ever since. So why have rates diverged? One simple answer is that debt has been used in a different way since the global crisis. De Grauwe, for example, points to the “flight to safety” of investors dumping private debt and turning to low-risk sovereign debt.

Flash Crash: A Trading Savant, a Global Manhunt, and the Most Mysterious Market Crash in History
by Liam Vaughan
Published 11 May 2020

Brought up with his brother in south London by their mother, a housewife, and father, a police detective, Paolo found school easy and took his math exam early, but he was restless, and when his friends went off to university, he landed a junior role at the Bank of England. After a couple of fusty years behind a desk learning about interest rates and yield curves, he got a position at a merchant bank, where he worked in a department that used futures to hedge its portfolios. One day a broker invited him on a tour of Liffe. They met by the Royal Exchange’s towering stone columns at 1:25 p.m., five minutes before a big economic announcement was due to be made.

Finding Alphas: A Quantitative Approach to Building Trading Strategies
by Igor Tulchinsky
Published 30 Sep 2019

Traditionally, the correlation between price and volatility is negative for equities, which generally are a risk-on asset. Therefore, high or increasing VIX levels are associated with money moving out of equity markets into safer assets, indicating the arrival of a risk-off regime. The VIX itself is a tradable futures instrument that is used by many to benefit from falling markets. Other indicators include the yield curve (higher and steeper is risk-on; lower and flatter or inverted is risk-off); sector flows among risk-on sectors such as consumer discretionary and risk-­ off sectors such as utilities, or among emerging (risk-on) and developed (risk-off) markets; carry currency pairs, such as AUD/JPY; and the covariance structure of the market (the top eigenvector is usually risk-off).

The Bogleheads' Guide to Investing
by Taylor Larimore , Michael Leboeuf and Mel Lindauer
Published 1 Jan 2006

Unrealized capital gain/loss: A gain or loss that would be realized if the fund's securities were sold. Wash sale: An IRS rule that disallows the loss from the sale of a fund if the investor invests in a "substantially identical" fund within 31 days. Yield: Income received from an investment expressed as a percentage of its current price. Yield curve: A line on a graph that depicts the yields of bonds of varying maturities. APPENDIX II Books We Recommend BOOKS FOR NOVICE INVESTORS The Coffeehouse Investor by Bill Shultheis (Kirkland, WA: Palouse Press, 2005). A little book with a big message: How to invest simply and successfully.

The Power of Passive Investing: More Wealth With Less Work
by Richard A. Ferri
Published 4 Nov 2010

unrealized capital gain/loss An increase (or decrease) in the value of a security that is not yet realized because the security has not been sold. volatility The degree of fluctuation in the value of a security, mutual fund, or index. Volatility is often expressed as a mathematical measure, such as a standard deviation or beta. The greater a fund’s volatility, the wider the fluctuations between highs and lows. yield curve A line plotted on a graph that depicts the yields of bonds of varying maturities, from short-term to long-term. The line, or curve, shows the relationship between short- and long-term interest rates. yield-to-maturity The rate of return an investor would receive if the securities held in his or her portfolio were held until their maturity dates.

Liar's Poker
by Michael Lewis
Published 1 Jan 1989

At what price were they attractive? There had to be some price where the customers would buy. A hundred basis points over treasuries [meaning one percentage point yield greater than U.S. treasury bonds]? Two hundred basis points? I mean, these things were three hundred and fifty basis points off the [U.S. treasury yield] curve!" All American homeowners had a feel for the value of the right to repay their mortgage at any time. They knew if they borrowed money when interest rates were high that they could pay it back once rates fell and reborrow at the lower rates. They liked having that option. Presumably they would be willing to pay for the option.

Fool's Gold: How the Bold Dream of a Small Tribe at J.P. Morgan Was Corrupted by Wall Street Greed and Unleashed a Catastrophe
by Gillian Tett
Published 11 May 2009

The European Central Bank had belatedly followed suit. Yet these moves hadn’t worked. Instead of rising, the cost of borrowing had stubbornly continued to fall in many corners of the market. In the US government bond sphere, yields on 10-year Treasuries even tumbled below short-term bond yields, creating a bizarre pattern known as an “inverted yield curve.” Alan Greenspan dubbed the situation a “conundrum.” There were other puzzles, too. In previous decades, the price of assets had been volatile when surprises hit the markets, be they an oil price shock, a rate rise, or a swing in the housing market. However, as Basel’s BIS noted at the time, the “striking feature of financial market behavior” in the twenty-first century was “the low level of price volatility over a wide range of financial assets and markets.”

Falter: Has the Human Game Begun to Play Itself Out?
by Bill McKibben
Published 15 Apr 2019

And economics professors, it turns out, “give significantly less money to charity than their worse-paid colleagues in many other disciplines.”11 This is the world where think tanks debate whether it’s cost-effective to save the Arctic, and where the Wall Street Journal runs a headline such as HOW DO YOU PRICE A PROBLEM LIKE KOREA: ANALYSTS ARE TRYING TO WORK OUT WHAT HAPPENS TO MARKETS IN THE EVENT OF AN ALL-OUT NUCLEAR WAR. (In case you’re wondering: in the event of a “potentially uncontained military conflict in which the global superpowers get involved,” the yield curve on Eurobonds would “likely flatten due to weaker risk appetite.”)12 Because this is so contrary to our nature, eventually even the U.S. political system will work its way back to some kind of balance. The Koch brothers may well have hit their zenith. Political scientists crunching the polling data said that the Kochs’ two signature laws (the attempted repeal of Obamacare and the successful tax “reform” package) were the “most unpopular pieces of major domestic legislation of the past quarter-century,” the journalist Michael Tomasky points out.

Systematic Trading: A Unique New Method for Designing Trading and Investing Systems
by Robert Carver
Published 13 Sep 2015

So if you buy shares in French supermarket Carrefour which currently has a dividend yield of 3%, and you pay 1% to borrow the purchase cost, then you earn 2% carry on the position if the share price is unchanged. Similarly today I can buy June 2018 Eurodollar futures at 97.94, or March 2018 at 98.01. If there is no change in the shape of the yield curve then in three months’ time June futures will rise to 98.01, earning 0.07 per contract. Academic theory predicts that prices should move against us to offset these returns, but it often doesn’t. Carry is usually earned steadily on these kinds of trades although occasionally they go horribly wrong and the relationship temporarily breaks down, giving this trading rule some evil negative skew.

13 Bankers: The Wall Street Takeover and the Next Financial Meltdown
by Simon Johnson and James Kwak
Published 29 Mar 2010

* The Tenth Amendment, part of the Bill of Rights, was technically not yet in force, but by the end of 1790 it had been ratified by nine states out of the ten necessary. * A trust was a form of legal organization used to combine multiple companies into a single business entity. * Lowering short-term interest rates can also help banks by “steepening the yield curve.” Since banks typically borrow for short periods of time and lend for long periods of time, if short-term rates fall while long-term rates remain unchanged, their profit margin—the spread between long- and short-term rates—increases. * An alternative explanation, advanced by Barry Eichengreen and Peter Temin, is that the Federal Reserve was constrained by its adherence to the international gold standard; expanding the money supply would have caused a severe devaluation of the dollar.93 2 OTHER PEOPLE’S OLIGARCHS Financial institutions have priced risks poorly and have been willing to finance an excessively large portion of investment plans of the corporate sector, resulting in high leveraging.

The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again
by Nicholas Dunbar
Published 11 Jul 2011

Just how heavily traded these contracts became can be gauged from the total “notional” amount of debt that was supposed to be transformed by the swaps (which is not the same as their value): by June 2008, a staggering $356 trillion of interest rate swaps had been written, according to the Bank for International Settlements.2 As with forward contracts on currencies and commodities, the rates quoted on these swaps are considered to be a more informative way of comparing different borrowing timescales (the so-called yield curve) than the underlying government bonds or deposit rates themselves. Derivatives—at least the simplest, most popular forms of them—functioned best by being completely neutral in purpose. The contracts don’t say how you feel about the derivative and its underlying quantity. They don’t specify that you are a hate-to-lose-money corporate treasurer looking to reduce uncertainty in foreign exchange or commodities.

The End of Doom: Environmental Renewal in the Twenty-First Century
by Ronald Bailey
Published 20 Jul 2015

Dale Langford, eds., Technological Trajectories and the Human Environment, National Academy of Engineering, 1997, 56–73. www.nap.edu/openbook.php?record_id=4767&page=56. India produces 31 bushels: Ronald Phillips, “Mobilizing Science to Break Yield Barriers.” Background paper to the CGIAR 2009 Science Forum workshop: “Beyond the Yield Curve: Exerting the Power of Genetics, Genomics and Synthetic Biology,” “2009, 17. www.scienceforum2009.nl/Portals/11/BGWS4.pdf. that past population growth: Julio A. Gonzalo, Félix-Fernando Muñoz, David J. Santos, “Using a Rate Equations Approach to Model World Population Trends.” Simulation: Transactions of the Society for Modeling and Simulation International 89 (February 2013): 192–198.

Capital Ideas Evolving
by Peter L. Bernstein
Published 3 May 2007

Kritzman, Mark, and Lee Thomas, 2004. “Re-Engineering Investment Management,” The Journal of Portfolio Management, 30th Anniversary Issue (September), pp. 70 –79. Kroszner, Randall, 2006. “The Conquest of Worldwide Inf lation: Currency Competition and Its Implications for Interest Rates and the Yield Curve,” Cato Monetary Policy Conference, November 16. Kurz, Mordecai, 1994. “On the Structure and Diversity of Rational Beliefs,” Economic Theory, Springer-Verlag, Vol. 4, pp. 877–900. Kurz, Mordecai, ed., 1997. Endogenous Economic Fluctuations: Studies in the Theory of Rational Beliefs, Springer Series in Economic Theory, No. 6 (August), Springer-Verlag.

The Quants
by Scott Patterson
Published 2 Feb 2010

A billionaire former blackjack card counter (in college he’d devoured Beat the Dealer and Beat the Market), Gross religiously applied his gambling acumen to his investment decisions on a daily basis. Pimco had gotten hold of Asness’s first published research, “OAS Models, Expected Returns, and a Steep Yield Curve,” and was interested in recruiting him. Over the course of the year, Asness had several interviews with Pimco. In 1993, the company offered him a job building quantitative models and tools. It was an ideal position, Asness thought, combining the research side of academia with the applied rigor of Wall Street.

Atrocity Archives
by Stross, Charles
Published 13 Jan 2004

"It's a selective yield gadget," says Howe. "We can set it to anything from fifteen kilotons to a quarter of a megaton--it's a mechanical process, screw jacks adjust the gap between the fusion sparkplug and the initiator charge so that we get more or less fusion output. Right now it's at the upper end of the yield curve, dialled all the way up to city-buster size. What's this got to do with anything?" "Well." I lick my lips; it's really cold in here now and my breath is steaming. "To open a gate big enough to bring through a large creature like whatever ate this universe takes a whole lot of entropy. The Ahnenerbe did it in this universe by ritually murdering roughly ten million people: information destruction increases entropy.

Planet Ponzi
by Mitch Feierstein
Published 2 Feb 2012

You’d want to cover your manipulation in plenty of complicated talk about statistics, but the talk wouldn’t signify a string bean. The second thing you’d want to do is to start churning out new dollar bills. You’d print like crazy. You wouldn’t talk about trashing the currency, of course; you’d talk about price stability, about quantitative easing, about Operation Twist and bringing down the long end of the yield curve. Ideally, too, you’d have someone in charge who really believed in the value of what he was doing, someone who didn’t really live in the real world. Maybe a professor of something. A guy who had studied a period of history from eighty years ago and who’s been yearning all his life to save the world using techniques which might or might not have worked back then, but which certainly don’t make sense in the present day.

Fed Up: An Insider's Take on Why the Federal Reserve Is Bad for America
by Danielle Dimartino Booth
Published 14 Feb 2017

The combination of Dodd-Frank, with its aim of limiting risk-taking, and Basel III, with its increased capital requirements, had proved to be a toxic combination. Was it any wonder that commercial bank officers were stumped? The stated aim of QE was to encourage banks to loan money. But other rules required they hold more capital against fresh loans if they did—to say nothing of the risk they assumed if yield curve normality ever made a comeback. Private equity kingpins had become the new overlords of the corporate bond market. They had also discovered the profitability of being landlords. Money was cheap for those who could access it. And investors were eager to buy into the next private equity fund in the hopes they could eke out positive returns.

An Extraordinary Time: The End of the Postwar Boom and the Return of the Ordinary Economy
by Marc Levinson
Published 31 Jul 2016

As the Fed began raising overnight interest rates aggressively to clamp down on inflation, interest rates on the Treasury’s short-term bonds rose close to those on its long-term bonds. On August 18, 1978, the lines crossed: investors earned more for lending to the government for two years than for ten. That unusual condition, known in the financial markets as an inverted yield curve, was an alarm bell, an unmistakable warning that a recession was likely in the second half of 1979. And then came the second oil crisis, driven by the revolution in Iran and a decision by Saudi Arabia to limit oil production. After holding steady since 1974, the average cost of a barrel of crude doubled over the course of 1979.

Unconventional Success: A Fundamental Approach to Personal Investment
by David F. Swensen
Published 8 Aug 2005

If Congress limits or eliminates the tax exemption, the values of municipal bonds would decline. Legislative uncertainty contributes to higher-than-expected long-term tax-exempt yields. Proving that generalizations invite exceptions, sometimes market forces fail to work on the short end of the yield curve. Consider yields for Vanguard’s money-market offerings. In September 2004, the tax-exempt money fund yield matched the taxable fund yield. A top-marginal-bracket taxpayer benefited to the tune of 0.4 percent on an after-tax basis by choosing the tax-exempt fund. The early-September yields represented more than a passing opportunity.

The Death of Money: The Coming Collapse of the International Monetary System
by James Rickards
Published 7 Apr 2014

Corporations in the EU are predominantly taxed on a national basis, meaning tax is paid to a host country only based on profits made in that country, which contrasts favorably with the U.S. system of global taxation, in which a U.S. corporation pays tax on foreign as well as domestic profits. Both the EU and the United States have managed to maintain low inflation in recent years, but Europe has done so with significantly less money printing and yield-curve manipulation, which means its potential for future inflation based on changes in the turnover or velocity of money is reduced. In contrast, China has had a persistent problem with inflation due to Chinese efforts to absorb Federal Reserve money printing to maintain a peg between the yuan and the dollar.

Shutdown: How COVID Shook the World's Economy
by Adam Tooze
Published 15 Nov 2021

One market correspondent described the “odour of screeching brakes and hot tyres skidding to an abrupt stop.”35 Investors dumped Italian stocks. Shares in low-cost European airlines easyJet and Ryanair plummeted. When markets opened in New York later in the day, demand for the benchmark ten-year Treasury surged. It was a classic run to safety. The yield curve inverted—it was cheaper to borrow long term than short term. Investors were more worried about the immediate future than the long term, a classic foreboding of a recession. For the first time, estimates began to circulate about the damage to be expected from an epidemic that was not confined to China but spread to the entire world.

The Bank That Lived a Little: Barclays in the Age of the Very Free Market
by Philip Augar
Published 4 Jul 2018

She worked through it, talking about derivatives and hedges, things she said financial institutions were doing all the time but which were new to Edwards. She showed him graphs and used terms he had never heard of like ‘structured collar cap with a double floor’, ‘mark-to-market’, ‘upward sloping yield curve’ and ‘forward rates’. The presentation included a page which showed the corporate logos of companies which used such products, for example Citigroup, Goldman Sachs and HBOS, and Carol said that Barclays Capital had produced a simplified version for smaller companies. The pack included a page asking ‘Which should I choose?

Narrative Economics: How Stories Go Viral and Drive Major Economic Events
by Robert J. Shiller
Published 14 Oct 2019

Memory in Oral Traditions: The Cognitive Psychology of Epic, Ballads, and Counting-Out Rhymes. Oxford: Oxford University Press. Rubinstein Mark, and Hayne Leland H. 1981. “Replicating Options with Positions in Stock and Cash.” Financial Analysts Journal 37(4):63–72. Rudebusch, Glenn D., and John C. Williams. 2009. “Forecasting Recessions: The Puzzle of the Enduring Power of the Yield Curve.” Journal of Business and Economic Statistics 27(4):492–503. Saavedra, Javier, Mercedes Cubero, and Paul Crawford. 2009. “Incomprehensibility in the Narratives of Individuals with a Diagnosis of Schizophrenia.” Qualitative Health Research 19(11):1548. Saiz, Albert. 2010. “The Geographic Determinants of Housing Supply.”

Crisis Economics: A Crash Course in the Future of Finance
by Nouriel Roubini and Stephen Mihm
Published 10 May 2010

.”: Paul McCulley, “Teton Reflections,” Global Central Bank Focus, PIMCO, August-September 2007. 81 “bond market conundrum”: Alan Greenspan, testimony before the Committee on Banking, Housing, and Urban Affairs, U.S. Senate, February 16, 2005, online at http://www.federalreserve.gov/boarddocs/hh/2005/february/testimony.htm. 81 determined in global markets: See, for example, Tao Wu, “Globalization’s Effects on Interest Rates and the Yield Curve,” Economic Letter, Federal Reserve Bank of Dallas, September 2006, 1-8; online at http://www.dallasfed.org/research/eclett/2006/el0609.pdf. 82 Leverage has been on the increase: Minsky, Stabilizing an Unstable Economy, 265; Martin Wolf, “Seeds of Its Own Destruction,” Financial Times, March 8, 2009; Susan Webber, “No Leverage,” Conference Board Review, May-June 2009, 61-65. 83 Leverage comes in many flavors: See, for example, Charles R.

Vulture Capitalism: Corporate Crimes, Backdoor Bailouts, and the Death of Freedom
by Grace Blakeley
Published 11 Mar 2024

Money, Trust, and Central Bank Legitimacy in the Age of Quantitative Easing,” Review of International Political Economy 23, no. 6 (November 2016): 1064–92, https://doi.org/10.1080/09692290.2016.1252415. 98. They have, in Braun’s words, “made the long-term interest rate a policy variable.” Benjamin S. Braun, “Central Bank Planning: Unconventional Monetary Policy and the Price of Bending the Yield Curve,” in Jens Beckert and Richard Bronk (eds.), Uncertain Futures: Imaginaries, Narratives, and Calculation in the Economy (Oxford: Oxford University Press, 2018). 99. To be fair to the central bankers, they had been given an almost impossible task of maintaining growth and reducing inflation while government fiscal policy often works in the opposite direction and inflation rose dramatically, driven by cost pressures largely outside policymakers’ control.

The Man Who Knew: The Life and Times of Alan Greenspan
by Sebastian Mallaby
Published 10 Oct 2016

“Bankers are willing to take on more risk than I have heard them admit to in recent years,” added Governor Mark Olson, who was himself a former banker. Vice Chairman Roger Ferguson pushed the argument further, linking the financial exuberance with the Fed’s forward guidance about future interest rates. “Perhaps we are anchoring the yield curve more than we’d like,” he suggested. “The fixed-income markets in particular are not in fact doing the appropriate job of pricing risks.” He was suggesting that the Fed’s forward guidance had made life too predictable, lulling speculators into complacency. “We need in some sense to remove the anchor that we have placed on those markets,” he concluded.

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The danger of a snapback had to be weighed against more certain and immediate goals: to allow as much growth and employment as possible, consistent with a stable consumer-price index.45 • • • For the next few months, the Fed continued to guide investors about its future policy, oblivious to Roger Ferguson’s warning that this might “anchor” the yield curve and lull investors into complacency. In March 2004 the FOMC repeated its promise to be patient about raising interest rates; in May it declared it would tighten “at a pace that is likely to be measured.” It was only in June, after fully twelve months with a 1 percent federal funds rate, that the FOMC ventured a quarter-point hike.

Principles: Life and Work
by Ray Dalio
Published 18 Sep 2017

He kept buying and buying as inflation and the price of silver went up, until he had essentially cornered the silver market. At that point, silver was trading at around $10. I told him I thought it might be a good time to get out because the Fed was becoming tight enough to raise short-term interest rates above long-term rates (which was called “inverting the yield curve”). Every time that happened, inflation-hedged assets and the economy went down. But Bunker was in the oil business, and the Middle East oil producers he talked to were still worried about the depreciation of the dollar. They had told him they were also going to buy silver as a hedge against inflation so he held on to it in the expectation that its price would continue to rise.

Wealth and Poverty: A New Edition for the Twenty-First Century
by George Gilder
Published 30 Apr 1981

PROLOGUE THE SECRET OF ENTERPRISE THIRTY YEARS AFTER THE publication of Wealth & Poverty, shaken by a global financial fiasco, I find myself buckling down to engage once again these central themes of human life and economics. Back during the tempestuous late years of the 1970s, with President Jimmy Carter waving limp white flags of national malaise, with hostages still held in Tehran, petroleum and gold prices shrilling doom-laden alarms, U.S. banks gasping for capital down a ferociously inverted yield curve (borrowing dear in short-term markets and lending low in long-term bonds and mortgages), with the Soviet Union battening rich on oil wealth, and John Kenneth Galbraith joining the CIA in acclaiming the robustness and fast growth of the “astonishing” Soviet economy, I declared that socialism was dead.

The Case Against Education: Why the Education System Is a Waste of Time and Money
by Bryan Caplan
Published 16 Jan 2018

Accessed August 18, 2015. http://www.dol.gov/whd/regs/compliance/childlabor101.pdf. ———. 2014. “State Unemployment Insurance Benefits.” Last modified June 3. http://workforcesecurity.doleta.gov/unemploy/uifactsheet.asp. United States Department of the Treasury. 2016. “Resource Center: Daily Treasury Yield Curve Rates.” Accessed March 30, 2016. https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield. United States Equal Opportunity Commission. 2015. “Prohibited Employment Policies/Practices.” Accessed February 28, 2015. http://www.eeoc.gov/laws/practices/index.cfm.

Crash of the Titans: Greed, Hubris, the Fall of Merrill Lynch, and the Near-Collapse of Bank of America
by Greg Farrell
Published 2 Nov 2010

The idea was simple enough, to package mortgages of various durations and interest rates into tranches, then securitize those tranches and sell them like bonds, where buyers could look forward to receiving annual payments, or “coupons,” on their investment. Thain immersed himself in the business, learning the arcane details of mortgage trading, from the payment cycles and coupon rates to the special considerations of prepayment pools and the “negative convexity”—an inversion of the standard price/yield curve—that creeps into the valuations of mortgage portfolios. Mortgage trading fell within Goldman’s fixed-income trading division, and the leader of that business, Jon Corzine—who would eventually be elected U.S. senator from New Jersey and governor of the Garden State—took a special interest in Thain, a fellow native of Illinois.

The Euro and the Battle of Ideas
by Markus K. Brunnermeier , Harold James and Jean-Pierre Landau
Published 3 Aug 2016

Interestingly, by eliminating the diabolic loop, national defaults become less likely and correlated, which also makes the junior bond less risky.14 As ESBies would be essentially free of default risk, the ECB could use them to conduct open-market operations without taking on any default risk, as the Fed does with US Treasury bonds. With ESBies of different maturities, one would get a whole risk-free yield curve that could serve as a European benchmark that the ECB could influence. Redenomination and Exit Risks Redenomination risk refers to the risk that, say, Greek households become concerned about the prospect that capital controls make it impossible to bring “Greek euros” outside of Greece or that they are involuntarily converted into a new Greek drachma.

Why Stock Markets Crash: Critical Events in Complex Financial Systems
by Didier Sornette
Published 18 Nov 2002

B2C Greenspan speaks Optimistic CNBC guest Pain Joe Ignore history Arggh! Larry Nothing matters Any gains lost in next day rally Ralph Bad breadth Wealth effect Abby Earnings slowdown Big volume Futures up Greenspan silent Rally!!! Bears bail Phew! MSFT breakup e-broker TV ads P/E’s of 2000 Weird yield curve Buy and hold forever “Bottom is in” Mergers Soros out Gold auctions Margin call W$W elves 401k inflows 16 year olds beat market vets Flight to safety Hot market Dollar goes every which way Old Economy New Economy Oil up DOW 36,000 IPO billionaires 30yr bond extinct Fig. 4.1. Cartoon illustrating the many factors influencing traders, as well as the psychological and social nature of the investment universe (source: anonymous).

Alpha Trader
by Brent Donnelly
Published 11 May 2021

Note in Figure 7.11 how USDJPY bashed against 108.00 four times (four arrows) before a huge false break and then it retested the 108.00 level again afterwards (fifth arrow). I am therefore adding a short USDJPY recommendation. You could either sell here or leave an offer at 107.75 with a stop at 108.26. With ISM and payrolls tomorrow, there is a decent chance you get done. And with Yield Curve Control on the horizon and the explosion of coronavirus cases in the US South, I doubt strong US data will impact yields much. Note by leaving an order to sell above market at 107.75 through nonfarm payrolls, I attempt to take advantage of the noisy volatility created by an event I think is meaningless to get set at a good level on a trade I like for a bunch of reasons.

Growth: From Microorganisms to Megacities
by Vaclav Smil
Published 23 Sep 2019

Ichihashi and Tateno (2015) tested this obvious hypothesis for nine deciduous liana species in Japan and found they had 3–5 times greater leaf and current-year stem mass for a given above-ground mass and that they reached the canopy at the same time as the co-occurring trees but needed only 1/10 of the phytomass to do so. But this growth strategy exacts a high cost as the lianas lost about 75% of stem length during their climb to the canopy. The addition of annual increments over the entire tree life span produces yield curves which are missing the earliest years of tree growth because foresters begin to measure annual increments only after a tree reaches a specified minimal diameter at breast height. Growth curves for both tree heights and stem diameters are available in forestry literature for many species from ages of five or ten to 30–50 years and for some long-lived species for a century or more, and they follow confined exponential trajectories with a species-specific onset of declining growth.

Money and Power: How Goldman Sachs Came to Rule the World
by William D. Cohan
Published 11 Apr 2011

“There’s no orientation, there’s none of that crap. It was just a phenomenal experience for me to be able to do something real in a very hot area at the time.” Goldman asked him to return the following summer. Once again, he structured CMOs. “It was still a great time to do it in 1993,” he said. “There was a steep yield curve”—meaning the cost of debt was higher the longer someone could take to pay it back—“so intellectually it was an interesting thing.” He had straight As when he graduated from the Wharton undergraduate program in December 1993—a semester early—and because of that, and having Goldman Sachs on his résumé for two summers, he had any number of job offers to choose from.