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Statistical Arbitrage: Algorithmic Trading Insights and Techniques

by Andrew Pole  · 14 Sep 2007  · 257pp  · 13,443 words

3 2 1 To Eliza and Marina Contents Preface xiii Foreword xix Acknowledgments CHAPTER 1 Monte Carlo or Bust Beginning Whither? And Allusions CHAPTER 2 Statistical Arbitrage Introduction Noise Models Reverse Bets Multiple Bets Rule Calibration Spread Margins for Trade Rules Popcorn Process Identifying Pairs Refining Pair Selection Event Analysis Correlation Search

Structural Change Recap CHAPTER 10 Arise Black Boxes Introduction Modeling Expected Transaction Volume and Market Impact Dynamic Updating More Black Boxes Market Deflation CHAPTER 11 Statistical Arbitrage Rising Catastrophe Process Catastrophic Forecasts Trend Change Identification Using the Cuscore to Identify a Catastrophe Is It Over? Catastrophe Theoretic Interpretation Implications for Risk Management

a named result and exists as a simple consequence, a textbook exercise, of basic distribution theory. No matter, the implication remains profoundly significant to the statistical arbitrage story.) Chapter 5 critiques a published article (whose authors remain anonymous here to protect their embarrassment) to clarify the broad conditions under which the phenomenon

experience has been accustomed ineluctably leads to excessive risk taking. Chapter 10 is interesting in its own right, notwithstanding any relationship to the evolution of statistical arbitrage opportunities. Algorithms and computer driven trading are changing the financial world in many ways. Electronic exchanges have already been seen off most of the world

forces, both deriving from the core nature of the discipline: the vagueness of practitioners and the lack of quantitative knowledge on the part of investors. Statistical arbitrage exploits mathematical models to generate returns from systematic movements in securities prices. Granted, no investment manager is inclined to divulge the intricate ‘‘how-tos’’ of

beyond the college level. This, naturally, limits the audience. The limitation is perpetuated by the lack of reference material from which to learn. Statistical Arbitrage now fills that void. Statistical arbitrage has been in existence for approximately 25 years. During that time, the general concepts have been widely xix xx FOREWORD disseminated via the

thrive everywhere and still make up by far the largest part of the planet’s biomass. So is it true in statistical arbitrage, where the basics underpin much of contemporary practice. Statistical Arbitrage describes the phenomena, the driving forces generating those phenomena, the patterns of dynamic development of exploitable opportunities, and models for exploitation

the dynamics follows a xxii FOREWORD catastrophe-theory explication of a possible rationale for the behavioral pattern. The unmistakable impression is that statistical arbitrage is rising once again. The tone of Statistical Arbitrage is direct and thorough. Obfuscation is in short supply. Occasionally, the tone is relieved with a bit of lightheartedness—the tadpole

the validity of understanding and coherent actions in exploiting emergent properties of components of the financial emporium. This volume presents a critical analysis of what statistical arbitrage is—a formal theoretical underpinning for the existence of opportunities and quantification thereof, and an explication of the enormous shifts in the structure of the

became more sophisticated and the models deployed more technical, so the sobriquet by which the discipline became known was elaborated. The term ‘‘statistical arbitrage’’ was first used in the early 1990s. Statistical arbitrage approaches range from the vanilla pairs trading scheme of old to sophisticated, dynamic, nonlinear models employing techniques including neural networks, wavelets

techniques from probability theory to differential and difference equations). With so much intellectual energy active in research, the label ‘‘pairs 9 10 STATISTICAL ARBITRAGE trading’’ seemed inadequate. Too mundane. Dowdy, even. ‘‘Statistical arbitrage’’ was invented, curiously, despite the lack of statisticians or statistical content of much of the work. 2.2 NOISE MODELS The

return variability became desirable and as experience showed where structural weaknesses lay. Individual manager preference became influential when hedge funds began marketing pairs trading and statistical arbitrage strategies. Maximizing correlations was an early filter applied to pair selection: Compute the correlation of each candidate pair (using, for example, two years of daily

estimated on average recent historical price series. In historical analysis, flags of unusual activity are extremely important in the evaluation of, for example, simulation 25 Statistical Arbitrage 80 $ 70 60 50 40 19970102 19970524 19971016 19980312 FIGURE 2.8 Adjusted close price trace (General Motors) with 20 percent turning points identified TABLE

to be aware of ‘‘unlikely’’ extreme situations notwithstanding routine, daily, ‘‘risk controlled’’ portfolio construction. The distinction of extreme and routine risk is deliberately vague.) 28 STATISTICAL ARBITRAGE The goal has, therefore, become: Maximize expected return subject to a limit on believed variation about that expected return. The variance constraint reduces the admissible

. A good estimate of the likely realizable fill price for desired trades enables the trading system to filter potentially unprofitable trades from the portfolio optimization. Statistical Arbitrage 31 Immediately, a question arises: Is market impact not subsumed in the construction of the forecast function? Superficially only. There is an implicit assumption that

it would otherwise have been. Simulation for 2000–2002 significantly exceeded that expectation as market developments caused a decline in performance of higher frequency 34 STATISTICAL ARBITRAGE compared with lower frequency strategies. See Chapter 9 for a detailed discussion of the issues involved. 2.6.1 Evolutionary Operation: Single Parameter Illustration Evolutionary

the parameter range to aim for gradually moves. The original range continues to deliver reasonable performance, but becomes less attractive over several years. Evolutionary 35 Statistical Arbitrage (a) (b) (c) (d) 4 2 1 3 FIGURE 2.9 Evolutionary operation: detecting sustained system response change operation, the continual monitoring of system performance

best calibration, enables one to identify transient and persistent system response changes. Transient changes provide information to update the view of normal system response 36 STATISTICAL ARBITRAGE variation; enduring system response changes can be adapted to, improving long-term system performance. As just exemplified, evolutionary operation monitoring looks beguilingly simple—and, indeed

models, for example. Note that cointegration models should presumably be of little value here because common factors are supposedly removed in the defactorization procedure. 58 STATISTICAL ARBITRAGE Many elaborations may be entertained. For instance, there may be more stability in factor estimation on time scales with granularity much longer than one day

of it will amplify appreciation of the impact of market developments that have led to the practical elimination of the discipline of statistical arbitrage in the public domain. 67 68 STATISTICAL ARBITRAGE 4.2 MODEL AND RESULT We present a model for forecasting prices of financial instruments that guarantees 75 percent forecasting accuracy. The

2003, however, volatility of stocks on the U.S. exchanges has been declining. Spread volatility reached unprecedented lows in 2003 76 STATISTICAL ARBITRAGE and 2004; implications of that development for statistical arbitrage are examined in Chapter 9. When volatility exhibits bursts, variances are not generated independently each day but exhibit serial correlation. The 75

window. Interesting? Once again, the analysis points to using a shorter, more local view when inferring reversion opportunity from average levels of spread volatility. 112 STATISTICAL ARBITRAGE With these archetypal models, one can undertake an appropriate time-frequency analysis to precisely quantify the magnitude of reversionary moves. Real spread series are less

distributions can pose. Two questions are immediately apparent: 1. Is the odds result exploitable in trading? ■ With artificial data following the assumed stationary process. 116 STATISTICAL ARBITRAGE With stock data using locally defined moments (to approximate conditional stationarity). 2. How should reversion be defined in this context? ■ Reversion to the center requires

series, observed differences in the proportion of reversionary moves unambiguously indicate differences in temporal structure other than in the random component. 118 7.2.2 STATISTICAL ARBITRAGE Amount of Reversion Following the preceding discussion of how often reversion is exhibited, some possible measures of the size of expected reversion from a price

without intervention schemes. Including monitors and related early exit [stop loss] rules would attenuate losses but complicate the description without changing the basic message.) 144 STATISTICAL ARBITRAGE Using an exponentially weighted moving average model for an assumed popcorn process with a constrained trend component (see Chapter 3) trades in [FRE, SAI] entered

-based return prediction model makes no difference at the outset. Losses are inevitable. As the discriminatory stock price patterns developed, discriminatory results distinguished types of statistical arbitrage strategy, Nobel Difficulties 147 though manager action in the face of persistent and cumulatively large losses complicates assessment: the mix of model versus manager (to

; the mechanics described in this section create the conditions for a blood bath for statistical arbitrage. 150 8.4.1 STATISTICAL ARBITRAGE Supercharged Destruction A large equity statistical arbitrage portfolio is perfectly designed to create, on liquidation, guaranteed losing conditions for other statistical arbitrage portfolios. Size matters because the sell-off of longs and the buy-in of

to a positive opinion to win underwriting business and then restoring the negative opinion! Activities eventually outlawed by Regulation FD had dramatic negative impact on statistical arbitrage portfolios in 1999. Most readily identifiable was the selective disclosure of earnings in the days before official announcements. Typically, favored analysts would receive a tip

become an unsaleable product. The year 2006 saw a resurgence in performance, vindicating those who had maintained that the performance collapse was explained 155 156 STATISTICAL ARBITRAGE by a multiplicity of factors, many of which were transitory. With the passing of those temporary disruptions to market coherence and consistently predictable security price

that decimalization itself is not a barrier to profit opportunity for the strategy; performance problems are created by changes in market structure which causes 158 STATISTICAL ARBITRAGE changes in temporal dynamics, disrupting the patterns that statistical arbitrageurs’ models are built to predict. European markets are fully electronic, closer to the NASDAQ than

supports nor contradicts such a hypothesis. It is much more likely than not that decimalization was a bit player in the explanation of statistical arbitrage performance decline. Suppose that statistical arbitrage’s historical performance was derived solely from systematic obtaining of the consumer surplus when spreads jump over a trade threshold and fills are

, notwithstanding performance problems, to support concomitant increase of market impact, and consequently no evidence that greater competition is the major cause of the decline of statistical arbitrage performance. Trinity Troubles 9.5 163 INSTITUTIONAL INVESTORS ‘‘Pension funds and mutual funds have become more efficient in their trading.’’ Three years of market decline

into 2002 managers everywhere (almost) were experiencing poor performance. The decline in market volatility was dragooned into service as ‘‘the’’ explanation for the lack of statistical arbitrage performance. Impressively quickly the volatility explanation became Antilochus’ hedgehog, a single ‘‘big’’ idea. Combined with investor pleading for silver bullet solutions to the performance drought

market structural change. Evolution and adaptation are possible in better models but large, abrupt shifts and repeated shifts are immensely difficult to manage well. 180 STATISTICAL ARBITRAGE Statistical arbitrage models have no special protection from the impact of market upheaval. The fact that performance diminished to little more than money market returns in conditions

not evaporate. The environment in which reversion occurred was changed, transforming how reversion is identified. Changes of state are typically unrewarding periods, even negative, for statistical arbitrage. Models, good models, are crafted carefully to adapt to changes in important characteristics of market price behavior pertinent to model predictive performance. But no matter

the central market. There are many buyers and sellers. Many points of agreement. But less unmitigated agitation than the traditional bazaar. Constrained volatility. CHAPTER 11 Statistical Arbitrage Rising . . .to worry about everything is unnerving. It is also counterproductive, for it can result in continual tinkering with a correctly operating system in response

to imagined phantoms in the data. —Statistical Control by Monitoring and Feedback Adjustment, Box and Luceno the end of 2004, statistical arbitrage practitioners had been B ybeleaguered for a year. Investors and commentators cite performance volatility but no return set against market advance (in 2003); adduce accusative

deliver reasonable to good returns while most have failed as described in earlier chapters. This evidence supports the claims of (a) incomplete destruction of traditional statistical arbitrage opportunities and (b) genesis and development of new opportunities, though only proprietary information could reveal to what extent the evidence supports each claim individually. Evidence

system. With trades managed by algorithms implemented on incredibly fast processing computers, what might be done by algorithms designed to go beyond passive market 194 STATISTICAL ARBITRAGE participation to active market determination? Possibly probing other algorithms for weakness, for opportunities to subvert naivete, or to mislead into false judgment. Warfare by another

by catastrophe, an understanding of market forces driving new dynamics and a cogent, plausible theory of how those forces interact and might produce (Continued) 206 STATISTICAL ARBITRAGE continuous moves through a two-dimensional space. The dimensions correspond to a ‘‘normal’’ factor and a ‘‘splitting’’ factor in catastrophe theory parlance. At low levels

Trading and Exchanges: Market Microstructure for Practitioners

by Larry Harris  · 2 Jan 2003  · 1,164pp  · 309,327 words

against markets that quickly and efficiently aggregate new information because the prices in such markets tend to accurately reflect fundamental values. 17.3.2.3 Statistical Arbitrage Statistical arbitrageurs use factor models to generalize the pairs trading strategy to many instruments. Factor models are statistical models that represent instrument returns by a

Hedge Fund Market Wizards

by Jack D. Schwager  · 24 Apr 2012  · 272pp  · 19,172 words

market neutral fund. He established the first successful quant hedge fund. He was the first to implement convertible arbitrage. He was the first to implement statistical arbitrage. He was likely the first person to uncover that Bernie Madoff was a fraud—he developed conclusive evidence of the fraud many years before Harry

strategy when the dealers dramatically widened their bid/ask spreads, wiping out about half the potential profit on each trade. Thorp had successfully traded a statistical arbitrage strategy since the mid-1980s. In 1992, he was asked to run the strategy for a large institutional client. Two years later, he started his

second hedge fund, Ridgeline Partners, to open the statistical arbitrage strategy to other investors. Ridgeline traded very actively, averaging about 6 million shares per day and accounting for about ½ percent of total NYSE volume. Thorp

will not be a long run. But there are situations in the stock market where you get to the long run pretty fast—for example, statistical arbitrage. In statistical arbitrage, you would place tens or hundreds of thousands of trades in a year. The Kelly criterion is the bet size that will produce the

some remote possibility that we overlooked something. There is always the possibility that there is some unknown factor. How did you first get involved in statistical arbitrage? In 1979, we launched a research effort that I called the indicators project. We looked for indicators that might have some forecasting power— items such

so well on a risk-adjusted basis with the strategies it had already that we put the statistical arbitrage strategy aside. It wasn’t clear that the marginal improvement that could have been obtained by adding statistical arbitrage to the existing strategies warranted diverting the resources that would have been needed for its implementation

. One of the calls we received in response to that ad was from Gerry Bamberger, who turned out to be the person who had discovered statistical arbitrage at Morgan Stanley. My recollection is that he developed the strategy around 1982 and was eventually shouldered aside by Nunzio Tartaglia who was his immediate

for an interview. He was very secretive at first, but as soon as he started talking about his strategy, I realized it was the same statistical arbitrage approach we had come up with, except that he had added a dimension that significantly reduced the risk. The innovation that Bamberger had added vis

say, “Why didn’t we think of that?” probably because we had put the project aside. I believe that if we had decided to include statistical arbitrage in our portfolio, we probably would have migrated to the sector neutral approach rather quickly. After Bamberger told you what he was doing, where did

you, and his innovation was one that you could have easily implemented and would likely have done on your own had you not put the statistical arbitrage project aside. So you really didn’t need Bamberger. Given that, what was your motivation for entering into a profit-sharing agreement with him? It

in working with him. He was also someone who was very honest and principled. In a series of articles Thorp wrote about his experiences with statistical arbitrage, he provided the following character sketch of Bamberger: Gerry Bamberger was a tall trim Orthodox Jew with a very high I.Q., an original way

. As I understand, he did go to law school and get his degree, but I don’t know what happened to him afterward. You took statistical arbitrage to the next level by applying factor analysis. Where did it go from there? There was a hiatus in running

statistical arbitrage between the time Bamberger left and the factor analysis approach was implemented. The October 1987 crash occurred during that gap in trading, which is too

spreads became so wide that the transaction costs were 15 percent. So we had to give it up as a strategy. Then I heard that statistical arbitrage was doing well, and one of my largest previous investors wanted me to resurrect it as an investable strategy. In 1992, we restarted the strategy

Princeton Newport Partners when you weren’t trading it? The period between 1989, when we closed Princeton Newport Partners, and August 1992, when we restarted statistical arbitrage, would have been good. We happened to restart trading in a low spot for the strategy, but we stayed with it, and the performance got

and do it. What was your involvement with David Shaw, who was another relatively early practitioner of statistical arbitrage? In 1988, David Shaw had left Solomon and was looking for someone to fund him in a statistical arbitrage startup. I didn’t know exactly what he wanted when he came out here, but we

working on the same thing, and there really wasn’t a match. That is exactly right. What did you do after you shut down the statistical arbitrage fund in 2002? I managed my investments in other people’s hedge funds. Do you have any recommendations on investing in hedge funds? I don

program. So the program had worked well while you’re using it. Reasonably well. It wasn’t as compelling as the Princeton Newport strategies or statistical arbitrage, but it would have been a good product, and it seemed to be better than most of the other trend-following programs out there that

will change their approach as dictated by the market. Finding success in the markets is a dynamic rather than static process. Thorp’s approach to statistical arbitrage is a case study in adapting to markets. The initial concept was to balance long positions in stocks that had gone down the most with

this strategy started to deteriorate, Thorp switched to a variation of the strategy that added sector neutrality to market neutrality. Then when even sector neutral statistical arbitrage started to lose its edge, Thorp switched to a strategy variation that neutralized the portfolio to the various factors. By the time the third iteration

stocks. We will buy the stock and sell the basket, and we will do the same thing with other stocks. So it is basically a statistical arbitrage approach. Yes it is. We have done a phenomenal amount of work on quantitatively selecting single stocks. The implication of that is that there have

down.” Even though it was market neutral? Yes, because I was afraid of a lack of liquidity. Actually, August 2007 was the month when many statistical arbitrage and some market neutral funds got killed. A 5 percent loss for a market neutral fund that month is not really that extreme. I have

efficacy or even become a losing strategy due to changing market conditions. For example, Thorp was able to maintain the strong return/risk of his statistical arbitrage approach by continually adapting it. By the time he got to the third iteration, the original system had significantly degraded. Platt, whose firm BlueCrest trades

market Soviet Union. See Russian financial crisis of 1998 Spear, Leeds & Kellogg (SLK) Specialists Special situation investing Spinoffs. See also Special situation investing Static hedging Statistical arbitrage strategy Statistical prediction Sticky businesses Stops Subprime mortgages/bonds Systematic trend-following strategy Systematic value approach TABX index Tangible book value (TBV) Tangible common equity

) Technology bubble. See also Dot-com bubble TED spread Thames River Capital Management Thorp, Edward firsts achieved by gambling experiments and strategies option pricing model statistical arbitrage strategy warrant pricing model Time arbitrage Time horizons Time value Trade implementation Traders, hiring Trade size. See also Kelly criterion Trading around a position Trading

Frequently Asked Questions in Quantitative Finance

by Paul Wilmott  · 3 Jan 2007  · 345pp  · 86,394 words

does not require rebalancing of positions • A dynamic arbitrage is an arbitrage that requires trading instruments in the future, generally contingent on market states • A statistical arbitrage is not an arbitrage but simply a likely profit in excess of the risk-free return (perhaps even suitably adjusted for risk taken) as predicted

this ‘spread’ is particularly large then you would have sound statistical reasons for thinking the spread might shortly reduce, giving you a possible source of statistical arbitrage profit. This can be the basis for pairs trading. Long Answer The correlations between financial quantities are notoriously unstable. Nevertheless correlations are regularly used in

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation

by Richard Bookstaber  · 5 Apr 2007  · 289pp  · 113,211 words

for more than two years, but when it ended, you didn’t want to be the one holding the tulips. PAIRING OFF: THE EMERGENCE OF STATISTICAL ARBITRAGE In the perfect market paradigm, assets can be bought and sold instantaneously with no transaction costs. For many financial markets, such as listed stocks and

liquidity and the prices of related stocks also became the primary driver of one of the most powerful trading models in the past 20 years—statistical arbitrage. 182 ccc_demon_165-206_ch09.qxd 7/13/07 2:44 PM Page 183 T H E B R AV E N E W

of most price movement; it is at the root of most trading strategies. It is this liquidity-oriented, tectonic market shift that has made statistical arbitrage so powerful. Statistical arbitrage originated in the 1980s from the hedging demand of Morgan Stanley’s equity block-trading desk, which at the time was the center of

less flamboyant, more analytical traders. Used on a different scale and applied for profit making rather than hedging, their pairwise hedges became the genesis of statistical arbitrage trading. Although IT is a support function, during the mid-1980s Morgan Stanley’s technology department was operated as a fiefdom by Bill Cooke, who

made, but the key was to hold many, many pairs to average out the market effects. The pairwise stock trades that form the elements of statistical arbitrage trading in the equity market are just one more flavor of spread trades. On an individual basis, they’re not very good spread trades. It

is the diversification that comes from holding many pairs that makes this strategy a success. But even then, although its name suggests otherwise, statistical arbitrage is a spread trade, not a true arbitrage trade. Bamberger pitched his strategy, and surprisingly, given the politics of the firm, the equity division was

of a mean reversion in price; it can also come from the demand reaching the laggards and having them run up in price as well. Statistical arbitrage is now past its prime. In mid-2002 the performance of stat arb strategies began to wane, and the standard methods have not recovered. This

in the position. The next line of liquidity providers includes hedge funds and other speculators, and then, working on a longer time frame, investors. The statistical arbitrage trader falls into this group. Traders and investors come to the market with a wide range of strategies. Some are value oriented, looking for deviations

type. This provides more information about the specifics of the investment process or strategy. For example, in the neutral classification there is relative value and statistical arbitrage; the event classification would include merger arbitrage, credit arbitrage, and distressed debt. Investment type is the one component of the analysis that will vary over

would include options and volatility trading and some of the fixed income strategies like relative value trading and complex mortgage products. It could also include statistical arbitrage strategies, which are usually computer driven, are often short-term, and are tightly controlled to maintain market neutrality. On the other extreme are the strategies

’s sold itself to Swiss Bank. On the heels of the cash-futures and index arbitrage opportunities came statistical arbitrage, which was the first to emerge in a hedge fund structure. In 1985, the first statistical arbitrage strategy was developed at Morgan Stanley, by Gerry Bamberger, a young information technology (IT) person who had

, 208–209 Soros, George, 179–180 Speculative traders, economic service, 219 Spread trades, holding periods, 83 Standard & Poor’s (S&P) futures contracts, sale, 20 Statistical arbitrage concept, 194 emergence, 182–188 origination, 184 traders, 191–192 Statistics, objective, 134–135 Stavis, Rob, 53, 59, 70–80, 84 Stock clearance/finance, 27

Market Sense and Nonsense

by Jack D. Schwager  · 5 Oct 2012  · 297pp  · 91,141 words

to revisions and override, and thus even computerized trading can reflect human emotions. A classic example of this phenomenon was the meltdown of statistical arbitrage funds in August 2007. Statistical arbitrage is a market neutral, mean reversion strategy that uses mathematical models to identify short-term anomalies in stock movements, balancing sales of stocks

will normally embed multidimensional neutrality (e.g., market, sector, capitalization, region, etc.), significant leverage is typically employed to achieve desired return levels. As a group, statistical arbitrage funds will often have significant overlap in the stocks they are long and short. In August 2007, large liquidations by some

statistical arbitrage funds caused other funds in this strategy to suddenly see their portfolios behaving perversely, with longs falling and shorts simultaneously rallying. The resulting losses were

magnified by the leverage that is an inherent part of the strategy. The sudden breakdown of the models and abrupt losses encouraged liquidation by other statistical arbitrage funds, setting off a chain reaction. In this highly chaotic and stressful environment, human decision making, and with it emotions, played an essential role in

-safety psychology in the market, the huge imbalance between supply and demand can result in managers being forced to liquidate positions at deeply discounted prices. Statistical arbitrage. The premise underlying statistical arbitrage is that short-term imbalances in buy and sell orders cause temporary price distortions, which provide short-term trading opportunities

. Statistical arbitrage is a mean-reversion strategy that seeks to sell excessive strength and buy excessive weakness based on statistical models that define when short-term price

moves in individual equities are considered out of line relative to price moves in related equities. The origin of the strategy was a subset of statistical arbitrage called pairs trading. In pairs trading, the price ratios of closely related stocks are tracked (e.g., Ford and General Motors), and when the mathematical

trading was successful in its early years, but lost its edge as too many proprietary trading groups and hedge funds employed similar strategies. Today’s statistical arbitrage models are far more complex, simultaneously trading hundreds or thousands of securities based on their relative price movements and correlations, subject to the constraint of

.g., market, sector, etc.). Although mean reversion is typically at the core of this strategy, statistical arbitrage models may also incorporate other types of uncorrelated or even inversely correlated strategies, such as momentum and pattern recognition. Statistical arbitrage involves highly frequent trading activity, with trades lasting between seconds and days. Fixed income arbitrage. This

Simons, Jim Soros, George Sortino ratio and Sharpe ratio upward bias in Speculative buying Speculators Standard deviation and expected return maximum drawdown (MDD) Stark & Company Statistical arbitrage Stewart, Jon Stock index Stock market news Stock selection Stock-picking skills Strategy overcrowding Strategy periods Strike price Strong efficiency Subprime ARMs, and foreclosure Subprime

High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems

by Irene Aldridge  · 1 Dec 2009  · 354pp  · 26,550 words

What Constitutes an Event? 167 Forecasting Methodologies 168 Tradable News 173 Application of Event Arbitrage 175 Conclusion 184 CHAPTER 13 Statistical Arbitrage in High-Frequency Settings 185 Mathematical Foundations 186 Practical Applications of Statistical Arbitrage 188 Conclusion 199 viii CONTENTS CHAPTER 14 Creating and Managing Portfolios of High-Frequency Strategies 201 Analytical Foundations of

Identifying trading party order flow through reverse engineering of observed quotes <10 minutes Event trading Short-term trading on macro events <1 hour Deviations arbitrage Statistical arbitrage of deviations from equilibrium: triangle trades, basis trades, and the like <1 day that fly under the radar of many market participants. Proprietary trading desks

“event arbitrage” strategies, work best with positions held from 30 minutes to 1 hour. Chapter 13 addresses a gamut of other strategies collectively known as “statistical arbitrage” with positions often held up to one trading day. Chapter 14 discusses the latest scientific thought in creating multistrategy portfolios. The strategies presented are based

quant models gave rise to “quant trading,” a mathematical model–fueled trading methodology that was a radical departure from established technical and fundamental trading styles. “Statistical arbitrage” strategies (stat-arb for short) became the new stars in the moneymaking arena. As the news of great stat-arb performances spread, their techniques became

of the dependent variable, in addition to separate linear models for large positive and large negative values. Such specification can be used in estimation of statistical arbitrage models. Figure 8.3 illustrates the idea. An example of the TAR of Figure 8.3 may be the following AR(1) specification: ⎧ −5yt−1

have reacted to the news. Short trading windows and estimation of the impact of historical announcements enable profitable trading decisions surrounding market announcements. CHAPTER 13 Statistical Arbitrage in High-Frequency Settings tatistical arbitrage (stat-arb) exploded on the trading scene in the late 1990s, with PhDs in physics and other “hard” sciences

reaping double-digit returns using simple statistical phenomena. Since then, statistical arbitrage has been both hailed and derided. The advanced returns generated before 2007 by many stat-arb shops popularized the technique. Yet some blame stat-arb

, a larger T of at least 30 daily observations is strongly recommended. For robust inferences, a T of 500 daily observations (two years) is desirable. Statistical Arbitrage in High-Frequency Settings 187 3. For each pair of securities, select the ones with the most stable rela- tionship—security pairs that move together

desirable gain, close out the positions. If the prices move against the predicted direction, activate stop loss. Instead of detecting statistical anomalies in price levels, statistical arbitrage can be applied to other variables, such as correlation between two securities and traditional fundamental relationships. The details of implementation of

statistical arbitrage based on fundamental factors are discussed in detail in the following text. Stat-arb strategies can be trained to dynamically adjust to changing market conditions.

standard deviation used in computations can be computed using a limited number of the most recent observations, reflecting the latest economic environment. The shortcomings of statistical arbitrage strategies are easy to see; often enough, detected statistical relationships are random or “spurious” and have little predictive staying power. Yet other statistical relationships, those

, in turn, improves the profitability of trading operations that use stat-arb methodology. In addition to the issues embedded in the estimation of statistical relationships, statistical arbitrage strategies are influenced by numerous adverse market conditions. r The strategies face a positive probability of bankruptcy of the parties issuing one or both of

excess of 4. High-frequency stat-arb delivers even higher performance numbers. PRACTICAL APPLICATIONS OF STATISTICAL ARBITRAGE General Considerations Most common statistical arbitrage strategies relying solely on statistical relationships with no economic background produce fair results, but these Statistical Arbitrage in High-Frequency Settings 189 relationships often prove to be random or spurious. A classic example

spurious statistical relationship is shown by Challe (2003), who documents statistical significance between the occurrence of sunspots and the predictability of asset returns. High-frequency statistical arbitrage based on economic models has ex-ante longer staying power, because it is based on solid economic principles. The stat-arb strategies arbitraging deviations in

, the pair of securities may be two options on the same underlying asset but with different times to expiration. This section discusses numerous examples of statistical arbitrage applied to various securities. Table 13.1 itemizes the strategies discussed subsequently. The selected strategies are intended to illustrate the ideas of fundamental arbitrage. The

be found. Foreign Exchange Foreign exchange has a number of classic models that have been shown to work in the short term. This section summarizes statistical arbitrage applied to triangular arbitrage and uncovered interest rate parity models. Other fundamental foreign exchange models, such as the flexible price 190 HIGH-FREQUENCY TRADING TABLE

Arbitrage Volatility Curve Arbitrage monetary model, the sticky price monetary model, and the portfolio model can be used to generate consistently profitable trades in the statistical arbitrage framework. Triangular Arbitrage Triangular arbitrage exploits temporary deviations from fair prices in three foreign exchange crosses. The following example illustrates triangular arbitrage of EUR/CAD

that affect the prices in the background; by the time the dealer receives the order, the prices may have adjusted to their noarbitrage equilibrium levels. Statistical Arbitrage in High-Frequency Settings 191 Uncovered Interest Parity Arbitrage The uncovered interest parity (UIP) is just one such relation. Chaboud and Wright (2005) find that

estimation: ln(St+1,CHF/USD ) − ln(St,CHF/USD ) = α + β(ln(1 + it,USD ) ∗ − ln(1 + it,CHF )) + εt+1 (13.7) A statistical arbitrage of this relationship would look into the statistical deviations of the two sides of equation (13.7) and make trading decisions accordingly. Equities Examples of

successful statistical arbitrage strategies involving fundamental equities models abound. This section reviews the following popular trading pair trading strategies: different equity classes of the same issuer, market-neutral

of trading models that are based on classical equilibrium finance literature. At core, most market arbitrage models are built on the capital asset pricing 193 Statistical Arbitrage in High-Frequency Settings TABLE 13.2 Closing Price and Daily Volume of Dual-Class Shares on NYSE on January 6, 2009 Company Name Blockbuster

horizon used in the forecast. Variations on the basic market-neutral pair trading strategy include strategies accounting for other security-specific factors, such as equity Statistical Arbitrage in High-Frequency Settings 195 fundamentals. For example, Fama and French (1993) show that the following three-factor model can be successfully used in equity

of large firms and firms with small bid-ask spread, however, exhibit no momentum and sometimes exhibit reversals following high-volume time periods. Profitable trading Statistical Arbitrage in High-Frequency Settings 197 strategies, therefore, involve trading small stocks based on the results of correlation or cointegration with lagged returns of large stocks

as well as the volume of large and small stocks’ records during preceding periods. Futures Statistical arbitrage can also be applied to pairs consisting of a security and its derivative. The derivative of choice is often a futures contract since futures prices

rt is the interest rate at time t. For foreign exchange futures, rt is the differential between domestic and foreign interest rates. Basis Trading The statistical arbitrage between a futures contract and the underlying asset is known as “basis trading.” As with equity pairs trading, the basis-trading process follows the following

log prices of constituent indexes in local currencies as independent (explanatory) variables: E AF Et = α + β1 x1,t + . . . + βn xn,t + εt (13.17) Statistical Arbitrage in High-Frequency Settings 199 where the statistically significant β 1 . . . β n coefficients indicate optimal allocations pertaining to their respective country indices x1 . . . xn

long in the indexes in proportions identified in step 2 and shorting EAFE. Options In options and other derivative instruments with a nonlinear payoff structure, statistical arbitrage usually works between a pair of instruments written on the same underlying asset but having one different characteristic. The different characteristic is most often either

the expiration date or the strike price of the derivative. The strategy development proceeds along the steps noted in the previous sections. CONCLUSION Statistical arbitrage is powerful in high-frequency settings as it provides a simple set of clearly defined conditions that are easy to implement in a systematic fashion

in high-frequency settings. Statistical arbitrage based on solid economic theories is likely to have longer staying power than strategies based purely on statistical phenomena. CHAPTER 14 Creating and Managing Portfolios

, Michael, 75, 91–92, 95, 257, 268–269 tick data and, 115, 117, 118, 120–121, 124 “Dark” liquidity pools, 12, 117 Data mining, in statistical arbitrage, 185 Datar, Vinay T, 195 Data set testing, automated system implementation, 246–247 Demsetz, Harold, 130 Dennis, Patrick J., 146 Derivatives, fundamental analysis and, 14

event arbitrage, 168–171 Disclosure specifications, for orders, 69–70 Discrete pair-wise (DPW) optimization, 214–215 Dodd, David, 14 330 Dual-class share strategy, statistical arbitrage, 192 Dufour, A., 123 Duration models, tick data and, 121–123 Dynamic risk hedging, 269 Easley, David, 121, 122, 148, 156 Econometric concepts, 91–114

, 101, 207, 274, 278 INDEX Engle, R.F., 102, 103, 123 Equities: algorithmic trading, 18–19 event arbitrage, 179–181 fundamental analysis, 14 liquidity, 38 statistical arbitrage, 191–197 suitability for high-frequency trading, 46 transparent costs, 287 Error correction model (ECM), 101–102 Errunza, V., 180 Estimation errors, portfolio optimization, 209

methodologies, event arbitrage, 168–173 Foreign currency exchange, 43–46 algorithmic trading and, 19 event arbitrage, 175–178 fundamental analysis and, 14 liquidity and, 38 statistical arbitrage, 189–191 transparent costs, 287 Foster, F., 158 Foucault, T., 66–67, 68, 122–123, 139, 142, 163, 274 Frankfurter, G.M., 209 Franklin, Benjamin

., 57, 58 Futures: algorithmic trading, 19 commodity markets, 46–47 event arbitrage, 183 fixed-income markets, 40–42 foreign exchange markets, 43–46 liquidity, 38 statistical arbitrage, 197–198 Galai, D., 130 Gambler’s Ruin Problem, 135–137, 268 Garlappi, L., 210 Garman, M.B., 107, 135–137 Gatev, Evan, 188 Generalized

MatLab, 25 Maximum drawdown, 50–51 McQueen, Grant V., 179 Mean absolute deviation (MAD), 220–221 Mean absolute percentage error (MAPE), 221 Mean-reversion. See Statistical arbitrage strategies Mean squared error (MES), 220–221 Mech, T., 86 Mehdian, S.M., 181 Meissner, G., 270 Mende, Alexander, 156–157 Mendelson, H., 37–38

costs, 294 Option-based portfolio insurance (OBPI), 211–212 Options: algorithmic trading and, 19 commodity markets, 46–47 electronic trading of, 9 liquidity and, 38 statistical arbitrage, 199 Order aggressiveness, information trading on, 157–160 Order distributions, 70–73 Order fill rate, 278 Order flow, information trading on, 160–163 Orders by

Standard & Poor’s, 261 Standard deviation, performance measurement and, 49–51 Standard iceberg (SI) orders, 69 Static equilibrium models, inventory trading and, 131 Stationarity, 98 Statistical arbitrage strategies, 15, 185–199 mathematical foundations, 186–188 practical applications, 188–199 shortcomings of, 188 Statistical models, for risk measurement, 254 Statistical properties of returns

, 68 measures of, 93 performance measurement and, 49–51 volatility clustering, 102–103 volatility modeling, 102–107 Volume-weighted average price (VWAP), 297 Voting rights, statistical arbitrage, 192 Wagner, W., 300 Wang, Jiang, 196 Wang, J., 274, 279 Wang, T., 210 Wang, X., 131, 139, 142 Warner, J.B., 277 Wasserfallen, W

Finding Alphas: A Quantitative Approach to Building Trading Strategies

by Igor Tulchinsky  · 30 Sep 2019  · 321pp

alpha, and the evaluation and improvement of quality alphas. The key technical aspects discussed in this section are turnover, backtesting, fundamental analysis, equity price volume, statistical arbitrage, overfitting, and alpha diversity. Part III explores ad hoc topics in alpha design, including alpha design for various asset classes like futures and currencies, the

stay relevant. In the next section, we will take a closer look at the alphas driving the quantitative strategies described above. 10 Finding Alphas STATISTICAL ARBITRAGE The term “statistical arbitrage” (stat arb) is sometimes used to describe a trading strategy based on the monetization of systematic price forecasts, or alphas. Unlike pure arbitrage, when

given stock on a given date in the future? Unfortunately, we probably cannot make single predictions with any reasonable confidence. It is the nature of statistical arbitrage that prediction is possible only in a “statistical” sense: only over a large number of predictions do random errors average out to a usable level

of accuracy in the aggregate. More interestingly, there are many ways of making such statistical price predictions. STATISTICAL ARBITRAGE The key underlying assumption of statistical arbitrage is that the prices of financial instruments are driven by consistent rules, which can be discovered from their historical behavior and applied to

the benefit of the improved fit. CONCLUSION The prices of financial instruments are driven by various rules and factors, which can form the basis of statistical arbitrage alphas. All alphas have failure modes, and no alpha works on all instruments under all conditions, but a reasonable combination of real alphas covering different

instead of a broader universe of potentially unfamiliar names. Another form of familiarity bias is to pursue exclusively a certain style of signals, such as statistical arbitrage, factor- and event-driven strategies, and so forth. Narrow Framing Narrow framing is the tendency to make investment decisions without considering the larger portfolio. One

social media. NEWS IN ALPHAS It is not easy for machines to accurately parse and interpret the meaning of news. As in other areas in statistical arbitrage, an algorithm has the advantages of fast response time and broad coverage, but at the expense of weaker accuracy than a human analyst. Nowadays, trading

broad market, specific sectors, markets in foreign countries, bond indexes, commodities, and currencies. Such variety makes it possible for short-term alpha traders to do statistical arbitrage across instruments. At the same time, a broad-based index ETF itself can be considered a well-diversified investment for some longer-term investors. RISKS

OPPORTUNITIES The huge number and wide variety of ETF instruments, together with the availability of different datasets, make it possible to find alphas and take statistical arbitrage in a manner similar to equities: coming up with an idea, designing a numerical alpha formula, assigning alpha values to the ETF instruments, and then

. Nonetheless, by studying such patterns one may come up with interesting technical or macro indicators, which, in turn, can be implemented as alphas to capture statistical arbitrage across some correlated instruments. ETFs and Alpha Research239 CHALLENGES IN ETF ALPHA RESEARCH From the diverse pool of ETF instruments, researchers can apply their

losses 17–21 data-based design 5 definition 3 evaluation 13, 20–21 existence of 11–12 expressions 4 implementation 12–13 quality evaluation 5 statistical arbitrage 10–11 step-by-step construction 5, 41 UnRule 17–18, 20–21 value of 27–30 batch statistics 117–118 from factors 148 WebSim

–117 cross-validation 75 drawdowns 107 importance of 70–71 out-of-sample tests 74 overfitting 72–75 samples selection 74–75 simulation 71–72 statistical arbitrage 69–70 WebSim 33–41 backwardation 248 balance sheets 143 band-pass filters 128 batch statistics 117–118 behavioral bias 80–82 behavioral economics 11

Transform 91 five-day reversion alpha 55–59 Float Boost 125 forecasting behavioral economics 11–12 computer adoption 7–9 frequencies 27 horizons 49–50 statistical arbitrage 10–11 UnRule 17–21 see also predictions formation of the industry 8–9 formulation bias 80 forward-looking bias 72 forwards 241–249 checklist

evaluation 13–14 exchange-traded funds 231–240 implementation 12–13 intraday data 207–216 machine learning 121–126 opportunities 14–15 perspectives 7–15 statistical arbitrage 10–11 triple-axis plan 83–88 restricted Boltzmann machine (RBM) 125 Reuleaux triangle 70 reversion alphas, five-day 55–59 risk 101–110 arbitrage

301 special considerations, financial statements 147 spin-offs 200–202 split-offs 200–202 spreads and liquidity 51 and volatility 51–52 stat arb see statistical arbitrage statistical arbitrage (stat arb) 10–11, 69–70 statistical models, machine learning 123 step-by-step construction 5, 41 storage costs 247–248 storytelling 80 subjectivity 17

How I Became a Quant: Insights From 25 of Wall Street's Elite

by Richard R. Lindsey and Barry Schachter  · 30 Jun 2007

management’s range is going to increase dramatically over the next 10 years. Today when people think about quantitative asset management they usually think about statistical arbitrage or global tactical asset allocation. Over time, I see quantitative methods being applied to an increasing range of products. Driving this will be increased liquidity

inflection point was in 1995, the year Cooper Neff was acquired by French bank BNP. Active Portfolio Strategies, or APS, was our version of equity statistical arbitrage, but no one ever used those terms at the firm. To us, equity stat arb meant pairs trading or exploiting the residuals of an equity

my dissertation was a simulation study I never published that I still think is neat and an early study of what is now known as statistical arbitrage, where I concluded that it’s interesting, but doesn’t cover transactions costs, and then ignored several easy improvements, thereby not participating in one of

More Money Than God: Hedge Funds and the Making of a New Elite

by Sebastian Mallaby  · 9 Jun 2010  · 584pp  · 187,436 words

. The computer may find fake ghosts—patterns that exist for no reason beyond chance, and that consequently have no predictive value. Eric Wepsic, who runs statistical arbitrage at D. E. Shaw, gives the example of the Super Bowl: It used to be said that if a team from the original National Football

what Shaw does, even if the firm does some of it. Again, this presents a contrast with Renaissance. Whereas D. E. Shaw grew out of statistical arbitrage in equities, with strong roots in fundamental intuitions about stocks, Renaissance grew out of technical trading in commodities, a tradition that treats price data as

alpha. The great thing about alpha was that it could be explained: Strategies such as Tom Steyer’s merger arbitrage or D. E. Shaw’s statistical arbitrage delivered uncorrelated, market-beating profits in a way that could be understood, replicated, and manufactured by professionals. And so the era of the manufacturer arrived

founder, Nick Maounis, was a convertible-arbitrage specialist by background, but he had hired experts in merger arbitrage, long/short equity investing, credit arbitrage, and statistical arbitrage; and in 2002, following the collapse of the corrupt energy company Enron, Maounis had snapped up several stranded employees to open an energy-trading operation

of Amaranth’s capital was focused on convertible arbitrage. Scroll forward another year, and the portfolio began to shift into bond trades, and then into statistical arbitrage and energy. There seemed no good reason for a pension plan to hire a fund of funds when it could go directly to Amaranth, bypassing

. Many of Amaranth’s strategies were faring poorly. Convertible arbitrage had hit a wall and showed no sign of recovering. Maounis had invested heavily in statistical arbitrage, telling colleagues he wanted a piece of James Simons’s action, but he had little to show for it. The one star act in the

since the year’s start, Amaranth was up roughly six times more; Maounis began to say that, although he had failed to strike gold in statistical arbitrage, he had discovered another secret weapon that was just as potent.11 And yet to some savvy observers, Hunter’s extraordinary profits were cause for

hedge funds make money by driving prices away from extremes and toward their rational level. This is what arbitrage funds do, including the fast-trading statistical arbitrage funds that are frequently excoriated. Equally, when a Julian Robertson–style stock picker buys underpriced companies and shorts overpriced ones, he is moving stocks closer

Sunday, August 5, and instructed them to cut risk. But the meeting did not include Aaron Sosnick, who managed the capital that Caxton committed to statistical arbitrage. Rather, Sosnick had cut his leverage substantially in the previous several days, so was not selling aggressively on Monday, August 6, the start of the

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