random walk

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Eleventh Edition)

by Burton G. Malkiel  · 5 Jan 2015  · 482pp  · 121,672 words

and Ambiguity in Their Forecasts Is There Momentum in the Stock Market? Just What Exactly Is a Random Walk? Some More Elaborate Technical Systems The Filter System The Dow Theory The Relative-Strength System Price-Volume Systems Reading Chart Patterns Randomness Is Hard to Accept A Gaggle of Other Technical Theories to Help

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Guide to Mutual Funds and ETFs Acknowledgments from Earlier Editions Index PREFACE IT HAS NOW been over forty years since the first edition of A Random Walk Down Wall Street. The message of the original edition was a very simple one: Investors would be far better off buying and holding an

…

business school will find this new edition rewarding reading. This edition takes a hard look at the basic thesis of earlier editions of Random Walk—that the market prices stocks so efficiently that a blindfolded chimpanzee throwing darts at the stock listings can select a portfolio that performs as well as those managed

…

AND CASTLES IN THE AIR What is a cynic? A man who knows the price of everything, and the value of nothing. — Oscar Wilde, Lady Windermere’s Fan IN THIS BOOK I will take you on a random walk down Wall Street, providing a guided tour of the complex world of finance and

…

individuals of all age groups specific portfolio recommendations for meeting their financial goals, including advice on how to invest in retirement. WHAT IS A RANDOM WALK? A random walk is one in which future steps or directions cannot be predicted on the basis of past history. When the term is applied to the stock

…

, the term “random walk” is an obscenity. It is an epithet coined by the academic world and hurled insultingly at

…

with one of two techniques, called fundamental analysis and technical analysis, which we will examine in Part Two. Academics parry these tactics by obfuscating the random-walk theory with three versions (the “weak,” the “semi-strong,” and the “strong”) and by creating their own theory, called the new investment technology. This

…

with deadly intent because the stakes are tenure for the academics and bonuses for the professionals. That’s why I think you’ll enjoy this random walk down Wall Street. It has all the ingredients of high drama—including fortunes made and lost and classic arguments about their cause. But before we

…

pay for it.) HOW THE RANDOM WALK IS TO BE CONDUCTED With this introduction out of the way, come join me for a random walk through the investment woods, with an ultimate stroll down Wall Street. My first task will be to acquaint you with the historical patterns of pricing and how they bear on

…

project that corporate earnings and dividends will also increase at a faster rate, causing stock prices to rise. A fuller discussion of inflation, interest rates, and stock prices is contained in Chapter 13. 6 TECHNICAL ANALYSIS AND THE RANDOM-WALK THEORY Things are seldom what they seem. Skim milk masquerades as cream. — Gilbert and

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the runs of luck in the fortunes of any gambler. This is what economists mean when they say that stock prices behave very much like a random walk. JUST WHAT EXACTLY IS A RANDOM WALK? To many people this appears to be errant nonsense. Even the most casual reader of the financial pages can easily

…

toss was still 50 percent. Mathematicians call a sequence of numbers produced by a random process (such as those on our simulated stock chart) a random walk. The next move on the chart is completely unpredictable on the basis of what has happened before. The stock market does not conform perfectly to

…

, investors often only partially adjust their estimates of the appropriate price of the stock. Slow adjustment can make stock prices rise steadily for a period, imparting a degree of momentum. The failure of stock prices to measure up perfectly to the definition of a random walk led the financial economists Andrew Lo and A. Craig

…

MacKinlay to publish a book entitled A Non-Random Walk Down Wall Street. In addition to some evidence of short-term momentum

…

—sometimes they overreact and price reversals can occur with terrifying suddenness. We shall see in chapter 11 that investment funds managed in accordance with a momentum strategy started off with subpar results. And even during periods when momentum is present (and the market fails to behave like a random walk), the systematic relationships

…

dependencies are far greater than any profits that might be obtained. Thus, an accurate statement of the “weak” form of the random-walk hypothesis goes as follows: The history of stock price movements contains no useful information that will enable an investor consistently to outperform a buy-and-hold strategy in managing a

…

portfolio. If the weak form of the random-walk hypothesis is valid, then, as my colleague Richard Quandt says, “Technical analysis is akin to

…

the placebo of a buy-and-hold strategy. Technical methods cannot be used to make useful investment strategies. This is the fundamental conclusion of the random-walk theory. A former colleague of mine believed that the capitalist system would weed out all useless growths such as the flourishing technicians. “The days of

…

yachts for the customers, but they do help generate the trading that provides yachts for the brokers. APPRAISING THE COUNTERATTACK As you might imagine, the random-walk theory’s dismissal of charting is not altogether popular among technicians. Academic proponents of the theory are greeted in some Wall Street quarters with as

…

“just plain academic drivel.” Let us pause, then, and appraise the counterattack by beleaguered technicians. Perhaps the most common complaint about the weakness of the random-walk theory is based on a distrust of mathematics and a misconception of what the theory means. “The market isn’t random,” the complaint goes, “and

…

market prices, and so does the temper of the crowd. We saw ample evidence of this in earlier chapters of the book. But, even if markets were dominated during certain periods by irrational crowd behavior, the stock market might well still be approximated by a random walk. The original illustrative analogy of a random walk

…

an earlier item of news, then it wouldn’t be news at all. The weak form of the random-walk theory says only that stock prices cannot be predicted on the basis of past stock prices. The technical analyst will also cite chapter and verse that the academic world has certainly not tested every

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—the efficient-market hypothesis. The “narrow” (weak) form of the EMH says that technical analysis—looking at past stock prices—cannot help investors. Prices move from period to period very much like a random walk. The “broad” (semi-strong and strong) forms state that fundamental analysis is not helpful either. All that is known

…

academics and practitioners who conclude that psychology, not rationality, rules the market, and that there is no such thing as a random walk. They argue that markets are not efficient, that market prices are predictable, and that a number of investment strategies can be followed to “beat the market.” These include a number

…

funds remain the undisputed champions in taking the most profitable stroll through the market. THE ROLE OF RISK The efficient-market hypothesis explains why the random walk is possible. It holds that the stock market is so good at adjusting to new information that no one can predict its future course in

…

rational valuation. Market prices can be expected to deviate substantially from those that could be expected in an efficient market. The remainder of this chapter explores the key arguments of behavioral finance in explaining why markets are not efficient and why there is no such thing as a random walk down Wall Street

…

fact, despite considerable efforts to tease some form of predictability out of stock-price data, the development of stock prices from period to period is very close to a random walk, where price changes in the future are essentially unrelated to changes in the past. Biases in judgments are compounded (get ready for some additional

…

, found that a sequence of random numbers had the same appearance as a time series of stock prices. But even though the earliest studies supported a general finding of randomness, more recent work indicated that the random-walk model does not strictly hold. Some patterns appear to exist in the development of stock

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real expertise does exist, they are unlikely to find it. But if you are sensible, you will take your random walk only after you have made detailed and careful preparations. Even if stock prices move randomly, you shouldn’t. Think of the advice that follows as a set of warm-up exercises that

…

of all the major securities. Finally, a wealth of information, including security analysts’ recommendations, is available on the Internet. In the first edition of A Random Walk Down Wall Street, over forty years ago, I proposed four rules for successful stock selection. I find them just as serviceable today. In abridged form

…

on which dividends could be earned for every $3 you invested. So even if the funds just equaled the market return, as believers in the random walk would expect, you would beat the averages. It was like having a $100 savings account paying 5 percent interest. You deposit $100 and earn $

…

time it doesn’t surprise me that anomalies do exist. There may be some $100 bills around at times, and I’ll certainly interrupt my random walk to stoop and pick them up. INVESTMENT ADVISERS If you follow the recommendations in this book carefully, you really don’t need an investment adviser

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Company, 120 Eastman Kodak, 68, 161 eBay, 85, 324 education, saving for, see “529” college saving accounts Efficient Market Hypothesis (EMH), 284–87 see also random-walk theory Einstein, Albert, 119, 292 electronics industry, 57–59, 165 electronic trading, 325 Elliot, R. N., 151–52 Elliot wave theory, 151–52 Ellis, Charles

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265, 274 friends, 253 FTC (Federal Trade Commission), 65 fundamental analysis, 26, 110–33, 160–85, 408 defined, 110 firm-foundation theory and, 110, 119 random-walk theory and, 182–84 technical analysis used with, 130–33 technical analysis vs., 110–11, 118–19 technique of, 118–26 gambling, patterns and, 156

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Hong, Harrison, 242, 253 Hoover, Herbert, 53 “hot hand” phenomenon, 145 hot streaks, 235–36 hot tips, 258 housing bubble, 97–104, 105–6, 251 random-walk theory and, 105–6 Hulbert, Mark, 148 Hydro-Space Technology, 58 Ibbotson, Roger, 349–50, 351 Ibbotson Associates, 194, 265 IBM (International Business Machines), 57

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70 NINJA loans, 101 Nobel Prize, 35, 183, 197, 209 No-Brainer Step, 379, 380–82 NO-DOC loans, 101 no-equity loans, 100 Non-Random Walk Down Wall Street, A (Lo and MacKinlay), 139 Nortel Networks, 83, 90, 161, 166 NSM, see National Student Marketing NTT Corporation, 76 nucleus theory of

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tossings, 138–39 trends revealed by, 112–15, 134–41, 144–45 stock market: in 1980s, 341–43 call options in, 39 efficiency of, see random-walk theory emerging markets vs., 204–8 hot streaks in, 235–36 Japanese, boom and bust in, 76–78 Japanese, collapse and correction of (1992), 77

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33 fundamental analysis vs., 110–11, 118–19 gurus, 151–54 implications for investors of, 158 limitations of, 116–17, 135–36, 154–58, 160 random-walk theory and, 137–41, 154–57 rationale for, 115–16 types of systems of, 141–51 see also chartists; stock charts Technical Analysis of Stock

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-4830 Book design by Chris Welch Production manager: Julia Druskin The Library of Congress has cataloged the printed edition as follows: Malkiel, Burton Gordon. A random walk down Wall Street : the time-tested strategy for successful investing / Burton G. Malkiel. — [Revised and updated edition]. pages cm Includes index. ISBN 978-0-393

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-24611-7 (hardcover) 1. Investments. 2. Stocks. 3. Random walks (Mathematics) I. Title. HG4521.M284 2015 332.6—dc23 2014041927 ISBN 978-0-393-24895-1 (e-book) W. W. Norton & Company, Inc. 500 Fifth

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and Ambiguity in Their Forecasts Is There Momentum in the Stock Market? Just What Exactly Is a Random Walk? Some More Elaborate Technical Systems The Filter System The Dow Theory The Relative-Strength System Price-Volume Systems Reading Chart Patterns Randomness Is Hard to Accept A Gaggle of Other Technical Theories to Help

…

and Ambiguity in Their Forecasts Is There Momentum in the Stock Market? Just What Exactly Is a Random Walk? Some More Elaborate Technical Systems The Filter System The Dow Theory The Relative-Strength System Price-Volume Systems Reading Chart Patterns Randomness Is Hard to Accept A Gaggle of Other Technical Theories to Help

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing

by Burton G. Malkiel  · 10 Jan 2011  · 416pp  · 118,592 words

A RANDOM WALK DOWN WALL STREET A RANDOM WALK DOWN WALL STREET The Time-Tested Strategy for Successful Investing BURTON G. MALKIEL W. W. NORTON & COMPANY New York • London Copyright © 2011, 2007, 2003, 1999

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to Permissions, W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, NY 10110 Library of Congress Cataloging-in-Publication Data Malkiel, Burton Gordon. A random walk down Wall Street: the time-tested strategy for successful investing / Burton G. Malkiel. p. cm. Rev. ed. ISBN: 978-0-393-08169-5 1. Investments

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. 2. Stocks. 3. Random walks (Mathematics) I. Title. HG4521.M284 2011 332.601’519282—dc22 2010041866 W. W. Norton & Company, Inc. 500 Fifth Avenue, New York, N.Y. 10110 www

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SKIPPER CONTENTS Preface Acknowledgments from Earlier Editions Part One STOCKS AND THEIR VALUE 1. FIRM FOUNDATIONS AND CASTLES IN THE AIR What Is a Random Walk? Investing as a Way of Life Today Investing in Theory The Firm-Foundation Theory The Castle-in-the-Air Theory How the

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Random Walk Is to Be Conducted 2. THE MADNESS OF CROWDS The Tulip-Bulb Craze The South Sea Bubble Wall Street Lays an Egg An Afterword 3

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and Ambiguity in Their Forecasts Is There Momentum in the Stock Market? Just What Exactly Is a Random Walk? Some More Elaborate Technical Systems The Filter System The Dow Theory The Relative-Strength System Price-Volume Systems Reading Chart Patterns Randomness Is Hard to Accept A Gaggle of Other Technical Theories to Help

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’s Address Book and Reference Guide to Mutual Funds PREFACE IT HAS NOW been forty years since I began writing the first edition of A Random Walk Down Wall Street. The message of the original edition was a very simple one: Investors would be far better off buying and holding an

…

business school will find this new edition rewarding reading. This edition takes a hard look at the basic thesis of earlier editions of Random Walk—that the market prices stocks so efficiently that a blindfolded chimpanzee throwing darts at the stock listings can select a portfolio that performs as well as those managed

…

AND CASTLES IN THE AIR What is a cynic? A man who knows the price of everything, and the value of nothing. —Oscar Wilde, Lady Windermere’s Fan IN THIS BOOK I will take you on a random walk down Wall Street, providing a guided tour of the complex world of finance and

…

individuals of all age groups specific portfolio recommendations for meeting their financial goals, including advice on how to invest in retirement. WHAT IS A RANDOM WALK? A random walk is one in which future steps or directions cannot be predicted on the basis of past history. When the term is applied to the stock

…

Street, the term “random walk” is an obscenity. It is an epithet coined by the academic world and hurled insultingly at

…

with one of two techniques, called fundamental analysis and technical analysis, which we will examine in Part Two. Academics parry these tactics by obfuscating the random-walk theory with three versions (the “weak,” the “semi-strong,” and the “strong”) and by creating their own theory, called the new investment technology. This

…

with deadly intent because the stakes are tenure for the academics and bonuses for the professionals. That’s why I think you’ll enjoy this random walk down Wall Street. It has all the ingredients of high drama—including fortunes made and lost and classic arguments about their cause. But before

…

pay for it.) HOW THE RANDOM WALK IS TO BE CONDUCTED With this introduction out of the way, come join me for a random walk through the investment woods, with an ultimate stroll down Wall Street. My first task will be to acquaint you with the historical patterns of pricing and how they bear on

…

of fundamentalists. Together they should help us evaluate how much confidence we should have in the advice of professional investment people. TECHNICAL ANALYSIS AND THE RANDOM-WALK THEORY Things are seldom what they seem. Skim milk masquerades as cream. —Gilbert and Sullivan, H.M.S. Pinafore NOT EARNINGS, NOR dividends, nor

…

the runs of luck in the fortunes of any gambler. This is what economists mean when they say that stock prices behave very much like a random walk. JUST WHAT EXACTLY IS A RANDOM WALK? To many people this appears to be errant nonsense. Even the most casual reader of the financial pages can easily

…

toss was still 50 percent. Mathematicians call a sequence of numbers produced by a random process (such as those on our simulated stock chart) a random walk. The next move on the chart is completely unpredictable on the basis of what has happened before. The stock market does not conform perfectly to

…

investors often only partially adjust their estimates of the appropriate price of the stock. Slow adjustment can make stock prices rise steadily for a period, imparting a degree of momentum. The failure of stock prices to measure up perfectly to the definition of a random walk led the financial economists Andrew Lo and A. Craig

…

MacKinlay to publish a book entitled A Non-Random Walk Down Wall Street. In addition to some evidence of short-term momentum

…

to news—sometimes they overreact and price reversals can occur with terrifying suddenness. Two mutual funds managed in accordance with a momentum strategy started off with distinctly subpar returns. And even during periods when momentum is present (and the market fails to behave like a random walk), the systematic relationships that exist are

…

dependencies are far greater than any profits that might be obtained. Thus, an accurate statement of the “weak” form of the random-walk hypothesis goes as follows: The history of stock price movements contains no useful information that will enable an investor consistently to outperform a buy-and-hold strategy in managing a

…

portfolio. If the weak form of the random-walk hypothesis is valid, then, as my colleague Richard Quandt says, “Technical analysis is akin

…

the placebo of a buy-and-hold strategy. Technical methods cannot be used to make useful investment strategies. This is the fundamental conclusion of the random-walk theory. A former colleague of mine believed that the capitalist system would weed out all useless growths such as the flourishing technicians. “The days of

…

yachts for the customers, but they do help generate the trading that provides yachts for the brokers. APPRAISING THE COUNTERATTACK As you might imagine, the random-walk theory’s dismissal of charting is not altogether popular among technicians. Academic proponents of the theory are greeted in some Wall Street quarters with as

…

“just plain academic drivel.” Let us pause, then, and appraise the counterattack by beleaguered technicians. Perhaps the most common complaint about the weakness of the random-walk theory is based on a distrust of mathematics and a misconception of what the theory means. “The market isn’t random,” the complaint goes, “and

…

market prices, and so does the temper of the crowd. We saw ample evidence of this in earlier chapters of the book. But, even if markets were dominated during certain periods by irrational crowd behavior, the stock market might well still be approximated by a random walk. The original illustrative analogy of a random walk

…

an earlier item of news, then it wouldn’t be news at all. The weak form of the random-walk theory says only that stock prices cannot be predicted on the basis of past stock prices. Thus, criticisms of the type quoted above are not valid. The technical analyst will also cite chapter and

…

the efficient-market theory. The “narrow” (weak) form of the theory says that technical analysis—looking at past stock prices—cannot help investors. Prices move from period to period very much like a random walk. The “broad” (semi-strong and strong) forms state that fundamental analysis is not helpful either. All that is known

…

academics and practitioners who conclude that psychology, not rationality, rules the market, and that there is no such thing as a random walk. They argue that markets are not efficient, that market prices are predictable, and that a number of investment strategies can be followed to “beat the market.” Then I conclude by

…

critics, it remains the undisputed champion in taking the most profitable stroll through the market. THE ROLE OF RISK Efficient-market theory explains why the random walk is possible. It holds that the stock market is so good at adjusting to new information that no one can predict its future course in

…

rational valuation. Market prices can be expected to deviate substantially from those that could be expected in an efficient market. The remainder of this chapter explores the key arguments of behavioral finance in explaining why markets are not efficient and why there is no such thing as a random walk down Wall Street

…

fact, despite considerable efforts to tease some form of predictability out of stock-price data, the development of stock prices from period to period is very close to a random walk, where price changes in the future are essentially unrelated to changes in the past. Biases in judgments are compounded (get ready for some

…

of financial economists, Andrew Lo (with A. Craig MacKinlay) of the Massachusetts Institute of Technology, published a book in the late 1990s entitled A Non-Random Walk Down Wall Street. And behavioralists such as Richard Thaler have suggested that some predictable patterns can be used by savvy investors to implement successful investment

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above, is not efficient and that there is no such thing as a profitable random walk through it. I will review all the recent research proclaiming the demise of the efficient-market theory and purporting to show that market prices are, in fact, predictable. My conclusion is that such obituaries are greatly exaggerated

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I am more convinced than ever of the wisdom of that advice, and I am persuaded that those who take potshots at the market’s random walk inevitably miss their target. POTSHOTS THAT COMPLETELY MISS THE TARGET Some attempts to discredit the unpredictability of the market are so ridiculous that perhaps they

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memory—the way a stock price behaved in the past is not useful in divining how it will behave in the future. Just because a stock has been rising doesn’t mean it will keep on rising. Several later studies have been inconsistent with this pure random-walk model. There is some degree

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prevent us from interpreting the empirical results reported above as an indication that markets are inefficient. While the stock market may not be a perfect random walk, it is important to distinguish statistical significance from economic significance. The statistical dependencies giving rise to momentum, in fact, are extremely small. Anyone who

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be. THE SURVIVORSHIP BIAS EFFECT* When all mutual funds sold to the public are considered, the original thesis propounded by the first edition of A Random Walk Down Wall Street in 1973 holds up remarkably well. Over the entire period since the first edition of this book, about two-thirds of the

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to eat well or sleep well. —J. Kenfield Morley, Some Things I Believe PART FOUR IS a how-to-do-it guide for your random walk down Wall Street. In this chapter, I offer general investment advice that should be useful to all investors, even if they don’t believe that

…

real expertise does exist, they are unlikely to find it. But if you are sensible, you will take your random walk only after you have made detailed and careful preparations. Even if stock prices move randomly, you shouldn’t. Think of the advice that follows as a set of warm-up exercises that

…

of all the major securities. Finally, a wealth of information, including security analysts’ recommendations, is available on the Internet. In the first edition of A Random Walk Down Wall Street, almost forty years ago, I proposed four rules for successful stock selection. I find them just as serviceable today. In abridged form

…

on which dividends could be earned for every $3 you invested. So even if the funds just equaled the market return, as believers in the random walk would expect, you would beat the averages. It was like having a $100 savings account paying 5 percent interest. You deposit $100 and earn

…

it doesn’t surprise me that anomalies do exist. There may be some $100 bills around at times, and I’ll certainly interrupt my random walk to stoop and pick them up. SOME LAST REFLECTIONS ON OUR WALK We are now at the end of our walk. Let’s look back

Beyond the Random Walk: A Guide to Stock Market Anomalies and Low Risk Investing

by Vijay Singal  · 15 Jun 2004  · 369pp  · 128,349 words

Sevebeck of K&B Designs, and especially, Sonia Mudbhatkal of Virginia Tech. BEYOND THE RANDOM WALK This page intentionally left blank 1 Market Efficiency and Anomalies This chapter addresses common questions related to market efficiency and anomalies. If prices properly reflect available information, then markets are said to be efficient. Although markets are

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or 1999 on the belief that the stocks were overvalued would have been wiped out before the prices eventually fell. In fact, many short sellers went bankrupt in the late 1990s 5 6 Beyond the Random Walk due to the ascent of the stock market. Even Warren Buffett, whom many regard as a

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may be reluctant to trade if large dollar positions cannot be taken without moving the price or if the bid-ask spreads are large. For example, the January effect has been known 15 16 Beyond the Random Walk for decades and is caused by tax-loss selling of small-size stocks. Nonetheless, the

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, Andrew W., and Craig MacKinlay. 1990. Data Snooping Biases in Tests of Financial Asset Pricing Models. Review of Financial Studies 3, 431–67. — — — . 1999. A Non-Random Walk Down Wall Street (Princeton: Princeton University Press). Malkiel, Burton. 1989. A Random Walk Down Wall Street (New York: Norton). Michaud, Richard O. 1999. Investment Styles, Market Anomalies

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to Behavioral Finance (Oxford: Oxford University Press). Thaler, Richard H. (editor). 1993. Advances in Behavioral Finance (New York: Russell Sage Foundation). 21 22 Beyond the Random Walk Notes 1. Correct prices are difficult to obtain because it is impossible to predict the future. However, market efficiency requires only that

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) that are likely have actively traded options. However, the Russell 2000 contains many stocks with insufficient volume or with a very low stock price. 49 50 Beyond the Random Walk Table 3.2 Weekend Effect During 1992–2001 (in percent) Year 1992–1993 mean 1992–1993 median 1994–1995 mean 1994–1995 median

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nontrading hours can be devastating to the short sellers. 55 56 Beyond the Random Walk 4 Short-Term Price Drift Events associated with high-quality information signals tend to exhibit price continuations. The quality of information is characterized by the magnitude of price change, volume, and public dissemination of information. There is evidence to suggest

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transaction costs, that is, 15–36 percent annually. 57 58 Beyond the Random Walk Evidence The evidence on the short-term price drift begins with a large price change as an indicator of a strong signal of new information. A large price change (stock return) can be defined in two different ways: as an absolute

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500 return for a particular day. Event day is the day of the large price change. Sources: Pritamani and Singal (2001), Park (1995), and Cox and Peterson (1994). 59 60 Beyond the Random Walk selected return be an extreme price change for the firm that lies more than three standard deviations away from the

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.2 reveal two return patterns. First, price changes that are accompanied by high volume have price continuations. Price increases with high volume are followed by subsequent increases of 0.20 percent and 0.95 percent over five-day 61 62 Beyond the Random Walk Table 4.2 Returns Following Large Price Changes, High Volume, and News

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in the sample. However, there is no uncertainty about the target’s price, assuming the merger is successful. Not surprisingly, the price moved within a narrow range of about 1 percent over the next several days. 63 64 Beyond the Random Walk On the other hand, Intel warned about impending underperformance after the close

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to underreact. According to this explanation, as investors realize their mistakes, they trade, but with a time lag, resulting in the 67 68 Beyond the Random Walk price drift. In addition, investors are averse to selling at a loss and will continue to delay selling in the hope that the stock

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the last year. e Column 5 = Column 4 but excluding continuations of earlier events. The original data set is from Quotes-Plus. b Beyond the Random Walk Table 4.4 Short-Term Price Drift satisfy these criteria each day. The total number of events selected for April 2002 is 114, including 55

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—only that none could be found. News type 9: Miscellaneous, not elsewhere classified. In this case, it is a complaint to the FCC. Beyond the Random Walk Table 4.5 Short-Term Price Drift Table 4.6 Returns for Stocks Selected in April 2002, by News Type Earnings and Distributions Panel A

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in an overreaction for the month of April 2002. 73 74 Beyond the Random Walk Surprisingly, the no-news sample (type 8) also exhibits significant price drift: an average of 4.78 percent following price increases and –2.73 percent following price decreases. There are two possible explanations. First, the media did not carry information

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becomes very important for news relating to earnings, distributions, and analyst recommendations, where the postevent 75 76 Beyond the Random Walk twenty-day price drift is +3.50 percent for positive events and –2.25 percent for negative events. The annualized return after transactions costs can be estimated at

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on the New York Mercantile Exchange, the semiconductor futures prices would more accurately reflect an aggregation of market information. For industries with futures prices, the forecasts are much easier and more accurate, and there may be a smaller momentum effect. 83 84 Beyond the Random Walk To illustrate momentum in an industry where futures

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funds. However, ProFunds funds are not considered, as they are relatively new. 103 104 Beyond the Random Walk 6 Mispricing of Mutual Funds The net asset values (NAVs) of mutual funds may be based on prices that are several hours old. That means the NAV may not reflect the most recent market movements

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’s Hong Kong fund show much lower volatility? Because Fidelity relied on fair value pricing, whereas the other fund families did not. With fair value pricing, Fidelity used stock futures prices to value the Hong 113 114 Beyond the Random Walk Kong fund, reducing the staleness in its NAV. On the negative side, Fidelity could

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rows of Table 6.1. Therefore, time restrictions may not be very effective in preventing arbitrage of mispriced mutual funds. 115 116 Beyond the Random Walk Fair Value Pricing All of the solutions listed above try to prevent arbitrageurs from timing purchases and sales but do not really tackle the underlying problem of

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the uninformed investors will wake up and adopt solutions to eliminate or reduce mispricing. 131 132 Beyond the Random Walk Bottom Line The net asset values of mutual funds are mispriced when stale prices are used for computation. Investors can make abnormal profits by buying mispriced funds on days when the market rises

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patterns may be completely different, insider trading may not continue to predict future price movements. Moreover, the refinements and other uses suggested in “Other Uses and Refinements of Insider Trading Information” are untested even with 157 158 Beyond the Random Walk prior-period data. Finally, the trading strategies based on insider trading may

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, and will buy another stock with equivalent risk-return characteristics. In such an event, any price change will be imperceptible. However, as reported in the previous section, there is a permanent 169 170 Beyond the Random Walk price impact. If there is no new information associated with index changes, then the only reason for

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(AD+2 to ED) 189 Abnormal Return (ED+1 to ED+5) Abnormal Return (ED+1 to ED+20) 190 Beyond the Random Walk an abnormal return, the limit price is adjusted at the end of each day to reflect the movement in the S&P 500. The results are given below: Stock

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different environment. Moreover, none of the evidence presented above includes deletion of any foreign companies. 195 196 Beyond the Random Walk 9 Merger Arbitrage When a merger is announced, the target’s price should rise close to the bidder’s offer for the target. However, in most cases it does not. Two reasons

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short position in AOL loses but the long position in TWX gains an equivalent amount. If AOL’s price falls, the short position gains and the long position in 199 200 Beyond the Random Walk TWX loses. In addition, if there are zero transactions costs and the merger completion is immediate, then the

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. However, Travelocity jumped to $24.91 in anticipation of higher bids. On March 18, 2002, Sabre Holdings sweetened its offer to $28 and Travelocity’s price held at 201 202 Beyond the Random Walk $27.97 on that date, with the market participants expecting that the deal would be completed at that

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are discussed below. Among these, mutual funds are the easiest to use and generate reasonable returns. 211 Beyond the Random Walk Bidder’s Offer and Target’s Actual Price 44 Price 42 Actual Offer Price 40 38 36 0 3 8 11 16 22 25 31 36 39 45 50 53 58 63 66 71

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is that the investor can hold potentially lucrative arbitrage positions 215 216 Beyond the Random Walk that a large arbitrageur is not interested in holding or is unable to hold due to small target size, insufficient volume, or low price. Large arbitrageurs may have resources to pick deals with a high probability of

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sold at the open, wait until later in the day and try again. 217 218 Beyond the Random Walk 4. Nasdaq acquirers for stock mergers. Due to high premarket trading in Nasdaq stocks and high price volatility immediately after the market opens, it is always prudent to wait until about 10 A.M

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5 5.5 13.2 11,900 1,350 10 24 108 221 222 Beyond the Random Walk the morning on December 4, 2000. PepsiCo’s closing price that day was $43.813, while Quaker Oats’ closing price was $91.06. However, PepsiCo’s offer for Quaker Oats was $43.813 × 2.3 = $100

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encounter any significant problems. However, the speculation spread of 223 224 Beyond the Random Walk 1.4 percent is too small. Since it is a cash deal, it is possible to place an order at a preselected limit price that would allow sufficient speculation spread. For example, place an order to buy RAMP

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to buy a particular stock at a specific price. If someone else is interested, that person will contact the broker and offer to trade with you. Bulletin board stocks are difficult to trade and have wide bid-ask spreads. 231 232 Beyond the Random Walk 10 International Investing and the Home Bias Financial

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example, all markets fell together during the 1974 oil price shock, the 1987 stock market crash, the 1991 Gulf crisis, and the 1997 East Asian currency crisis. Clearly, the higher correlation in times of crisis is not desirable. 243 244 Beyond the Random Walk Rejoinder From Table 10.2, the average correlation is

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. • Global funds. These funds invest in all countries, including the domestic market, and include Templeton World, GT Global 251 252 Beyond the Random Walk Worldwide, Dreyfus Global, Vanguard Global Equity, Price Global Stock, and so on. • Regional funds. Examples include Fidelity Europe Capital Appreciation, Fidelity Nordic, Vanguard European Stock Index, and T. Rowe

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Make Sense? Yes, and Here’s Why. Journal of Investing 3(4), 12–17. 257 258 Beyond the Random Walk Explanations of the Home Bias Coen, Alain. 2001. Home Bias and International Capital Asset Pricing Model with Human Capital. Journal of Multinational Financial Management 11(4–5), 497–513. Coval, Joshua D., and

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at the end of the following month. 275 276 Beyond the Random Walk The process is repeated for the next month again with yen. Note, however, that the closing futures price in the first row, $0.009100/¥, is not the opening price in the second row even though the yen contract continues to be

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’ beliefs can add risk to stock returns. If risk aversion keeps rational investors from taking 291 292 Beyond the Random Walk large arbitrage positions, then uninformed traders can affect prices. In this way, prices can move away from fundamental values for an extended period of time, which makes arbitrage positions riskier and less profitable

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standard finance theory claim that prices are accurate; only that prices are unbiased based on available information. 3. See Barberis, Shleifer, and Vishny (1998), p. 320. 4. If all investors know about all securities, the model collapses to the CAPM. See Merton (1987). 297 298 Beyond the Random Walk 13 A Description of Other

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of underpricing depends on market conditions surrounding the IPO. Accurate estimates of underpricing based on market conditions and actual prices can be useful in predicting issue-day price movements. 303 304 Beyond the Random Walk The one-day return of 9 percent (or 20 percent) comes with several caveats. First, it is not easy

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more accurate than when a company operates in multiple segments. A reduction in information asymmetry means that there is less risk and, therefore, the stock price is higher. 313 314 Beyond the Random Walk References for Further Reading Abarbanell, Jeffrey S., Brian J. Bushee, and Jana Smith Raedy. 2003. Institutional Investor Preferences and

Risk Management in Trading

by Davis Edwards  · 10 Jul 2014

a special type of random process that describes the path taken by a series of random steps. In finance, random walk processes are commonly used to model how prices or interest rates might move in the future. In finance, most models are usually limited to a single dimension (like an interest rate

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an input is a model that adds random movement onto an existing price (this is called stochastic process). For example, gold prices might be modeled assuming they start at the current price (observed in the market today) and then follow a random walk into the future where each day a random adjustment is applied to

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who can predict the future would already have made trades, and kept borrowing money to make trades, until prices change enough to remove the potential for profit. This makes future price movements a random walk where prices are equally likely to move up or down around a time‐ value of money adjusted for fair value

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, 255 settlement, 262–263 trading decisions and, 10–11 transfer via hedging, 178 types of, 25 rogue trading, 113–114 R random numbers, 63–66 random walks, 72–75 randomness, results and, 111 real assets, 35–36 real estate investment trusts, 45 recursive calculations, 158 reduction, risk, 29, 267 regression tests,

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined

by Lasse Heje Pedersen  · 12 Apr 2015  · 504pp  · 139,137 words

P&L (profits and losses), I saw new million-dollar losses every 10 minutes for a couple of days—a clear pattern that defied the random walk theory of efficient markets and, ironically, showed remarkable likeness to my own theories. Let me explain, but let’s start from the beginning. My

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were facing a liquidity spiral or an unlucky step in the random walk of an efficient market. The efficient market theory says that, going forward, prices should fluctuate randomly, whereas the liquidity spiral theory says that when prices are depressed by forced selling, prices will likely bounce back later. These theories clearly had different

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implications for how to position our portfolio. On Monday, we became completely convinced that we were facing a liquidity event. All market dynamics pointed clearly in the direction of liquidity and defied the random walk

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intervals on Tuesday, August 7. This predictability provides strong evidence of a liquidity event, as it is statistically significantly different from the behavior of a random walk. Notice the magnitude of the losses in figure 9.6. The simulated strategy loses about 25% from Monday to Thursday, and it has been

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coefficient b mean? Clearly, a coefficient of zero means that the dividend yield is not helpful as a predictor. This would be consistent with the random walk hypothesis, which states that nothing should be able to predict excess returns (except perhaps by chance). A positive b coefficient indicates that the predictor

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it is part of the stock return (as seen in equation 10.3), but it does not predict the price appreciation. In contrast, the random walk hypothesis b = 0 means that the price appreciation is expected to be low when the dividend yield is high, such that the overall expected equity return is

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110; Asness on, 162–64; types of, 134–35, 134t. See also fundamental quantitative investing; high-frequency trading; statistical arbitrage quantitative global macro investing, 185 random walk hypothesis, 173 RAROC (risk-adjusted return on capital), 31–32 reactive risk management. See drawdown control real assets, in strategic asset allocation, 168, 171 real

Extreme Money: Masters of the Universe and the Cult of Risk

by Satyajit Das  · 14 Oct 2011  · 741pp  · 179,454 words

with high returns simply took higher risk rather than possessing supernatural skill. Demon of Chance The efficient market hypothesis (EMH) stated that the stock prices followed a random walk, a formal mathematical statement of a trajectory consisting of successive random steps. Pioneers Jules Regnault (in the nineteenth century) and Louis Bachelier (early

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a stock market newsletter, Eugene Fama noticed patterns in stock prices that would appear and disappear rapidly. In his doctoral dissertation, he laid out the argument that stock prices were random, reflecting all available information relevant to its value. Prices followed a random walk and market participants could not systematically profit from market inefficiencies.

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historical knowledge of claims, and the premiums paid, plus investment income on the premiums. Applying insurance theory to options proved difficult. Louis Bachelier applied random walk models to pricing options. Paul Cootner and Paul Samuleson worked on the problem. In their 1967 book Beat the Market, mathematicians Sheen Kassouf and Edward Thorp outlined

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year, then most of the time the share price moves up or down a small amount. On some days you may get a large or very large price change. VAR ranks the price changes from largest fall to largest rise. Assuming that prices follow a random walk and price changes fit a normal distribution, you can calculate

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211 Raines, Sylvain, 309 Rains, Claude, 77 Rajaratnam, Raj, 244 Ralphie’s Funds, 191, 204 Ramones, The, 79 RAND Corporation, 35 Rand, Ayn, 294, 296 random walks, 118 rands, 21 Range Rover, 346 Ranieri, Lewis, 170 Rapid American, 143 Rappaport, Alfred, 124 Raskob, John, 97 Ratergate (2008), 285 ratings agencies, 141 bonds

Priceless: The Myth of Fair Value (And How to Take Advantage of It)

by William Poundstone  · 1 Jan 2010  · 519pp  · 104,396 words

administration) was the first to make an extended case for what might now be called the coherent arbitrariness of stock prices. From day to day the market reacts promptly to the latest economic news. The resulting “random walk” of prices has been cited as proof that the market knows true values. Because stock

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change prices. Summers astutely pointed out that this “proof” doesn’t hold water. The random walk is a prediction of the efficient market model, just as missing your train is a prediction of the Friday

Making Sense of Chaos: A Better Economics for a Better World

by J. Doyne Farmer  · 24 Apr 2024  · 406pp  · 114,438 words

true, and I liked the idea of disproving it. Fama was not the first to suggest that stock-price changes are random. In fact, financial markets were the original inspiration of the random-walk model, introduced by the French mathematician Louis Bachelier in 1900. In his PhD dissertation, he proposed that the

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or the left; we cannot predict the direction of his movement. Similarly, if stock prices follow a random walk, we can estimate how far prices will drift from current prices after a given time, but not whether the change in price will be up or down. Beating the market seemed like a good challenge, so

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can buy an option to purchase oil at a fixed price, no matter how high the market price rises.18 Mathematical methods for pricing options are based on the efficient-markets hypothesis. This is done by assuming that the underlying stock price follows a random walk. For example, suppose we want to estimate the value

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of an option to buy – a call option. We do so by computing how often and by how much the random walk

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surpasses the strike price, its value is the price that was reached minus the strike price. The value of the option is then computed by averaging all possible realizations of the random walk. (This idea was introduced at a practical level by Edward Thorp and

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we couldn’t explain: Even though the agents in our model placed random orders, the resulting price movements weren’t random. Rather than making a random walk, the price movements were mean-reverting, meaning that, if the price went up at one point in time, it was more likely to go down at the

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clustered together. Figure 10. The clustered volatility of price movements. The daily returns of the S&P index measured in per cent from 1929–2023. Without clustered volatility, large market movements like the 1987 crash would be impossible. Under Louis Bachelier’s random-walk theory, if the step sizes of the drunk

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a simple formula for the accuracy of Moore’s Law. We began by generalizing the law, reformulating it as what is called a geometric random walk with drift.17 Our underlying hypothesis was so simple that we assumed that our formula would give mixed results, but when François tested it on

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187 Ramsey-Cass-Koopmans (RCK) model 100–102, 124–5 Ramsey, Frank 100 random order-placement 155–6 random process 39 random walk/random-walk model 49, 144, 150, 155, 165, 242 geometric random walk with drift 242 rationality/rational expectations, theory of behavioral economics and 5–6, 103–5 bounded rationality and see bounded rationality

Capital Ideas: The Improbable Origins of Modern Wall Street

by Peter L. Bernstein  · 19 Jun 2005  · 425pp  · 122,223 words

describes this phenomenon was one of Bachelier’s crowning achievements. Over time, in the literature on finance, Brownian motion came to be called the random walk, which someone once described as the path a drunk might follow at night in the light of a lamppost. No one knows who first used

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annoyance of financial practitioners. Eugene Fama of the University of Chicago, one of the first and most enthusiastic proponents of the concept, tells me that random walk “is an ancient statistical term; nobody alive can claim it.”13 In later years, the primary focus of research on capital markets was on

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determining whether or not the random walk is a valid description of security price movements. Bachelier himself, hardly a modest man, ended his dissertation with this flat statement: “It is evident that the present theory

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interested in the stock market for its own sake. The title of Alexander’s article, “Price Movements in Speculative Markets: Trends or Random Walks,” sums up its subject matter. His aim was to discover whether stock prices display trends that investors can identify in advance. After the fact, investors can readily see that

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of Paper I must be replaced with rather puny ones. The question still remains whether even these profits could plausibly be the result of a random walk. But I must confess that the fun has gone out of it somehow. . . . I should advise any reader who is interested only in

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abridged and less technical version, so that his evidence and arguments could be brought to the attention of investment professionals. This simplified version, “Random Walks in Stock Market Prices,” appeared in the Financial Analysts Journal nine months after the full version had appeared in the Journal of Business. It made such a

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precisely that. “Most individuals make hash of their portfolios,” he asserted.12 Pierre Rinfret, a well-known economist with experience in investment management, debated the random walk and declared flatly: “The value of investment advice is substantial. . . . I will say to the random theorists, as was said to the aeronautical engineer

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throws down the gauntlet to the chartists and technical analysts who believe that the past pattern of stock prices makes future prices predictable: The chartist must admit that the evidence in favor of the random walk model is both consistent and voluminous, whereas there is precious little published in discussion of rigorous empirical

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tests of the various technical theories. If the chartist rejects the evidence of the random walk model, his position is weak

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if his own theories have not been subjected to equally rigorous tests. This, I believe, is the challenge that the random walk theory makes.14 Now Fama moves to a deeper matter: the uses and value of information itself. This is a more serious issue than the

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worth more than just throwing darts at the Wall Street Journal—although the so-called “dart-board portfolio” soon became a sour joke and the random walk bogey to beat. This was the selling pitch that we in the investment advisory business used with potential clients. “We may not know everything,”

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answered, referring to the academic proponents of the efficient market and random walk. But, he added, “I don’t see how you can say that the prices made in Wall Street are the right prices in any intelligent definition of what right prices would be.”20 That was a curious statement. As far back

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series of challenging short editorials, and contributed articles himself under the pseudonym Walter Bagehot. His role was not to be an easy one. Concepts like random walks, efficient markets, complicated versions of risk/return tradeoffs, and betas, with their complex mathematical formulations, scandalized the more traditional members of the Journal’s

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is an activity doomed to fail and that technical analysis is a dangerous waste of time. If the stock market is efficient and stock prices are a random walk, who needs security analysts to make recommendations to portfolio managers? The worst was yet to come. According to Sharpe, the market portfolio is

…

client can communicate with one another.1 The first two issues contained articles by Sharpe on risk and performance measurement, by Fischer Black on the random walk, by James Lorie on diversification, and by Paul Samuelson on efficient markets. I invited James Vertin to contribute the lead article in the first

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Kirby(1979). 3. Schwert (1990a). 4. Markowitz(1991). Notes “PC&I” refers to personal correspondence and interviews. Bibliography and Other Sources Alexander, Sidney S. 1961. “Price Movements in Speculative Markets: Trends or Random Walks.” Industrial Management Review, Vol. 2, No. 2 (May), pp. 7–26. Also in Cootner (1964). Alexander, Sidney S. 1964

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. “Price Movements in Speculative Markets: Trends or Random Walks, No. 2.” Industrial Management Review, Vol. 5, No. 2 (Spring). Also in Cootner (1964). Aristotle. Politics. Book I, Chapter 11. Bachelier, Louis. 1900. Theory

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of Business, Vol. 37, No. 1 (January), pp. 34–105. Fama, Eugene F. 1965b. “Random Walks in Stock Prices.” Financial Analysts Journal (September-October), pp. 55–59. Fama, Eugene F. 1968a. “What Random Walk’ Really Means.” Institutional Investor, April, pp. 38–40. Fama, Eugene F. 1968b. “Risk and the Evaluation of Pension Fund Performance.”

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and interest rates and intrinsic value and manipulation risk and security analysis and shadow transfer trends value differentiation zero downside limit on “Price Movements in Speculative Markets: Trends or Random Walks” (Alexander) “Pricing of Options and Corporate Liabilities, The” (Black/Scholes) Probability theory Procter & Gamble Profit maximization Program trading Prospective yield “Proposal for

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Analysis of Time Series, A” (Working) Random price fluctuations/random walks selection of securities and “Random Walks in Stock Market Prices” (Fama) Rational Expectations Hypothesis “Rational Theory of Warrant Pricing” (Samuelson) Regulation of markets Return analysis: see Risk/return ratios Review of Economics and Statistics Review of Economic

Empirical Market Microstructure: The Institutions, Economics and Econometrics of Securities Trading

by Joel Hasbrouck  · 4 Jan 2007  · 209pp  · 13,138 words

and ask quotes, order arrivals, and the resulting transaction price process. 3.2 The Random-Walk Model of Security Prices Before financial economists began to concentrate on the trading process, the standard statistical model for a security price was the random walk. THE ROLL MODEL OF TRADE PRICES The random-walk model is no longer considered to be a complete

…

. Because it is unlikely that trades occur exactly at these times, we will approximate these observations by using the prices of the last (most recent) trade, for example, the day’s closing price. The random-walk model (with drift) is: pt = pt−1 + µ + ut , (3.1) where the ut , t = 0, . . . , are independently and

…

imposing economic or statistical structure, though, it is often possible to identify a martingale component of the price (with respect to a particular information set). Later chapters will indicate how this can be accomplished. A random-walk is a process constructed as the sum of independently and identically distributed (i.i.d.) zero

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of these securities over short samples may still be empirically well approximated by a random-walk model, but the random walk is not a valid description of the long-run behavior. 3.3 Statistical Analysis of Price Series Statistical inference in the random-walk model appears straightforward. Suppose that we have a sample {p1 , p2 , . . . , pT }, generated

…

generally be lower than that of the arithmetic mean. For example, suppose that t indexes days. Consider the properties of the annual log price change implied by the log random-walk model: p365 − p0 = 365
t=1 pt = µAnnual + 365
ut (3.2) t=1 where µAnnual = 365 µ. The annual variance is Var

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̂0 (see Fuller (1996), pp. 313–20). The increments (changes) in a random walk are uncorrelated. So we would expect to find ρ̂k ≈ 0 for k  = 0. In actual samples, however, the firstorder autocorrelations of short-run speculative price changes are usually negative. In October 2003, there were roughly 7,000 trades

…

Roll model. 3.4 The Roll Model of Bid, Ask, and Transaction Prices In returning to the economic perspective, we keep the random-walk assumption but now apply it to the (martingale) efficient price instead of the actual transaction price. Denoting this efficient price by mt , we assume that mt = mt−1 + ut , where, as before

…

allow us to infer qt , this is not universally the case. In many data samples and markets, only trade prices are recorded. 8.2 The Structural Model The efficient price still behaves as a random walk, but the increments have two components. 67 68 EMPIRICAL MARKET MICROSTRUCTURE mt = mt−1 + wt (8.1) wt

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. The intuition for this property lies in the behavior of long-term returns. 2 is the variance per unit time of the random-walk component of the σw security price. This variance is time-scaled: If we use a longer interval to compute the change, the variance is simply multiplied by the length

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like this might justify at least a provisional assumption about how stale the price is likely to be, but they must be based on economics rather than statistics. Statistical analysis does not provide an upper bound. 2 is the random-walk variance per unit time. For example, if Finally, σw 2 is variance

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is estimated over one-minute intervals, then σw minute. It may be rescaled, of course, to give an implied hourly or daily random-walk variance (see exercise 8.3). The pricing error variance σs2 , on the other hand, is the variance of a difference between two level variables at a point in time

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. It does not have a time dimension. 8.6 General Univariate Random-Walk Decompositions Up to now, the chapter has explored the correspondence between a

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of order one but is instead of arbitrary order: pt = θ(L)εt . The only economic structure we impose on the prices is pt = mt + st where mt follows a random walk (mt = mt−1 + wt ) and st is (as in the preceding section) a tracking error that may be serially correlated and

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case described in Watson (1986). Later chapters explore multivariate extensions and cointegration. In macroeconomics applications, random-walk decompositions are usually called permanent/transitory. The random-walk terminology is used here to stress the financial economics connection to the random-walk efficient prices. The permanent/transitory distinction is in some respects more descriptive, however, of the attributions that

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that φ(1)−2 σε2 = σw Exercise 8.3 For log price changes over five-minute intervals, we estimate a second-order moving average model: pt = εt − 0.3εt−1 + 0.1εt−2 , where σε2 = 0.00001. a. What is the random-walk standard deviation per five-minute interval? b. Assuming a six

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-hour trading day, what is the implied randomwalk standard deviation over the day? c. Compute the lower bound for the standard deviation of the pricing error. 8.7 Other Approaches There is a

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long tradition in empirical finance of measuring market efficiency (informational and operational) by measuring or assessing how closely security prices follow a random walk. Statistical measures commonly focus on autocovariances, autocorrelations, or variance ratios

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. The autocovariances and autocorrelations of a random-walk are zero at all nonzero leads and lags. This makes for a clean null hypothesis, and

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approach is to compare the variances of returns computed at different intervals or endpoints. It was noted before that transaction price returns computed over long horizons are dominated by the random-walk component. A variance ratio compares the variance per unit time implied by a long horizon with a variance per unit time

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generally declines as M approaches N from below. In a sense, then, this can summarize how quickly (in terms of return interval) the prices come to resemble a random walk. As a single summary statistic, though, V M ,N is problematic. There are few principles to apply in choosing M and N. Furthermore

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86 EMPIRICAL MARKET MICROSTRUCTURE 2 is a relative measure, essentially the coefficient of determination λ2 σv2 /σw in a project of price changes on trades. More generally, decomposition of the random-walk variance provides a basis for measuring the importance of different sources of market information. The xt variable set can potentially include

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category. Some analyses of foreign exchange dynamics include prices and quantities of recent trades. Yet there is no general trade reporting in this market, and the details of the trade are often known only to the buyer and seller. In a decomposition of the random-walk variance, a nonpublic variable may well possess

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directly relate to security payoffs. Section 5.6, for example, demonstrates that knowing that previous traders were uninformed may be valuable. From a random-walk decomposition perspective, a price change that appears permanent conditional on the public information set may be transitory when the expectation is conditioned on private information. This discussion ends

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 −0.830 θ1 = −0.100 (10.3) The variance-covariance matrix of the random-walk components is θ(1)θ(1)′ . Using (10.3), this is equal to 2 × 2 identity matrix. This is structurally correct: The efficient price innovations (the uit ) have unit variance, and they are uncorrelated. We next seek to

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, however, run up against arbitrage. A similar principle applies to the prices of options and their underlying assets, as long as appropriate correction is made for nonlinearities in the valuation relationship. When two or more variables individually follow random walk–like (formally, “integrated”) processes, but there exists a linear combination of them that

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in a primary market and a crossing market (discussed in section 2.6). The second price is the quote midpoint in the primary market, lagged to reflect transmission and processing delays. 10.2.2 The VMA Representation Both prices are integrated (contain random-walk components), but p1t − p2t = ut + cqt is stationary. Thus, the

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computing the impulse response functions for unit shocks in each variable, we may obtain the VMA representation for the price changes pt = θ(L)εt . We may posit for the n prices a random-walk decomposition of the form pt = mt × ι + st (n×1) (n×1) (n×1) where mt = mt−1 + wt

…

, (10.15) where ι is a vector of ones. It is important to note that mt is a scalar: The random-walk (“efficient price”) component is the same

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for all prices in 2 = [θ(1)] [θ(1)]′ , where [ · ] the model. The random-walk variance is: σw 1 1 1 denotes the first row of the matrix. One property developed

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, however, one usually tries to preserve balance in the analysis by treating all prices symmetrically. In practice, this suggests calculating and reporting for each information share the minimum and maximum over all causal permutations. Random-walk variance decompositions are probably more important here than in any other microstructure application. VECM models are often

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.3 Stationarity In the first place, how do we decide whether a time series is a random walk or covariance stationary? The question is actually ill-phrased. In the Roll model, for example, the price is neither a random walk nor stationary. It’s a mixture of both sorts of components. A somewhat better question

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is, how do we know if a time series contains a random-walk component? From a statistical viewpoint, however, even this is too

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+ θ1 L. The autoregressive representation for the price level is φ(L)pt = εt where φ(L) = θ(L)−1 (1 − L). We can identify at least one root here, and its value is unity. This is not surprising because we built a random walk into the structural model. If we did not

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limit order. Thus, as drift increases, limit prices are more aggressive at PROSPECTIVE TRADING COSTS AND EXECUTION STRATEGIES Figure 15.4. Dependence of limit order strategies on drift and volatility. all times. Panel B depicts volatility dependence. As volatility increases, the probability that a random walk will hit a given barrier increases. Volatility

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and trading strategies, 153; Price improvement, 142 Pricing error, multivariate, 86; univariate, 70 Priority rules, 11 Probability of informed trading (PIN), 56 Projection, bivariate normal, 62; and linear forecasting, 37 Quote display rule (SEC). See also Securities and Exchange Commission Rule on Order Execution Obligations Quote matching, 48 Random-walk, 26 Random-walk decomposition: multivariate, 85

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; univariate, 71. See also Information share Random-walk

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Darwin's Dangerous Idea: Evolution and the Meanings of Life

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To Sleep in a Sea of Stars

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Alex's Adventures in Numberland

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Turing's Cathedral

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The Children of the Sky

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Outnumbered: From Facebook and Google to Fake News and Filter-Bubbles – the Algorithms That Control Our Lives

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Advanced Software Testing—Vol. 3, 2nd Edition

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Seveneves

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Being Geek: The Software Developer's Career Handbook

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The Immortalization Commission: Science and the Strange Quest to Cheat Death

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Clojure Programming

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Coders at Work

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Revelation Space

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Think OCaml

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Science in the Soul: Selected Writings of a Passionate Rationalist

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Skyfaring: A Journey With a Pilot

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Overcomplicated: Technology at the Limits of Comprehension

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Power, Sex, Suicide: Mitochondria and the Meaning of Life

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Lost in Math: How Beauty Leads Physics Astray

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I Am a Strange Loop

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Life as We Made It: How 50,000 Years of Human Innovation Refined--And Redefined--Nature

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Seven Databases in Seven Weeks: A Guide to Modern Databases and the NoSQL Movement

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