A Non-Random Walk Down Wall Street [NOOK Book]

Overview

For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that ...

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A Non-Random Walk Down Wall Street

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Overview

For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future.

The articles track the exciting course of Lo and MacKinlay's research on the predictability of stock prices from their early work on rejecting random walks in short-horizon returns to their analysis of long-term memory in stock market prices. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. This book invites scholars to reconsider the Random Walk Hypothesis, and, by carefully documenting the presence of predictable components in the stock market, also directs investment professionals toward superior long-term investment returns through disciplined active investment management.

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Editorial Reviews

Constance Loizos
Here's an interesting case for actively managed mutual funds over index funds. Performance numbers for the active managers would be a lot better if you looked only at nimbler new funds and left out the bloated old ones that are the real underperformers. "Active funds that have been more recently invested outperform in a significant way the active funds that were long ago invested," Wharton School Professor A. Craig MacKinlay observed during the Investment Management Consultants Association conference in San Francisco late last month.
Investment News
Peter Coy
But markets don't know everything, say the authors of A Non-Random Walk Down Wall Street. People who devote enough time, money, and brain power can beat the market by finding undervalued companies or discovering persistent price patterns, say Lo and MacKinlay. Their profits are "simply the fair reward to breakthroughs in financial technology," they argue.
Business Week
Wall Street Journal
What Andrew W. Lo and A. Craig MacKinlay impressively do . . . [is look] for hard statistical evidence of predictable patterns in stock prices. . . . Here they marshal the most sophisticated techniques of financial theory to show that the market is not completely random after all.
— Jim Holt
BusinessWeek
Where are today's exploitable anomalies? Lo and MacKinlay argue that fast computers, chewing on newly available, tick-by-tick feeds of market-transaction data, can detect regularities in stock prices that would have been invisible as recently as five years ago. One example: 'clientele bias,' in which certain stocks are popular with investors who have certain trading styles. A case in point that doesn't take a supercomputer to detect, is day traders' current enthusiasm for Internet stocks. Lo says that day traders tend to overreact to news—whether that news is positive or negative—so it should be possible to profit by taking the opposite side of their trades.
— Peter Coy
The Independent
With all its equations, this book is going to turn out to be a classic text in the theory of finance. But it is also one for practitioners.
— Diane Coyle
Business Week

Where are today's exploitable anomalies? Lo and MacKinlay argue that fast computers, chewing on newly available, tick-by-tick feeds of market-transaction data, can detect regularities in stock prices that would have been invisible as recently as five years ago. One example: 'clientele bias,' in which certain stocks are popular with investors who have certain trading styles. A case in point that doesn't take a supercomputer to detect, is day traders' current enthusiasm for Internet stocks. Lo says that day traders tend to overreact to news--whether that news is positive or negative--so it should be possible to profit by taking the opposite side of their trades.
— Peter Coy
Wall Street Journal - Jim Holt
What Andrew W. Lo and A. Craig MacKinlay impressively do . . . [is look] for hard statistical evidence of predictable patterns in stock prices. . . . Here they marshal the most sophisticated techniques of financial theory to show that the market is not completely random after all.
The Independent - Diane Coyle
With all its equations, this book is going to turn out to be a classic text in the theory of finance. But it is also one for practitioners.
BusinessWeek - Peter Coy
Where are today's exploitable anomalies? Lo and MacKinlay argue that fast computers, chewing on newly available, tick-by-tick feeds of market-transaction data, can detect regularities in stock prices that would have been invisible as recently as five years ago. One example: 'clientele bias,' in which certain stocks are popular with investors who have certain trading styles. A case in point that doesn't take a supercomputer to detect, is day traders' current enthusiasm for Internet stocks. Lo says that day traders tend to overreact to news—whether that news is positive or negative—so it should be possible to profit by taking the opposite side of their trades.
From the Publisher
"What Andrew W. Lo and A. Craig MacKinlay impressively do . . . [is look] for hard statistical evidence of predictable patterns in stock prices. . . . Here they marshal the most sophisticated techniques of financial theory to show that the market is not completely random after all."—Jim Holt, Wall Street Journal

"With all its equations, this book is going to turn out to be a classic text in the theory of finance. But it is also one for practitioners."—Diane Coyle, The Independent (London)

"Where are today's exploitable anomalies? Lo and MacKinlay argue that fast computers, chewing on newly available, tick-by-tick feeds of market-transaction data, can detect regularities in stock prices that would have been invisible as recently as five years ago. One example: 'clientele bias,' in which certain stocks are popular with investors who have certain trading styles. A case in point that doesn't take a supercomputer to detect, is day traders' current enthusiasm for Internet stocks. Lo says that day traders tend to overreact to news—whether that news is positive or negative—so it should be possible to profit by taking the opposite side of their trades."—Peter Coy, Business Week

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Product Details

  • ISBN-13: 9781400829095
  • Publisher: Princeton University Press
  • Publication date: 11/14/2011
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition description: Core Textbook
  • Pages: 448
  • Sales rank: 1,304,891
  • File size: 15 MB
  • Note: This product may take a few minutes to download.

Meet the Author

Andrew W. Lo is the Harris & Harris Group Professor of Finance at the Sloan School of Management, Massachusetts Institute of Technology. A. Craig MacKinlay is Joseph P. Wargrove Professor of Finance at the Wharton School, University of Pennsylvania. With John Y. Campbell, they are the authors of "The Econometrics of Financial Markets" (Princeton), which received the Paul A. Samuelson Award in 1997.
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Read an Excerpt

Introduction

One of the earliest and most enduring models of the behavior of security prices is the Random Walk Hypothesis, an idea that was conceived in the sixteenth century as a model of games of chance. Closely tied to the birth of probability theory, the Random Walk Hypothesis has had an illustrious history, with remarkable intellectual forbears such as Bachelier, Einstein, L'evy, Kolmogorov, and Wiener.

More recently, and as with so many of the ideas of modern economics, the first serious application of the Random Walk Hypothesis to financial markets can be traced back to Paul Samuelson (1965), whose contribution is neatly summarized by the title of his article: "Proof that Properly Anticipated Prices Fluctuate Randomly." In an informationally efficient market--not to be confused with an allocationally or Pareto-efficient market--price changes must be unforecastable if they are properly anticipated, i.e., if they fully incorporate the expectations and information of all market participants. Fama (1970) encapsulated this idea in his pithy dictum that "prices fully reflect all available information."

Unlike the many applications of the Random Walk Hypothesis in the natural and physical sciences in which randomness is assumed almost by default, because of the absence of any natural alternatives, Samuelson argues that randomness is achieved through the active participation of many investors seeking greater wealth. Unable to curtail their greed, an army of investors aggressively pounce on even the smallest informational advantages at their disposal, and in doing so, they incorporate their information into market prices and quickly eliminate the profit opportunities that gave rise to their aggression. If this occurs instantaneously, which it must in an idealized world of "frictionless" markets and costless trading, then prices must always fully reflect all available information and no profits can be garnered from information-based trading (because such profits have already been captured). This has a wonderfully counter-intuitive and seemingly contradictory flavor to it: the more efficient the market, the more random the sequence of price changes generated by such a market, and the most efficient market of all is one in which price changes are completely random and unpredictable.

For these reasons, the Random Walk Hypothesis and its close relative, the Efficient Markets Hypothesis, have become icons of modern financial economics that continue to fire the imagination of academics and investment professionals alike. The papers collected in this volume comprise our own foray into this rich literature, spanning a decade of research that we initiated in 1988 with our rejection of the Random Walk Hypothesis for US stock market prices, and then following a course that seemed, at times, to be self-propelled, the seeds of our next study planted by the results of the previous one.

If there is one central theme that organizes the papers contained in this volume, it is this: financial markets are predictable to some degree, but far from being a symptom of inefficiency or irrationality, predictability is the oil that lubricates the gears of capitalism. Indeed, quite by accident and rather indirectly, we have come face to face with an insight that Ronald Coase hit upon as an undergraduate over half a century ago: price discovery is neither instantaneous nor costless, and frictions play a major role in determining the nature of competition and the function of markets.

1.1 The Random Walk and Efficient Markets

One of the most common reactions to our early research was surprise and disbelief. Indeed, when we first presented our rejection of the Random Walk Hypothesis at an academic conference in 1986, our discussant--a distinguished economist and senior member of the profession--asserted with great confidence that we had made a programming error, for if our results were correct, this would imply tremendous profit opportunities in the stock market. Being too timid (and too junior) at the time, we responded weakly that our programming was quite solid thank you, and the ensuing debate quickly degenerated thereafter. Fortunately, others were able to replicate our findings exactly, and our wounded pride has healed quite nicely with the passage of time (though we still bristle at the thought of being prosecuted for programming errors without "probable cause"). Nevertheless, this experience has left an indelible impression on us, forcing us to confront the fact that the Random Walk Hypothesis was so fully ingrained into the canon of our profession that it was easier to attribute our empirical results to programming errors than to accept them at face value. Is it possible for stock market prices to be predictable to some degree in an efficient market?

This question hints at the source of disbelief among our early critics: an implicit--and incorrect--link between the Random Walk Hypothesis and the Efficient Markets Hypothesis. It is not difficult to see how the two ideas might be confused. Under very special circumstances, e.g., risk neutrality, the two are equivalent. However, LeRoy (1973), Lucas (1978), and many others have shown in many ways and in many contexts that the Random Walk Hypothesis is neither a necessary nor a sufficient condition for rationally determined security prices. In other words, unforecastable prices need not imply a well-functioning financial market with rational investors, and forecastable prices need not imply the opposite.

These conclusions seem sharply at odds with Samuelson's "proof" that properly anticipated prices fluctuate randomly, an argument so compelling that it is reminiscent of the role that uncertainty plays in quantum mechanics. Just as Heisenberg's uncertainty principle places a limit on what we can know about an electron's position and momentum if quantum mechanics holds, Samuelson's version of the Efficient Markets Hypothesis places a limit on what we can know about future price changes if the forces of economic self-interest hold.

Nevertheless, one of the central insights of modern financial economics is the necessity of some trade-off between risk and expected return, and although Samuelson's version of the Efficient Markets Hypothesis places a restriction on expected returns, it does not account for risk in any way. In particular, if a security's expected price change is positive, it may be just the reward needed to attract investors to hold the asset and bear the associated risks. Indeed, if an investor is sufficiently risk averse, he might gladly pay to avoid holding a security that has unforecastable returns.

In such a world, the Random Walk Hypothesis--a purely statistical model of returns--need not be satisfied even if prices do fully reflect all available information. This was demonstrated conclusively by LeRoy (1973) and Lucas (1978), who construct explicit examples of informationally efficient markets in which the Efficient Markets Hypothesis holds but where prices do not follow random walks.

Grossman (1976) and Grossman and Stiglitz (1980) go even further. They argue that perfectly informationally efficient markets are an impossibility, for if markets are perfectly efficient, the return to gathering information is nil, in which case there would be little reason to trade and markets would eventually collapse. Alternatively, the degree of market inefficiency determines the effort investors are willing to expend to gather and trade on information, hence a non-degenerate market equilibrium will arise only when there are sufficient profit opportunities, i.e., inefficiencies, to compensate investors for the costs of trading and information-gathering. The profits earned by these industrious investors may be viewed as economic rents that accrue to those willing to engage in such activities. Who are the providers of these rents? Black (1986) gives us a provocative answer: noise traders, individuals who trade on what they think is information but is in fact merely noise. More generally, at any time there are always investors who trade for reasons other than information--for example, those with unexpected liquidity needs--and these investors are willing to "pay up" for the privilege of executing their trades immediately.

These investors may well be losing money on average when they trade with information-motivated investors, but there is nothing irrational or inefficient about either group's behavior. In fact, an investor may be trading for liquidity reasons one day and for information reasons the next, and losing or earning money depending on the circumstances surrounding the trade.

1.2 The Current State of Efficient Markets

There is an old joke, widely told among economists, about an economist strolling down the street with a companion when they come upon a $100 bill lying on the ground. As the companion reaches down to pick it up, the economist says "Don't bother--if it were a real $100 bill, someone would have already picked it up."

This humorous example of economic logic gone awry strikes dangerously close to home for students of the Efficient Markets Hypothesis, one of the most important controversial and well-studied propositions in all the social sciences. It is disarmingly simple to state, has far-reaching consequences for academic pursuits and business practice, and yet is surprisingly resilient to empirical proof or refutation. Even after three decades of research and literally thousands of journal articles, economists have not yet reached a consensus about whether markets--particularly financial markets--are efficient or not.

What can we conclude about the Efficient Markets Hypothesis? Amazingly, there is still no consensus among financial economists. Despite the many advances in the statistical analysis, databases, and theoretical models surrounding the Efficient Markets Hypothesis, the main effect that the large number of empirical studies have had on this debate is to harden the resolve of the proponents on each side.

One of the reasons for this state of affairs is the fact that the Efficient Markets Hypothesis, by itself, is not a well-defined and empirically refutable hypothesis. To make it operational, one must specify additional structure, e.g., investors' preferences, information structure, business conditions, etc. But then a test of the Efficient Markets Hypothesis becomes a test of several auxiliary hypotheses as well, and a rejection of such a joint hypothesis tells us little about which aspect of the joint hypothesis is inconsistent with the data. Are stock prices too volatile because markets are inefficient, or is it due to risk aversion, or dividend smoothing? All three inferences are consistent with the data. Moreover, new statistical tests designed to distinguish among them will no doubt require auxiliary hypotheses of their own which, in turn, may be questioned.

More importantly, tests of the Efficient Markets Hypothesis may not be the most informative means of gauging the efficiency of a given market. What is often of more consequence is the relative efficiency of a particular market, relative to other markets, e.g., futures vs. spot markets, auction vs. dealer markets, etc. The advantages of the concept of relative efficiency, as opposed to the all-or-nothing notion of absolute efficiency, are easy to spot by way of an analogy. Physical systems are often given an efficiency rating based on the relative proportion of energy or fuel converted to useful work. Therefore, a piston engine may be rated at 60% efficiency, meaning that on average 60% of the energy contained in the engine's fuel is used to turn the crankshaft, with the remaining 40% lost to other forms of work, e.g., heat, light, noise, etc.

Few engineers would ever consider performing a statistical test to determine whether or not a given engine is perfectly efficient--such an engine exists only in the idealized frictionless world of the imagination. But measuring relative efficiency--relative to a frictionless ideal--is commonplace. Indeed, we have come to expect such measurements for many household products: air conditioners, hot water heaters, refrigerators, etc. Therefore, from a practical point of view, and in light of Grossman and Stiglitz (1980), the Efficient Markets Hypothesis is an idealization that is economically unrealizable, but which serves as a useful benchmark for measuring relative efficiency.

A more practical version of the Efficient Markets Hypothesis is suggested by another analogy, one involving the notion of thermal equilibrium in statistical mechanics. Despite the occasional "excess" profit opportunity, on average and over time, it is not possible to earn such profits consistently without some type of competitive advantage, e.g., superior information, superior technology, financial innovation, etc. Alternatively, in an efficient market, the only way to earn positive profits consistently is to develop a competitive advantage, in which case the profits may be viewed as the economic rents that accrue to this competitive advantage. The consistency of such profits is an important qualification--in this version of the Efficient Markets Hypothesis, an occasional free lunch is permitted, but free lunch plans are ruled out.

To see why such an interpretation of the Efficient Markets Hypothesis is a more practical one, consider for a moment applying the classical version of the Efficient Markets Hypothesis to a non-financial market, say the market for biotechnology. Consider, for example, the goal of developing a vaccine for the AIDS virus. If the market for biotechnology is efficient in the classical sense, such a vaccine can never be developed--if it could, someone would have already done it! This is clearly a ludicrous presumption since it ignores the difficulty and gestation lags of research and development in biotechnology. Moreover, if a pharmaceutical company does succeed in developing such a vaccine, the profits earned would be measured in the billions of dollars. Would this be considered "excess" profits, or economic rents that accrue to biotechnology patents?

Financial markets are no different in principle, only in degrees. Consequently, the profits that accrue to an investment professional need not be a market inefficiency, but may simply be the fair reward to breakthroughs in financial technology. After all, few analysts would regard the hefty profits of Amgen over the past few years as evidence of an inefficient market for pharmaceuticals--Amgen's recent profitability is readily identified with the development of several new drugs (Epogen, for example, a drug that stimulates the production of red blood cells), some considered breakthroughs in biotechnology. Similarly, even in efficient financial markets there are very handsome returns to breakthroughs in financial technology.

Of course, barriers to entry are typically lower, the degree of competition is much higher, and most financial technologies are not patentable (though this may soon change) hence the "half life" of the profitability of financial innovation is considerably smaller. These features imply that financial markets should be relatively more efficient, and indeed they are. The market for "used securities" is considerably more efficient than the market for used cars. But to argue that financial markets must be perfectly efficient is tantamount to the claim that an AIDS vaccine cannot be found. In an efficient market, it is difficult to earn a good living, but not impossible.

1.3 Practical Implications

Our research findings have several implications for financial economists and investors. The fact that the Random Walk Hypothesis hypothesis can be rejected for recent US equity returns suggests the presence of predictable components in the stock market. This opens the door to superior long-term investment returns through disciplined active investment management. In much the same way that innovations in biotechnology can garner superior returns for venture capitalists, innovations in financial technology can garner equally superior returns for investors.

However, several qualifications must be kept in mind when assessing which of the many active strategies currently being touted is appropriate for an particular investor. First, the riskiness of active strategies can be very different from passive strategies, and such risks do not necessarily "average out" over time. In particular, an investor's risk tolerance must be taken into account in selecting the long-term investment strategy that will best match the investor's goals. This is no simple task since many investors have little understanding of their own risk preferences, hence consumer education is perhaps the most pressing need in the near term. Fortunately, computer technology can play a major role in this challenge, providing scenario analyses, graphical displays of potential losses and gains, and realistic simulations of long-term investment performance that are user-friendly and easily incorporated into an investor's world view. Nevertheless, a good understanding of the investor's understanding of the nature of financial risks and rewards is the natural starting point for the investment process.

Second, there are a plethora of active managers vying for the privilege of managing institutional and pension assets, but they cannot all outperform the market every year (nor should we necessarily expect them to). Though often judged against a common benchmark, e.g., the S&P 500, active strategies can have very diverse risk characteristics and these must be weighed in assessing their performance. An active strategy involving high-risk venture-capital investments will tend to outperform the S&P 500 more often than a less aggressive "enhanced indexing" strategy, yet one is not necessarily better than the other.

In particular, past returns should not be the sole or even the major criterion by which investment managers are judged. This statement often surprises investors and finance professionals--after all, isn't this the bottom line? Put another way, "If it works, who cares why?". Selecting an investment manager this way is one of the surest paths to financial disaster. Unlike the experimental sciences such as physics and biology, financial economics (and most other social sciences) relies primarily on statistical inference to test its theories. Therefore, we can never know with perfect certainty that a particular investment strategy is successful since even the most successful strategy can always be explained by pure luck (see Chapter 8 for some concrete illustrations).

Of course, some kinds of success are easier to attribute to luck than others, and it is precisely this kind of attribution that must be performed in deciding on a particular active investment style. Is it luck, or is it genuine?

While statistical inference can be very helpful in tackling this question, in the final analysis the question is not about statistics, but rather about economics and financial innovation. Under the practical version of the Efficient Markets Hypothesis, it is difficult--but not impossible--to provide investors with consistently superior investment returns. So what are the sources of superior performance promised by an active manager and why have other competing managers not recognized these opportunities? Is it better mathematical models of financial markets? Or more accurate statistical methods for identifying investment opportunities? Or more timely data in a market where minute delays can mean the difference between profits and losses? Without a compelling argument for where an active manager's value-added is coming from, one must be very skeptical about the prospects for future performance. In particular, the concept of a "black box"--a device that performs a known function reliably but obscurely--may make sense in engineering applications where repeated experiments can validate the reliability of the box's performance, but has no counterpart in investment management where performance attribution is considerably more difficult. For analyzing investment strategies, it matters a great deal why a strategy is supposed to work.

Finally, despite the caveats concerning performance attribution and proper motivation, we can make some educated guesses about where the likely sources of value-added might be for active investment management in the near future.

  • The revolution in computing technology and datafeeds suggest that highly computation-intensive strategies--ones that could not have been implemented five years ago--that exploit certain regularities in securities prices, e.g., clientele biases, tax opportunities, information lags, can add value.
  • Many studies have demonstrated the enormous impact that transactions costs can have on long-term investment performance. More sophisticated methods for measuring and controlling transactions costs--methods which employ high-frequency data, economic models of price impact, and advanced optimization techniques--can add value. Also, the introduction of financial instruments that reduce transactions costs, e.g., swaps, options, and other derivative securities, can add value.
  • Recent research in psychological biases inherent in human cognition suggest that investment strategies exploiting these biases can add value. However, contrary to the recently popular "behavioral" approach to investments which proposes to take advantage of individual "irrationality," I suggest that value-added comes from creating investments with more attractive risk-sharing characteristics suggested by psychological models. Though the difference may seem academic, it has far-reaching consequences for the long-run performance of such strategies: taking advantage of individual irrationality cannot be a recipe for long-term success, but providing a better set of opportunities that more closely matches what investors desire seems more promising.
Of course, forecasting the sources of future innovations in financial technology is a treacherous business, fraught with many half-baked successes and some embarrassing failures. Perhaps the only reliable prediction is that the innovations of future are likely to come from unexpected and underappreciated sources. No one has illustrated this principal so well as Harry Markowitz, the father of modern portfolio theory and a winner of the 1990 Nobel Prize in economics. In describing his experience as a Ph.D. student on the eve of his graduation in the following way, he wrote in his Nobel address:
. . . [W]hen I defended my dissertation as a student in the Economics Department of the University of Chicago, Professor Milton Friedman argued that portfolio theory was not Economics, and that they could not award me a Ph.D. degree in Economics for a dissertation which was not Economics. I assume that he was only half serious, since they did award me the degree without long debate. As to the merits of his arguments, at this point I am quite willing to concede: at the time I defended my dissertation, portfolio theory was not part of Economics. But now it is.
It is our hope and conceit that the research contained in this volume will be worthy of the tradition that Markowitz and others have so firmly established.
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Table of Contents

List of Figures
List of Tables
Preface

1 Introduction
1.1 The Random Walk and Efficient Markets
1.2 The Current State of Efficient Markets
1.3 Practical Implications

Part I
2 Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test
2.1 The Specification Test
2.1.1 Homoskedastic Increments
2.1.2 Heteroskedastic Increments
2.2 The Random Walk Hypothesis for Weekly Returns
2.2.1 Results for Market Indexes
2.2.2 Results for Size-Based Portfolios
2.2.3 Results for Individual Securities
2.3 Spurious Autocorrelation Induced by Nontrading
2.4 The Mean-Reverting Alternative to the Random Walk
2.5 Conclusion
Appendix A2: Proof of Theorems

3 The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation
3.1 Introduction
3.2 The Variance Ratio Test
3.2.1 The IID Gaussian Null Hypothesis
3.2.2 The Heteroskedastic Null Hypothesis
3.2.3 Variance Ratios and Autocorrelations
3.3 Properties of the Test Statistic under the Null Hypotheses
3.3.1 The Gaussian IID Null Hypothesis
3.3.2 A Heteroskedastic Null Hypothesis
3.4 Power
3.4.1 The Variance Ratio Test for Large q
3.4.2 Power against a Stationary AR(1) Alternative
3.4.3 Two Unit Root Alternatives to the Random Walk
3.5 Conclusion

4 An Econometric Analysis of Nonsynchronous Trading
4.1 Introduction
4.2 A Model of Nonsynchronous Trading
4.2.1 Implications for Individual Returns
4.2.2 Implications for Portfolio Returns
4.3 Time Aggregation
4.4 An Empirical Analysis of Nontrading
4.4.1 Daily Nontrading Probabilities Implicit in Autocorrelations
4.4.2 Nontrading and Index Autocorrelations
4.5 Extensions and Generalizations
Appendix A4: Proof of Propositions

5 When Are Contrarian Profits Due to Stock Market Overreaction?
5.1 Introduction
5.2 A Summary of Recent Findings
5.3 Analysis of Contrarian Profitability
5.3.1 The Independently and Identically Distributed Benchmark
5.3.2 Stock Market Overreaction and Fads
5.3.3 Trading on White Noise and Lead-Lag Relations
5.3.4 Lead-Lag Effects and Nonsynchronous Trading
5.3.5 A Positively Dependent Common Factor and the Bid-Ask Spread
5.4 An Empirical Appraisal of Overreaction
5.5 Long Horizons Versus Short Horizons
5.6 Conclusion
Appendix A5

6 Long-Term Memory in Stock Market Prices
6.1 Introduction
6.2 Long-Range Versus Short-Range Dependence
6.2.1 The Null Hypothesis
6.2.2 Long-Range Dependent Alternatives
6.3 The Rescaled Range Statistic
6.3.1 The Modified R/S Statistic
6.3.2 The Asymptotic Distribution of Qn
6.3.3 The Relation Between Qn and [tilde]Qn
6.3.4 The Behavior of Qn Under Long Memory Alternatives
6.4 R/S Analysis for Stock Market Returns
6.4.1 The Evidence for Weekly and Monthly Returns
6.5 Size and Power
6.5.1 The Size of the R/S Test
6.5.2 Power Against Fractionally-Differenced Alternatives
6.6 Conclusion
Appendix A6: Proof of Theorems

Part II
7 Multifactor Models Do Not Explain Deviations from the CAPM
7.1 Introduction
7.2 Linear Pricing Models, Mean-Variance Analysis, and the Optimal Orthogonal Portfolio
7.3 Squared Sharpe Measures
7.4 Implications for Risk-Based Versus Nonrisk-Based Alternatives
7.4.1 Zero Intercept F-Test
7.4.2 Testing Approach
7.4.3 Estimation Approach
7.5 Asymptotic Arbitrage in Finite Economies
7.6 Conclusion

8 Data-Snooping Biases in Tests of Financial Asset Pricing Models
8.1 Quantifying Data-Snooping Biases With Induced Order Statistics
8.1.1 Asymptotic Properties of Induced Order Statistics
8.1.2 Biases of Tests Based on Individual Securities
8.1.3 Biases of Tests Based on Portfolios of Securities
8.1.4 Interpreting Data-Snooping Bias as Power
8.2 Monte Carlo Results
8.2.1 Simulation Results for [theta]p
8.2.2 Effects of Induced Ordering on F-Tests
8.2.3 F-Tests With Cross-Sectional Dependence
8.3 Two Empirical Examples
8.3.1 Sorting By Beta
8.3.2 Sorting By Size
8.4 How the Data Get Snooped
8.5 Conclusion

9 Maximizing Predictability in the Stock and Bond Markets
9.1 Introduction
9.2 Motivation
9.2.1 Predicting Factors vs. Predicting Returns
9.2.2 Numerical Illustration
9.2.3 Empirical Illustration
9.3 Maximizing Predictability
9.3.1 Maximally Predictable Portfolio
9.3.2 Example: One-Factor Model
9.4 An Empirical Implementation
9.4.1 The Conditional Factors
9.4.2 Estimating the Conditional-Factor Model
9.4.3 Maximizing Predictability
9.4.4 The Maximally Predictable Portfolios
9.5 Statistical Inference for the Maximal R2
9.5.1 Monte Carlo Analysis
9.6 Three Out-of-Sample Measures of Predictability
9.6.1 Naive vs. Conditional Forecasts
9.6.2 Merton's Measure of Market Timing
9.6.3 The Profitability of Predictability
9.7 Conclusion

Part III
10 An Ordered Probit Analysis of Transaction Stock Prices
10.1 Introduction
10.2 The Ordered Probit Model
10.2.1 Other Models of Discreteness
10.2.2 The Likelihood Function
10.3 The Data
10.3.1 Sample Statistics
10.4 The Empirical Specification
10.5 The Maximum Likelihood Estimates
10.5.1 Diagnostics
10.5.2 Endogeneity of [Delta]tk and IBSk
10.6 Applications
10.6.1 Order-Flow Dependence
10.6.2 Measuring Price Impact Per Unit Volume of Trade
10.6.3 Does Discreteness Matter?
10.7 A Larger Sample
10.8 Conclusion

11 Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices
11.1 Arbitrage Strategies and the Behavior of Stock Index Futures Prices
11.1.1 Forward Contracts on Stock Indexes (No Transaction Costs)
11.1.2 The Impact of Transaction Costs
11.2 Empirical Evidence
11.2.1 Data
11.2.2 Behavior of Futures and Index Series
11.2.3 The Behavior of the Mispricing Series
11.2.4 Path Dependence of Mispricing
11.3 Conclusion

12 Order Imbalances and Stock Price Movements on October 19 and 20, 1987
12.1 Some Preliminaries
12.1.1 The Source of the Data
12.1.2 The Published Standard and Poor's Index
12.2 The Constructed Indexes
12.3 Buying and Selling Pressure
12.3.1 A Measure of Order Imbalance
12.3.2 Time-Series Results
12.3.3 Cross-Sectional Results
12.3.4 Return Reversals
12.4 Conclusion
Appendix A12
A12.1 Index Levels
A12.2 Fifteen-Minute Index Returns

References
Index

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