A Non-Random Walk Down Wall Street

A Non-Random Walk Down Wall Street

Andrew W. Lo
A. Craig MacKinlay
Copyright Date: 1999
Pages: 448
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  • Book Info
    A Non-Random Walk Down Wall Street
    Book Description:

    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.

    eISBN: 978-1-4008-2909-5
    Subjects: Finance

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-xii)
  3. List of Figures
    (pp. xiii-xiv)
  4. List of Tables
    (pp. xv-xx)
  5. Preface
    (pp. xxi-2)
  6. 1 Introduction
    (pp. 3-12)

    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.² 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, Lévy, 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...

  7. Part I
    • [Part I Introduction]
      (pp. 13-16)

      The five chapters in this first part focus squarely on whether the Random Walk Hypothesis is a plausible description of recent US stock market prices. At the time we started our investigations—in 1985, just a year after we arrived at the Wharton School—the Random Walk Hypothesis was taken for granted as gospel truth. A number of well-known empirical studies had long since established the fact that markets were “weak-form efficient” in Roberts’s (1967) terminology, implying that past prices could not be used to forecast future prices changes (see, for example, Cowles and Jones (1973), Kendall (1953), Osborne (1959,...

    • 2 Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test
      (pp. 17-46)

      Since Keynes’ (1936) now famous pronouncement that most investors’ decisions “can only be taken as a result of animal spirits—of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of benefits multiplied by quantitative probabilities,” a great deal of research has been devoted to examining the efficiency of stock market price formation. In Fama’s (1970) survey, the vast majority of those studies were unable to reject the “efficient markets” hypothesis for common stocks. Although several seemingly anomalous departures from market efficiency have been well documented,¹ many financial economists would agree with...

    • 3 The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation
      (pp. 47-84)

      Whether or not an economic time series follows a random walk has long been a question of great interest to economists. Although its origins lie in the modelling of games of chance, the random walk hypothesis is also an implication of many diverse models of rational economic behavior.¹ Several recent studies have tested the random walk theory of exploiting the fact that the variance of random walk increments is linear in the sampling interal.² Therefore the variance of, for example, quarterly increments must be three times as large as the variance of monthly differences. Comparing the (per unit time) variance...

    • 4 An Econometric Analysis of Nonsynchronous Trading
      (pp. 85-114)

      It has long been recognized that the sampling of economic time series plays a subtle but critical role in determining their stochastic properties. Perhaps the best example of this is the growing literature on temporal aggregation biases which are created by confusing stock and flow variables. This is the essence of Working’s (1960) now classic result in which time-averages are mistaken for point-sampled data. More generally, econometric problems are bound to arise when we ignore the fact that the statistical behavior of sampled data may be quite different from the behavior of the underlying stochastic process from which the sample...

    • 5 When Are Contrarian Profits Due to Stock Market Overreaction?
      (pp. 115-146)

      Since the publication of Louis Bachelier’s thesisTheory of Speculationin 1900, the theoretical and empirical implications of the random walk hypothesis as a model for speculative prices have been subjects of considerable interest to financial economists. First developed by Bachelier from rudimentary economic considerations of “fair games,” the random walk has received broader support from the many early empirical studies confirming the unpredictability of stock-price changes.¹ Of course, as Leroy (1973) and Lucas (1978) have shown, the unforecastability of asset returns is neither a necessary nor a sufficient condition of economic equilibrium. And, in view of the empirical evidence...

    • 6 Long-Term Memory in Stock Market Prices
      (pp. 147-184)

      That economic time series can exhibit long-range dependence has been a hypothesis of many early theories of the trade and business cycles. Such theories were often motivated by the distinct but nonperiodic cyclical patterns that typified plots of economic aggregates over time, cycles of many periods, some that seem nearly as long as the entire span of the sample. In the frequency domain such time series are said to have power at low frequencies. So common was this particular feature of the data that Granger (1966) considered it the “typical spectral shape of an economic variable.” It has also been...

  8. Part II
    • [Part II Introduction]
      (pp. 185-188)

      The focus of the five chapters in Part I has been the Random Walk Hypothesis and the forecastability of asset returns through time. In the three chapters of Part II, we shift our focus to questions of the predictability of relative returns for a given time period. On average, is the return to one stock or portfolio higher than the return to another stock or portfolio? If the answer to this age-old question is yes, can we explain the difference, perhaps through differences in risk?

      These questions are central to financial economics since they bear directly on the trade-off between...

    • 7 Multifactor Models Do Not Explain Deviations from the CAPM
      (pp. 189-212)

      One of the important problems of modern financial economics is the quantification of the tradeoff between risk and expected return. Although common sense suggests that investments free of risk will generally yield lower returns than riskier investments such as the stock market, it was only with the development of the Sharpe-Lintner capital asset pricing model (CAPM) that economists were able to quantify these differences in returns. In particular, the CAPM shows that the cross-section of expected excess returns of financial assets must be linearly related to the market betas, with an intercept of zero. Because of the practical importance of...

    • 8 Data-Snooping Biases in Tests of Financial Asset Pricing Models
      (pp. 213-248)

      The reliance of economic science upon nonexperimental inference is, at once, one of the most challenging and most nettlesome aspects of the discipline. Because of the virtual impossibility of controlled experimentation in economics, the importance of statistical data analysis is nowwell-established. However, there is a growing concern that the procedures under which formal statistical inference have been developed may not correspond to those followed in practice.¹ For example, the classical statistical approach to selecting a method of estimation generally involves minimizing an expected loss function, irrespective of the actual data. Yet in practice the properties of the realized data almost...

    • 9 Maximizing Predictability in the Stock and Bond Markets
      (pp. 249-284)

      The search for predictability in asset returns has occupied the attention of investors and academics since the advent of organized financial markets. While investors have an obvious financial interest in predictability, its economic importance can be traced to at least three distinct sources: implications for how aggregate fluctuations in the economy are transmitted to and from financial markets, implications for optimal consumption and investment policies, and implications for market efficiency. For example, several recent papers claim that the apparent predictability in long-horizon stock return indexes is due to business cycle movements and changes in aggregate risk premia.¹ Others claim that...

  9. Part III
    • [Part III Introduction]
      (pp. 285-286)

      In Parts I and II we have documented the presence of statistically significant sources of predictability in recent US stock and bond returns. The natural question that follows is whether such predictability is also economically significant, i.e., is it something that investors should consider in formulating their portfolio strategies, or are the effects too small, too short-lived, or too concentrated in illiquid securities to be of any practical value? In other words, is there value left after trading costs have been deducted? This depends, of course, on the magnitude of trading costs, the frequency of trades, and the impact of...

    • 10 An Ordered Probit Analysis of Transaction Stock Prices
      (pp. 287-346)

      Virtually all empirical investigations of the microstructure of securities markets require a statistical model of asset prices that can capture the salient features of price movements from one transaction to the next. For example, because there are several theories of why bid/ask spreads exist, a stochastic model for prices is a prerequisite to empirically decomposing observed spreads into components due to order-processing costs, adverse selection, and specialist market power.¹ The benefits and costs of particular aspects of a market’s microstructure, such as margin requirements, the degree of competition faced by dealers, the frequency that orders are cleared, and intraday volatility...

    • 11 Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices
      (pp. 347-368)

      The spectacular growth in the volume of trading in stock index futures contracts reveals the interest in these instruments that is shared by a broad cross section of market participants. It is generally agreed that the linkage in prices between the underlying basket of stocks and the futures is maintained by arbitrageurs. If this link is maintained effectively, then investors who are committed to trade will recognize these markets as perfect substitutes, and their choice between these markets will be dictated by convenience and their transaction costs. However, researchers have reported substantial and sustained deviation in futures prices from their...

    • 12 Order Imbalances and Stock Price Movements on October 19 and 20, 1987
      (pp. 369-394)

      The various official reports on the October Crash all point to the breakdown of the linkage between the pricing of the future contract on the S&P 500 and the stocks making up that index.¹ On October 19 and 20, 1987, the future contract often sold at substantial discounts from the cash index, when theoretically it should have been selling at a slight premium. The markets had become “delinked.”

      On October 19, the S&P 500 dropped by more than twenty percent. On October 20, the S&P 500 initially rose and then fell off for the rest of the day to close...

  10. References
    (pp. 395-416)
  11. Index
    (pp. 417-424)