Research Dialogues

Issue Number 52 September 1997 A publication of External Affairs — Corporate Research

A Nonrandom Walk Down Wall Street: Recent Advances in Financial Technology

(those who select managers of large December 1996, the $1 investment In this issue: portfolios) listened. But as time went on, would have grown to $14. If, on the Introduction it became apparent that they should have. other hand, the had put $1 into Because of fees and turnover, the the market, e.g., the S&P 500, and Prices and managers they picked typically under- continued reinvesting the proceeds in the the Random Walk performed the market. And the worse an stock market month by month over this active manager did relative to a market same seventy-year period, the $1 The Martingale Model index, the more attractive seemed the low- investment would have grown to $1,370, The Random Walk Hypothesis cost alternative of buying and holding the a considerably larger sum. Now suppose index itself. that each month, an investor could tell in Rejecting the Random Walk advance which of these two investments But as luck would have it, just as Implications for Investment would a higher return for that indexing was gaining ground, a new month, and took advantage of this Management wave of academic research was being information by switching the running published that weakened some of the The Efficient Markets Hypothesis total of his initial $1 investment into the results of the earlier research and thereby higher-yielding asset, month by month. A Modern View of Efficient Markets undercut part of the justification for What would a $1 investment in such a indexing. It didn’t obviate all the “perfect foresight” investment strategy Practical Considerations reasons for indexing (indexing was still yield by December 1996? a low-cost way to create diversification for an entire fund or as part of an The startling answer—$2,303,981,824 In this issue of Research Dialogues, (yes, over $2 billion; this is no typo- Andrew W. Lo, Harris & Harris active/passive strategy), but it did tend to silence the index-because-you-can’t-do- graphical error)—often comes as a shock Group Professor, Sloan School of to even the most seasoned professional in- Management, Massachusetts Institute better school. vestment manager. Of course, few in- of Technology, takes a look at an old Andrew Lo was, and continues to be, at vestors have perfect foresight. But this issue in investment risk management in the forefront of this new research. In a new way. In the ’50s and ’60s, just extreme example suggests that even a 1988, for example, he and MacKinlay modest ability to forecast financial asset re- as the era of the professional portfolio (see references, page 7) published evidence manager was dawning, financial that resulted in the rejection of the turns may be handsomely rewarded: it economists were telling anyone who Random Walk Hypothesis. That does not take a large fraction of would listen that active management evidence is summarized below and $2,303,981,824 to beat $1,370! For this was probably a big mistake—a waste fittingly constitutes the first step in reason, quantitative models of the risks of time and money. Their research Professor Lo’s interesting nonrandom and rewards of financial investments— demonstrated that historical prices were walk. now known collectively as financial technol- of little use in helping to predict where ogy or financial engineering—have become future prices would go. Prices simply Introduction virtually indispensable to institutional in- took a “random walk.” The better part vestors throughout the world. If, in January 1926, an investor put of wisdom, they advised, was to be a Of course, financial engineering is still passive investor. $1 into one-month U.S. Treasury bills— one of the “safest” assets in the world— in its infancy when compared with the At first, not too many of the people who and continued reinvesting the proceeds mathematical and natural sciences. influence the way money is managed in Treasury bills month by month until However, it has enjoyed a spectacular

© 1997 Teachers Insurance and Annuity Association College Retirement Equities Fund period of growth over the past three model, whose origins lie in the history of information contained in past prices is in- decades, thanks in part to the break- games of chance and the birth of probabili- stantly, fully, and perpetually reflected in throughs pioneered by academics such as ty theory.1 The prominent Italian mathe- the asset’s current price. However, one of Fischer Black, John Cox, Harry Markowitz, matician Girolamo Cardano proposed an the central ideas of modern financial eco- Robert Merton, Stephen Ross, Paul elementary theory of gambling in his 1565 nomics is the necessity of some trade-off Samuelson, Myron Scholes, William manuscript Liber de ludo aleae (The Book of between risk and expected return, and al- Sharpe, and many others. Moreover, paral- Games of Chance), in which he writes: though the martingale hypothesis places a lel breakthroughs in mathematics, statis- The most fundamental principle of all restriction on expected returns, it does not tics, and computational power have in gambling is simply equal conditions, account for risk in any way. enabled the financial community to imple- e.g., of opponents, of bystanders, of In particular, if an asset’s expected price ment such financial technology almost im- money, of situation, of the dice box, and change is positive, it may be the reward mediately, giving it an empirical relevance of the die itself. To the extent to which necessary to attract to hold the and practical urgency shared by few other you depart from that equality, if it is in asset and bear its associated risks. Indeed, if disciplines in the social sciences. your opponent’s favour, you are a fool, an investor is risk averse, he would gladly This brief article describes one simple and if in your own, you are unjust.2 pay to avoid holding an asset with the mar- example of modern financial technology: This clearly contains the notion of a “fair tingale property. Therefore, despite the in- testing the Random Walk Hypothesis— game,” a game which is neither in your tuitive appeal that the “fair game” the hypothesis that past prices cannot be favor nor your opponent’s, and this is the interpretation might have, it has been used to forecast future prices—for aggre- essence of a martingale, a precursor to the shown that the martingale property is nei- gate U.S. stock market indexes. Although ther a necessary nor a sufficient condition Random Walk Hypothesis (RWH). If Pt the random walk is a very old idea, dating represents one’s cumulative winnings or for rationally determined asset prices (see, back to the sixteenth century, recent studies wealth at date t from playing some game of for example, LeRoy [1973], and Lucas have shed new light on this important chance each period, then a fair game is one [1978]). model of financial prices. The findings in which the expected wealth next period is Nevertheless, the martingale has be- suggest that stock market prices do contain simply equal to this period’s wealth. come a powerful tool in probability and predictable components and that there may If P is taken to be an asset’s price at date statistics, and also has important applica- be significant returns to active investment t tions in modern theories of asset prices. For management. t, then the martingale hypothesis states that tomorrow’s price is expected to be example, once asset returns are properly ad- justed for risk, the martingale property Stock Market Prices and equal to today’s price, given the asset’s en- the Random Walk tire price history. Alternatively, the asset’s does hold (see Lucas [1978], Cox and Ross expected price change is zero when condi- [1976], and Harrison and Kreps [1979]), One of the most enduring questions of and the combination of this risk adjust- is whether or not finan- tioned on the asset’s price history; hence its price is just as likely to rise as it is to fall. ment and the martingale property has led cial asset prices are forecastable. Perhaps to a veritable revolution in the pricing of because of the obvious analogy between fi- From a forecasting perspective, the martin- gale hypothesis implies that the “best” fore- complex financial instruments such as op- nancial investments and games of chance, tions, swaps, and other derivative securities. mathematical models of asset prices have an cast of tomorrow’s price is simply today’s price, where the “best” forecast is defined to Moreover, the martingale led to the devel- unusually rich history that predates virtual- opment of a closely related model that has be the one that minimizes the average ly every other aspect of economic analysis. now become an integral part of virtually squared error of the forecast. The vast number of prominent mathemati- every scientific discipline concerned with cians and scientists who have plied their Another implication of the martingale dynamic uncertainty: the Random Walk considerable skills in forecasting stock and hypothesis is that nonoverlapping price Hypothesis. commodity prices is a testament to the fas- changes are uncorrelated at all leads and cination and the challenges that this prob- lags, which further implies the ineffective- The Random Walk Hypothesis lem poses. Indeed, the intellectual roots of ness of all linear forecasting rules for future The simplest version of the RWH states modern financial economics are firmly price changes that are based on the price that future returns cannot be forecast from planted in early attempts to “beat the mar- history. The fact that so sweeping an im- past returns. For example, under the ket,” an endeavor that is still of current in- plication could come from so simple a RWH, if stock XYZ performed poorly last terest and is discussed and debated even in model foreshadows the central role that the month, this has no bearing on how XYZ the most recent journals, conferences, and martingale hypothesis plays in the model- will perform this month, or in any future cocktail parties! ing of asset price dynamics (see, for exam- month. In this respect, the RWH is not ple, Huang and Litzenberger [1988]). The Martingale Model unlike a sequence of fair-coin tosses: the In fact, the martingale was consid- fact that one toss comes up heads, or that a One of the earliest mathematical models ered to be a necessary condition for an effi- sequence of five tosses is composed of all of financial asset prices was the martingale cient asset market, one in which the heads, has no implications for what the

Page 2 Research Dialogues next toss is likely to be. In , past re- restrictive version of the RWH—the uncor- that variances grow less than linearly with turns cannot be used to forecast future re- related-increments version—has sharp impli- the return horizon. turns under the RWH. In the jargon of cations: it rules out the efficacy of linear economic theory, all information contained forecasting techniques such as regression Rejecting the Random Walk in past returns has been impounded into analysis.3 Whether or not the variance ratio is the current market price: therefore nothing All versions of the RWH have one com- close to 1 depends on what “close” means; can be gleaned from past returns if the goal mon implication: the of returns Lo and MacKinlay [1988] provide a precise is to forecast the next price change, i.e., the must increase one-for-one with the return statistical measure in their variance ratio future return. horizon. For example, under the RWH, statistic. They apply the variance ratio The RWH has dramatic implications the volatility of two-week returns must be statistic to two broad-based weekly indexes for the typical investor. In its most strin- exactly twice the volatility of one-week re- of U.S. equity returns—equal- and value- gent form—the independently-and-identi- turns; the volatility of four-week returns weighted indexes of all securities traded on cally-distributed or IID version—it implies must be exactly twice the volatility of two- the New York and American Stock that optimal investment policies do not de- week returns; and so on. Therefore, one test Exchanges—derived from the University pend on historical performance, so that a of the RWH is to compare the volatility of of Chicago’s Center for Research in spell of below-average returns does not re- two-week returns with twice the volatility Securities Prices (CRSP) daily stock returns quire rethinking the wisdom of the opti- of one-week returns. If they are close, this database.4 lends support for the RWH; if they are not, mal policy. A somewhat less restrictive Despite the fact that the CRSP monthly this suggests that the RWH is false. version of the RWH—the independent- database begins in 1926, whereas the returns version—allows historical perfor- This aspect of the RWH is particularly daily database begins in 1962, Lo and mance to influence investment policies, relevant for long-term investors: under the MacKinlay choose to construct weekly re- but rules out the efficacy of nonlinear fore- RWH, the riskiness of an investment—as turns from the daily database; hence their casting techniques. For example, “chart- measured by the return variance—increas- data span the period from 1962 to 1992.5 ing” or “”—the practice es linearly with the investment horizon and They focus on weekly returns for two rea- of predicting future price movements by is not “averaged out” over time (see Bodie sons: (1) more-recent data are likely to be attempting to spot geometrical shapes and [1996] for further discussion). Therefore, more relevant to current practice—the in- other regularities in historical price any claim that an investment becomes less stitutional features of equity markets and charts—will not work if the independent- risky over time must be based on the as- investment behavior are considerably dif- returns RWH is true. And even the least sumption that the RWH does not hold and ferent now than in the 1920s; (2) since their test is based on variances, it is not the Table 1 calendar time span that affects the accuracy Variance Ratio Test of the RWH of their estimates but rather the sample Sample period Number nq of Number q of base observations aggregated size, and weekly data are the best compro- base observations to form variance ratio mise between maximizing the sample size 24 816and minimizing the effects of market fric- A. CRSP NYSE/AMEX Equal-Weighted Index tions, e.g., the bid/ask spread, that affect 621212-921223 1,568 1.27 1.58 1.86 1.94 daily data. (5.29)* (6.66)* (7.15)* (5.93)* Lo and MacKinlay’s findings are sum- 621212-771214 784 1.31 1.67 1.98 2.11 marized in Table 1. The values reported in (5.99)* (7.18)* (6.80)* (5.41)* the main rows are the ratios of the variance 771221-921223 784 1.23 1.47 1.70 1.72 of q-week returns to q times the variance (2.40)* (3.01)* (3.52)* (2.91)* of one-week returns, and the entries en- B. CRSP NYSE/AMEX Value-Weighted Index closed in parentheses are measures of 621212-921223 1,568 1.06 1.12 1.15 1.13 “closeness” to 1, where larger values repre- (1.54)* (1.64)* (1.43)* (0.86)* sent more statistically significant devia- 621212-771214 784 1.07 1.16 1.22 1.26 tions from the RWH.6 Panel A contains (1.49)* (1.73)* (1.59)* (1.24)* results for the equal-weighted index and 771221-921223 784 1.06 1.09 1.07 0.98 Panel B contains similar results for the (0.87)* (0.76)* (0.48)* (0.09)* value-weighted index. Within each Variance ratios for weekly equal- and value-weighted indexes of all NYSE and AMEX , derived panel, the first row presents the variance from the CRSP daily stock returns database. The variance ratios are reported in the main rows, with the ratios and test statistics for the entire heteroskedasticity-robust test statistics z*(q) given in parentheses immediately below each main row. 1,568-week sample and the next two rows Under the Random Walk Null hypothesis, the value of the variance ratio is 1 and the test statistics have give the results for the two equally parti- a standard normal distribution asymptotically. Test statistics marked with asterisks indicate that the corresponding variance ratios are statistically different from 1 at the 5 percent level of significance. tioned 784-week subsamples.

Research Dialogues Page 3 Table 1 shows that the RWH can be re- Implications for This humorous example of economic jected at all the usual significance levels for Investment Management logic gone awry strikes dangerously close to the entire time period and all subperiods. The rejection of the RWH for U.S. eq- home for students of the Efficient Markets For example, the typical cutoff value for the uity indexes raises the possibility of im- Hypothesis (EMH), one of the most con- measure of closeness is ±1.96—a value be- proving investment returns by active troversial and well-studied propositions in tween –1.96 and +1.96 indicates that the portfolio management. After all, if the all the social sciences. Briefly, the EMH variance ratio is close enough to 1 to be RWH implies that stock returns are un- states that in an efficient market, all avail- consistent with the RWH. However, a forecastable, its rejection would seem to say able information is fully reflected in current 7 value outside this range indicates an incon- that stock returns are forecastable. But sev- market prices. Therefore, any attempt to sistency between the RWH and the behav- eral caveats are in order before we begin our forecast future price movements is futile— ior of volatility over different return attempts to “beat the market.” any information on which the forecast is horizons. The value 5.29, corresponding to based has already been impounded into the the variance ratio 1.27 of two-week returns First, the rejection of the RWH is based current price. to one-week returns of the equal-weighted on historical data, and past performance is no guarantee of future success. While the The EMH is disarmingly simple to index, demonstrates a gross inconsistency state, has far-reaching consequences for aca- between the RWH and the data. The other statistical inferences performed by Lo and MacKinlay [1988] are remarkably robust, demic pursuits and business practice, and variance ratios in Table 1 document simi- yet is surprisingly resilient to empirical nevertheless all statistical inference requires lar inconsistencies. proof or refutation. Even after three a certain willing suspension of disbelief re- The statistics in Table 1 also tell us decades of research and literally thousands garding structural changes in institutions how the RWH is inconsistent with the of journal articles, economists have not yet and business conditions. data: variances grow faster than linearly reached a consensus about whether mar- with the return horizon. In particular, for Second, we have not considered the im- kets—particularly financial markets—are the equal-weighted index, the entry 1.27 pact of trading costs on investment perfor- efficient or not. mance. While a rejection of the RWH in the “q=2” column implies that two- One of the reasons for this state of affairs implies a degree of predictability in stock week returns have a variance that is 27 is the fact that the EMH, by itself, is not a percent higher than twice the variance of returns, the trading costs associated with well-defined and empirically refutable one-week returns. This suggests that the exploiting such predictability may out- hypothesis. To make it operational, one riskiness of an investment in the equal- weigh the benefits. Without a more careful must specify additional structure, e.g., in- weighted index increases with the return investigation of trading costs, it is virtually vestors’ preferences, information structure, horizon; there is “antidiversification” over impossible to assess the economic signifi- etc. But then a test of the EMH becomes a time in this case. cance of the rejections reported in Table 1. test of several auxiliary hypotheses as well, Of course, it should be emphasized Finally, and perhaps most important, and a rejection of such a joint hypothesis that this antidiversification applies only to suppose the rejections of the RWH are tells us little about which aspect of the joint return horizons from q=2 to q=16. For both statistically and economically signifi- hypothesis is inconsistent with the data. much longer return horizons, e.g., q=150 cant, even after adjusting for trading costs For example, academics in the 1960s equat- or greater, there is some weak evidence and other institutional frictions; does this ed the EMH with the RWH, but more re- that variances grow less than linearly with imply some sort of “free lunch”? Should all cent studies by LeRoy [1973] and Lucas the return horizon. However, those infer- investors, young and old, attempt to fore- [1978] have shown that the RWH may be ences are not based on as many data points cast the stock market and trade more ac- violated in a perfectly efficient market. and are considerably less accurate than the tively according to such forecasts? In other More important, tests of the EMH may shorter-horizon inferences drawn from words, is the stock market efficient or can not be the most informative means of Table 1 (see Campbell, Lo, and one achieve superior investment returns by gauging the efficiency of a given market. MacKinlay [1997, Chapter 2] for further trading intelligently? What is often of more consequence is the discussion). relative efficiency of a particular market, rel- Although the test statistics in Table 1 The Efficient Markets Hypothesis ative to other markets, e.g., futures vs. spot are based on nominal stock returns, it is ap- There is an old joke, widely told among markets, auction vs. dealer markets, etc. parent that virtually the same results would economists, about an economist strolling The advantages of the concept of relative ef- obtain with real or excess returns. Since the down the street with a companion when ficiency, as opposed to the all-or-nothing volatility of weekly nominal returns is so they come upon a $100 bill lying on the notion of absolute efficiency, are easy to much larger than that of the inflation and ground. As the companion reaches down spot by way of an analogy. Physical systems Treasury-bill rates, the use of nominal, real, to pick it up, the economist says, “Don’t are often given an efficiency rating based on or excess returns in a volatility-based test bother—if it were a real $100 bill, some- the relative proportion of energy or fuel will yield practically identical inferences. one would have already picked it up.” converted to useful work. Therefore, a pis-

Page 4 Research Dialogues ton engine may be rated at 60 percent effi- presumption since it ignores the difficulty ciplined active investment management. ciency, meaning that on average, 60 per- and gestation lags of research and develop- In much the same way that innovations in cent of the energy contained in the engine’s ment in biotechnology. Moreover, if a biotechnology can garner superior returns fuel is used to turn the crankshaft, with the pharmaceutical company does succeed in for venture capitalists, innovations in finan- remaining 40 percent lost to other forms of developing such a vaccine, the profits cial technology can garner equally superior work, e.g., heat, light, noise, etc. earned would be measured in the billions of returns for investors. dollars. Would this be considered “excess” Few engineers would ever consider per- However, several qualifications must be profits, or rather the fair economic return forming a statistical test to determine kept in mind when assessing which of the that accrues to biotechnology patents? whether or not a given engine is perfectly many active strategies being touted is ap- efficient—such an engine exists only in the Financial markets are no different in propriate for a particular investor. First, the idealized frictionless world of the imagina- principle, only in degrees. Consequently, riskiness of active strategies can be very dif- tion. But measuring relative efficiency— the profits that accrue to an investment ferent from that of passive strategies, and relative to the frictionless ideal—is professional need not be a market inefficien- such risks do not necessarily “average out” commonplace. Indeed, we have come to cy, but may simply be the fair reward to over time. In particular, the investor’s risk expect such measurements for many house- breakthroughs in financial technology. tolerance must be taken into account in se- hold products: air conditioners, hot water After all, few analysts would regard the lecting the long-term investment strategy heaters, refrigerators, etc. Therefore, from a hefty profits of Amgen over the past few that will best match his or her goals. This practical point of view, and in light of years as evidence of an inefficient market for is no simple task, since many investors have Grossman and Stiglitz [1980], the EMH is pharmaceuticals—Amgen’s recent prof- little understanding of their own risk pref- an idealization that is economically unreal- itability is readily identified with the devel- erences. Consumer education is therefore izable, but serves as a useful benchmark for opment of several new drugs (Epogen, for perhaps the most pressing need in the near measuring relative efficiency. example, a drug that stimulates the pro- term. Fortunately, computer technology duction of red blood cells), some considered can play a major role in this challenge, pro- A Modern View of Efficient Markets breakthroughs in biotechnology. Similarly, viding scenario analyses, graphical displays A more practical version of the EMH is even in efficient financial markets there are of potential losses and gains, and realistic suggested by another analogy, one involv- very handsome returns to breakthroughs in simulations of long-term investment per- ing the notion of thermal equilibrium in financial technology. formance that are user-friendly and easily statistical mechanics. Despite the occasion- Of course, barriers to entry are typically incorporated into an investor’s worldview. al “excess” profit opportunity, on average lower, the degree of competition is much Nevertheless, a good understanding of the and over time, it is not possible to earn such higher, and most financial technologies are investor’s understanding of the nature of fi- profits consistently without some type of not patentable (though this may soon nancial risks and rewards is the natural competitive advantage, e.g., superior infor- change); hence the “half life” of the prof- starting point for the investment process. mation, superior technology, financial in- itability of financial innovation is consider- Second, there are a plethora of active novation, etc. Alternatively, in an efficient ably smaller. These features imply that managers vying for the privilege of manag- market, the only way to earn positive prof- financial markets should be relatively more ing pension assets, but they cannot all out- its consistently is to develop a competitive efficient, and indeed they are. The market perform the market every year (nor should advantage, in which case the profits may be for used securities is considerably more effi- we necessarily expect them to). Though viewed as the economic rents that accrue to cient than the market for used cars. But to often judged against a common bench- this competitive advantage. The consisten- argue that financial markets must be per- mark, e.g., the S&P 500, active strategies cy of such profits is an important qualifica- fectly efficient is tantamount to the claim can have very diverse risk characteristics, tion—in this version of the EMH, an that an AIDS vaccine cannot be found. In and these must be weighed in assessing occasional free lunch is permitted, but free an EMH, it is difficult to earn a good liv- their performance. An active strategy in- lunch plans are ruled out. ing, but not impossible. volving high-risk venture-capital invest- To see why such an interpretation of the ments will tend to outperform the S&P EMH is a more practical one, consider for a Practical Considerations 500 more often than a less aggressive “en- hanced indexing” strategy, yet one is not moment applying the classical version of These recent research findings have sev- necessarily better than the other. the EMH to a nonfinancial market—say, eral implications for both long-term in- the market for biotechnology. Consider, for vestors in defined-contribution pension In particular, past performance should example, the goal of developing a vaccine plans and for plan sponsors. The fact that not be the sole or even the major criterion by for the AIDS virus. If the market for the RWH hypothesis can be rejected for re- which investment managers are judged. biotechnology is efficient in the classical cent U.S. equity returns suggests the pres- This statement often surprises investors sense, such a vaccine can never be devel- ence of predictable components in the stock and finance professionals—after all, isn’t oped—if it could, someone would have al- market. This opens the door to superior this the bottom line? Put another way, “If ready done it! This is clearly a ludicrous long-term investment returns through dis- it works, who cares why?” Selecting an in-

Research Dialogues Page 5 vestment manager solely by past perfor- vation, we can make some educated guesses and underappreciated sources. No one has mance is one of the surest paths to financial about where the likely sources of value- illustrated this principle so well as Harry disaster. Unlike the experimental sciences added might be for active investment man- Markowitz, the father of modern portfolio such as physics and biology, financial eco- agement in the near future. theory and a winner of the 1990 Nobel nomics (and most other social sciences) re- • The revolution in computing technolo- Prize in economics. In describing his ex- lies primarily on statistical inference to test gy and data sources suggests that highly perience as a Ph.D. student on the eve of its theories. Therefore, we can never know computation-intensive strategies—ones his graduation in the following way, he with perfect certainty that a particular in- that could not have been implemented wrote in his Nobel address: “[W]hen I de- vestment strategy is successful, since even fended my dissertation as a student in the the most successful strategy can always be five years ago—which exploit certain regularities in securities prices, e.g., Economics Department of the University explained by pure luck (see Lo [1994] and of Chicago, Professor Milton Friedman ar- Lo and MacKinlay [1990] for some con- clientele biases, tax opportunities, infor- mation lags, can add value. gued that portfolio theory was not crete illustrations). Economics, and that they could not award Of course, some kinds of success are eas- • Many studies have demonstrated the me a Ph.D. degree in Economics for a dis- ier to attribute to luck than others, and it is enormous impact that transaction costs sertation which was not Economics. I as- precisely this kind of attribution that must can have on long-term investment per- sume that he was only half serious, since be performed in deciding on a particular formance. More sophisticated methods they did award me the degree without active investment style. Is it luck, or is it for measuring and controlling transac- long debate. As to the merits of his argu- genuine? tion costs—methods that employ high- ments, at this point I am quite willing to While statistical inference can be very frequency data, economic models of concede: at the time I defended my dis- helpful in tackling this question, in the price impact, and advanced optimiza- sertation, portfolio theory was not part of 8 ❑ final analysis the question is not about tion techniques—can add value. Also, Economics. But now it is.” statistics, but rather about economics and the introduction of financial instru- financial innovation. Under the practical ments that reduce transaction costs, e.g., version of the EMH, it is difficult (but not swaps, options, and other derivative se- References impossible) to provide investors with con- curities, can add value. sistently superior investment returns. So • Recent research in psychological biases Bodie, Z., 1996, “Risks in the Long Run,” Finan- what are the sources of superior perfor- inherent in human cognition suggest cial Analysts Journal 52, 18_22. mance promised by an active manager, and that investment strategies exploiting Campbell, J., A. Lo, and C. MacKinlay, 1997, The why have other competing managers not these biases can add value. However, Econometrics of Financial Markets. Princeton, NJ: recognized these opportunities? Is it better Princeton University Press. contrary to the recently popular “behav- Cox, J., and S. Ross, 1976, “The Valuation of Op- mathematical models of financial markets? ioral” approach to investments, which Or more accurate statistical methods for tions for Alternative Stochastic Processes,” Jour- proposes to take advantage of individual nal of Financial Economics 3, 145_166. identifying investment opportunities? Or “irrationality,” I suggest that value- Fama, E., 1970, “Efficient Capital Markets: A Re- more timely data in a market where minute added comes from creating investments view of Theory and Empirical Work,” Journal of delays can mean the difference between Finance 25, 383_417. profits and losses? Without a compelling with more attractive risk-sharing char- acteristics suggested by psychological Grossman, S., and J. Stiglitz, 1980, “On the Im- argument for where an active manager’s possibility of Informationally Efficient Mar- value-added is coming from, one must be models. Though the difference may kets,” American Economic Review 70, 393_408. very skeptical about the prospects for future seem academic, it has far-reaching con- Hald, A., 1990, A History of Probability and Statis- performance. In particular, the concept of a sequences for the long-run performance tics and Their Applications Before 1750. New “black box”—a device that performs a of such strategies: taking advantage of York: John Wiley & Sons. known function reliably but obscurely— individual irrationality cannot be a Harrison, J., and D. Kreps, 1979, “Martingales recipe for long-term success, but pro- and Arbitrage in Multi-period Securities Mar- may make sense in engineering applica- _ viding a better set of opportunities that kets,” Journal of Economic Theory 20, 381 408. tions, where repeated experiments can Huang, C., and R. Litzenberger, 1988, Founda- validate the reliability of the box’s perfor- more closely match what investors de- tions for Financial Economics. New York: North mance, but it has no counterpart in invest- sire seems more promising. Holland. ment management, where performance Of course, forecasting the sources of fu- LeRoy, S., 1973, “Risk Aversion and the Martin- attribution is considerably more difficult. gale Property of Stock Returns,” International ture innovations in financial technology is _ For analyzing investment strategies, it a treacherous business, fraught with many Economic Review 14, 436 446. matters a great deal why a strategy is sup- half-baked successes and some embarrass- Lo, A., 1994, “Data-Snooping Biases in Financial posed to work. Analysis,” in H. Russell Fogler, ed.: Blending ing failures. Perhaps the only reliable pre- Quantitative and Traditional Equity Analysis. Finally, despite the caveats concerning diction is that the innovations of the Charlottesville, VA: Association for Investment performance attribution and proper moti- future are likely to come from unexpected Management and Research.

Page 6 Research Dialogues Lo, A., and C. MacKinlay, 1988, “Stock Market Endnotes tial in determining the behavior of the index, Prices Do Not Follow Random Walks: Evi- e.g., the S&P 500 index. 1 The etymology of martingale as a mathematical dence from a Simple Specification Test,” Review 5 Lo and MacKinlay’s (1988) original sample _ term is unclear. Its French root has two mean- of Financial Studies 1, 41 66. ings: a leather strap tied to a horse’s bit and period was 1962 to 1985; it has been extended Lo, A., and C. MacKinlay, 1990, “Data Snooping reins to ensure that they stay in place, and a to 1992 in Table 1, and the qualitative features remain unchanged. Biases in Tests of Financial Mod- gambling system involving doubling the bet 6 els,” Review of Financial Studies 3, 431_468. when one is losing. Specifically, the parenthetical entries are z-statistics, which are approximately normally Lucas, R. E., 1978, “Asset Prices in an Exchange 2 See Hald (1990, Chapter 4) for further details. _ 3 distributed with zero mean and unit variance. Economy,” Econometrica 46, 1429 1446. See Campbell, Lo, and MacKinlay (1997, 7 Chapter 2) for a more detailed discussion of the Although the EMH has a long and illustrious Roberts, H., May 1967, “Statistical versus Clini- history, three authors are usually credited with cal Prediction of the Stock Market,” unpub- various versions of the RWH. 4 An equal-weighted index is one in which all its development: Fama (1970), Roberts lished manuscript, Center for Research in (1967), and Samuelson (1965). stocks are weighted equally in computing the 8 Security Prices, University of Chicago. index, e.g., the Value-Line Index. A value- Tore Frängsmyr, ed., Les Prix Nobel (Stock- Samuelson, P., 1965, “Proof That Properly Antic- weighted index is one in which all stocks are holm: Norstedts Tryckeri AB, 1990), 302. ipated Prices Fluctuate Randomly,” Industrial weighted by their ; hence Management Review 6, 41_49. larger-capitalization stocks are more influen-

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