Introduction

If, in January 1926, an investor put$1 into one-month U.S. Treasury billsone of the safest assets in the worldand continued reinvesting the proceedsin Treasury bills month by month until

December 1996, the $1 investmentwould have grown to $14. If, on theother hand, the investor had put $1 intothe stock market, e.g., the S&P 500, andcontinued reinvesting the proceeds in thestock market month by month over thissame seventy-year period, the $1investment would have grown to $1,370,a considerably larger sum. Now supposethat each month, an investor could tell inadvance which of these two investmentswould yield a higher return for thatmonth, and took advantage of thisinformation by switching the runningtotal of his initial $1 investment into thehigher-yielding asset, month by month.What would a $1 investment in such aperfect foresight investment strategyyield by December 1996?

The startling answer$2,303,981,824(yes, over $2 billion; this is no typo-graphical error)often comes as a shockto even the most seasoned professional in-vestment manager. Of course, few in-vestors have perfect foresight. But thisextreme example suggests that even amodest ability to forecast financial asset re-turns may be handsomely rewarded: itdoes not take a large fraction of$2,303,981,824 to beat $1,370! For thisreason, quantitative models of the risksand rewards of financial investmentsnow known collectively as financial technol-ogy or financial engineeringhave becomevirtually indispensable to institutional in-vestors throughout the world.

Of course, financial engineering is stillin its infancy when compared with themathematical and natural sciences.However, it has enjoyed a spectacular

1997 Teachers Insurance and Annuity Association College Retirement Equities Fund

Research DialoguesIssue Number 52

September 1997

A publication of External Affairs Corporate Research

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

In this issue:

Introduction

Stock Market Prices and the Random Walk

The Martingale Model

The Random Walk Hypothesis

Rejecting the Random Walk

Implications for InvestmentManagement

The Efficient Markets Hypothesis

A Modern View of Efficient Markets

Practical Considerations

In this issue of Research Dialogues,Andrew W. Lo, Harris & HarrisGroup Professor, Sloan School ofManagement, Massachusetts Instituteof Technology, takes a look at an oldissue in investment risk management ina new way. In the 50s and 60s, justas the era of the professional portfoliomanager was dawning, financialeconomists were telling anyone whowould listen that active managementwas probably a big mistakea wasteof time and money. Their researchdemonstrated that historical prices wereof little use in helping to predict wherefuture prices would go. Prices simplytook a random walk. The better partof wisdom, they advised, was to be apassive investor.

At first, not too many of the people whoinfluence the way money is managed

(those who select managers of largeportfolios) listened. But as time went on,it became apparent that they should have.Because of fees and turnover, themanagers they picked typically under-performed the market. And the worse anactive manager did relative to a marketindex, the more attractive seemed the low-cost alternative of buying and holding theindex itself.

But as luck would have it, just asindexing was gaining ground, a newwave of academic research was beingpublished that weakened some of theresults of the earlier research and therebyundercut part of the justification forindexing. It didnt obviate all thereasons for indexing (indexing was stilla low-cost way to create diversificationfor an entire fund or as part of anactive/passive strategy), but it did tend tosilence the index-because-you-cant-do-better school.

Andrew Lo was, and continues to be, atthe forefront of this new research. In1988, for example, he and MacKinlay(see references, page 7) published evidencethat resulted in the rejection of theRandom Walk Hypothesis. Thatevidence is summarized below andfittingly constitutes the first step inProfessor Los interesting nonrandomwalk.

Page 2 Research Dialogues

period of growth over the past threedecades, thanks in part to the break-throughs pioneered by academics such asFischer Black, John Cox, Harry Markowitz,Robert Merton, Stephen Ross, PaulSamuelson, Myron Scholes, WilliamSharpe, and many others. Moreover, paral-lel breakthroughs in mathematics, statis-tics, and computational power haveenabled the financial community to imple-ment such financial technology almost im-mediately, giving it an empirical relevanceand practical urgency shared by few otherdisciplines in the social sciences.

This brief article describes one simpleexample of modern financial technology:testing the Random Walk Hypothesisthe hypothesis that past prices cannot beused to forecast future pricesfor aggre-gate U.S. stock market indexes. Althoughthe random walk is a very old idea, datingback to the sixteenth century, recent studieshave shed new light on this importantmodel of financial prices. The findingssuggest that stock market prices do containpredictable components and that there maybe significant returns to active investmentmanagement.

Stock Market Prices and the Random Walk

One of the most enduring questions offinancial economics is whether or not finan-cial asset prices are forecastable. Perhapsbecause of the obvious analogy between fi-nancial investments and games of chance,mathematical models of asset prices have anunusually rich history that predates virtual-ly every other aspect of economic analysis.The vast number of prominent mathemati-cians and scientists who have plied theirconsiderable skills in forecasting stock andcommodity prices is a testament to the fas-cination and the challenges that this prob-lem poses. Indeed, the intellectual roots ofmodern financial economics are firmlyplanted in early attempts to beat the mar-ket, an endeavor that is still of current in-terest and is discussed and debated even inthe most recent journals, conferences, andcocktail parties!

The Martingale Model

One of the earliest mathematical modelsof financial asset prices was the martingale

model, whose origins lie in the history ofgames of chance and the birth of probabili-ty theory.1 The prominent Italian mathe-matician Girolamo Cardano proposed anelementary theory of gambling in his 1565manuscript Liber de ludo aleae (The Book ofGames of Chance), in which he writes:

The most fundamental principle of allin gambling is simply equal conditions,e.g., of opponents, of bystanders, ofmoney, of situation, of the dice box, andof the die itself. To the extent to whichyou depart from that equality, if it is inyour opponents favour, you are a fool,and if in your own, you are unjust.2

This clearly contains the notion of a fairgame, a game which is neither in yourfavor nor your opponents, and this is theessence of a martingale, a precursor to theRandom Walk Hypothesis (RWH). If Ptrepresents ones cumulative winnings orwealth at date t from playing some game ofchance each period, then a fair game is onein which the expected wealth next period issimply equal to this periods wealth.

If Pt is taken to be an assets price at datet, then the martingale hypothesis statesthat tomorrows price is expected to beequal to todays price, given the assets en-tire price history. Alternatively, the assetsexpected price change is zero when condi-tioned on the assets price history; hence itsprice is just as likely to rise as it is to fall.From a forecasting perspective, the martin-gale hypothesis implies that the best fore-cast of tomorrows price is simply todaysprice, where the best forecast is defined tobe the one that minimizes the averagesquared error of the forecast.

Another implication of the martingalehypothesis is that nonoverlapping pricechanges are uncorrelated at all leads andlags, which further implies the ineffective-ness of all linear forecasting rules for futureprice changes that are based on the pricehistory. The fact that so sweeping an im-plication could come from so simple amodel foreshadows the central role that themartingale hypothesis plays in the model-ing of asset price dynamics (see, for exam-ple, Huang and Litzenberger [1988]).

In fact, the martingale was long consid-ered to be a necessary condition for an effi-cient asset market, one in which the

information contained in past prices is in-stantly, fully, and perpetually reflected inthe assets current price. However, one ofthe central ideas of modern financial eco-nomics is the necessity of some trade-offbetween risk and expected return, and al-though the martingale hypothesis places arestriction on expected returns, it does notaccount for risk in any way.

In particular, if an assets expected pricechange is positive, it may be the rewardnecessary to attract investors to hold theasset and bear its associated risks. Indeed, ifan investor is risk averse, he would gladlypay to avoid holding an asset with the mar-tingale property. Therefore, despite the in-tuitive appeal that the fair gameinterpretation might have, it has beenshown that the martingale property is nei-ther a necessary nor a sufficient conditionfor rationally determined asset prices (see,for example, LeRoy [1973], and Lucas[1978]).

Nevertheless, the martingale has be-come a powerful tool in probability andstatistics, and also has important applica-tions in modern theories of asset prices. Forexample, once asset returns are properly ad-justed for risk, the martingale propertydoes hold (see Lucas [1978], Cox and Ross[1976], and Harrison and Kreps [1979]),and the combination of this risk adjust-ment and the martingale property has ledto a veritable revolution in the pricing ofcomplex financial instruments such as op-tions, swaps, and other derivative securities.Moreover, the martingale led to the devel-opment of a closely related model that hasnow become an integral part of virtuallyevery scientific discipline concerned withdynamic uncertainty: the Random WalkHypothesis.

The Random Walk Hypothesis

The simplest version of the RWH statesthat future returns cannot be forecast frompast returns. For example, under theRWH, if stock XYZ performed poorly lastmonth, this has no bearing on how XYZwill perform this month, or in any futuremonth. In this respect, the RWH is notunlike a sequence of fair-coin tosses: thefact that one toss comes up heads, or that asequence of five tosses is composed of allheads, has no implications for what the

next toss is likely to be. In short, past re-turns cannot be used to forecast future re-turns under the RWH. In the jargon ofeconomic theory, all information containedin past returns has been impounded intothe current market price: therefore nothingcan be gleaned from past returns if the goalis to forecast the next price change, i.e., thefuture return.

The RWH has dramatic implicationsfor the typical investor. In its most strin-gent formthe independently-and-identi-cally-distributed or IID versionit impliesthat optimal investment policies do not de-pend on historical performance, so that aspell of below-average returns does not re-quire rethinking the wisdom of the opti-mal policy. A somewhat less restrictiveversion of the RWHthe independent-returns versionallows historical perfor-mance to influence investment policies,but rules out the efficacy of nonlinear fore-casting techniques. For example, chart-ing or technical analysisthe practiceof predicting future price movements byattempting to spot geometrical shapes andother regularities in historical pricechartswill not work if the independent-returns RWH is true. And even the least

restrictive version of the RWHthe uncor-related-increments versionhas sharp impli-cations: it rules out the efficacy of linearforecasting techniques such as regressionanalysis.3

All versions of the RWH have one com-mon implication: the volatility of returnsmust increase one-for-one with the returnhorizon. For example, under the RWH,the volatility of two-week returns must beexactly twice the volatility of one-week re-turns; the volatility of four-week returnsmust be exactly twice the volatility of two-week returns; and so on. Therefore, one testof the RWH is to compare the volatility oftwo-week returns with twice the volatilityof one-week returns. If they are close, thislends support for the RWH; if they are not,this suggests that the RWH is false.

This aspect of the RWH is particularlyrelevant for long-term investors: under theRWH, the riskiness of an investmentasmeasured by the return varianceincreas-es linearly with the investment horizon andis not averaged out over time (see Bodie[1996] for further discussion). Therefore,any claim that an investment becomes lessrisky over time must be based on the as-sumption that the RWH does not hold and

that variances grow less than linearly withthe return horizon.

Rejecting the Random WalkWhether or not the variance ratio is

close to 1 depends on what close means;Lo and MacKinlay [1988] provide a precisestatistical measure in their variance ratiostatistic. They apply the variance ratiostatistic to two broad-based weekly indexesof U.S. equity returnsequal- and value-weighted indexes of all securities traded onthe New York and American StockExchangesderived from the Universityof Chicagos Center for Research inSecurities Prices (CRSP) daily stock returnsdatabase.4

Despite the fact that the CRSP monthlydatabase begins in 1926, whereas thedaily database begins in 1962, Lo andMacKinlay choose to construct weekly re-turns from the daily database; hence theirdata span the period from 1962 to 1992.5

They focus on weekly returns for two rea-sons: (1) more-recent data are likely to bemore relevant to current practicethe in-stitutional features of equity markets andinvestment behavior are considerably dif-ferent now than in the 1920s; (2) sincetheir test is based on variances, it is not thecalendar time span that affects the accuracyof their estimates but rather the samplesize, and weekly data are the best compro-mise between maximizing the sample sizeand minimizing the effects of market fric-tions, e.g., the bid/ask spread, that affectdaily data.

Lo and MacKinlays findings are sum-marized in Table 1. The values reported inthe main rows are the ratios of the varianceof q-week returns to q times the varianceof one-week returns, and the entries en-closed in parentheses are measures ofcloseness to 1, where larger values repre-sent more statistically significant devia-tions from the RWH.6 Panel A containsresults for the equal-weighted index andPanel B contains similar results for thevalue-weighted index. Within eachpanel, the first row presents the varianceratios and test statistics for the entire1,568-week sample and the next two rowsgive the results for the two equally parti-tioned 784-week subsamples.

Research Dialogues Page 3

Table 1Variance Ratio Test of the RWH

Sample period Number nq of Number q of base observations aggregatedbase observations to form variance ratio

2 4 8 16

A. CRSP NYSE/AMEX Equal-Weighted Index621212-921223 1,568 1.27 1.58 1.86 1.94

(5.29)* (6.66)* (7.15)* (5.93)*621212-771214 784 1.31 1.67 1.98 2.11

(5.99)* (7.18)* (6.80)* (5.41)*771221-921223 784 1.23 1.47 1.70 1.72

(2.40)* (3.01)* (3.52)* (2.91)*B. CRSP NYSE/AMEX Value-Weighted Index

621212-921223 1,568 1.06 1.12 1.15 1.13(1.54)* (1.64)* (1.43)* (0.86)*

621212-771214 784 1.07 1.16 1.22 1.26(1.49)* (1.73)* (1.59)* (1.24)*

771221-921223 784 1.06 1.09 1.07 0.98(0.87)* (0.76)* (0.48)* (0.09)*

Variance ratios for weekly equal- and value-weighted indexes of all NYSE and AMEX stocks, derivedfrom the CRSP daily stock returns database. The variance ratios are reported in the main rows, with theheteroskedasticity-robust test statistics z*(q) given in parentheses immediately below each main row.Under the Random Walk Null hypothesis, the value of the variance ratio is 1 and the test statistics havea standard normal distribution asymptotically. Test statistics marked with asterisks indicate that thecorresponding variance ratios are statistically different from 1 at the 5 percent level of significance.

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Table 1 shows that the RWH can be re-jected at all the usual significance levels forthe entire time period and all subperiods.For example, the typical cutoff value for themeasure of closeness is 1.96a value be-tween 1.96 and +1.96 indicates that thevariance ratio is close enough to 1 to beconsistent with the RWH. However, avalue outside this range indicates an incon-sistency between the RWH and the behav-ior of volatility over different returnhorizons. The value 5.29, corresponding tothe variance ratio 1.27 of two-week returnsto one-week returns of the equal-weightedindex, demonstrates a gross inconsistencybetween the RWH and the data. The othervariance ratios in Table 1 document simi-lar inconsistencies.

The statistics in Table 1 also tell ushow the RWH is inconsistent with thedata: variances grow faster than linearlywith the return horizon. In particular, forthe equal-weighted index, the entry 1.27in the q=2 column implies that two-week returns have a variance that is 27percent higher than twice the variance ofone-week returns. This suggests that theriskiness of an investment in the equal-weighted index increases with the returnhorizon; there is antidiversification overtime in this case.

Of course, it should be emphasizedthat this antidiversification applies only toreturn horizons from q=2 to q=16. Formuch longer return horizons, e.g., q=150or greater, there is some weak evidencethat variances grow less than linearly withthe return horizon. However, those infer-ences are not based on as many data pointsand are considerably less accurate than theshorter-horizon inferences drawn fromTable 1 (see Campbell, Lo, andMacKinlay [1997, Chapter 2] for furtherdiscussion).

Although the test statistics in Table 1are based on nominal stock returns, it is ap-parent that virtually the same results wouldobtain with real or excess returns. Since thevolatility of weekly nominal returns is somuch larger than that of the inflation andTreasury-bill rates, the use of nominal, real,or excess returns in a volatility-based testwill yield practically identical inferences.

Implications for Investment Management

The rejection of the RWH for U.S. eq-uity indexes raises the possibility of im-proving investment returns by activeportfolio management. After all, if theRWH implies that stock returns are un-forecastable, its rejection would seem to saythat stock returns are forecastable. But sev-eral caveats are in order before we begin ourattempts to beat the market.

First, the rejection of the RWH is basedon historical data, and past performance isno guarantee of future success. While thestatistical inferences performed by Lo andMacKinlay [1988] are remarkably robust,nevertheless all statistical inference requiresa certain willing suspension of disbelief re-garding structural changes in institutionsand business conditions.

Second, we have not considered the im-pact of trading costs on investment perfor-mance. While a rejection of the RWHimplies a degree of predictability in stockreturns, the trading costs associated withexploiting such predictability may out-weigh the benefits. Without a more carefulinvestigation of trading costs, it is virtuallyimpossible to assess the economic signifi-cance of the rejections reported in Table 1.

Finally, and perhaps most important,suppose the rejections of the RWH areboth statistically and economically signifi-cant, even after adjusting for trading costsand other institutional frictions; does thisimply some sort of free lunch? Should allinvestors, young and old, attempt to fore-cast the stock market and trade more ac-tively according to such forecasts? In otherwords, is the stock market efficient or canone achieve superior investment returns bytrading intelligently?

The Efficient Markets Hypothesis

There is an old joke, widely told amongeconomists, about an economist strollingdown the street with a companion whenthey come upon a $100 bill lying on theground. As the companion reaches downto pick it up, the economist says, Dontbotherif it were a real $100 bill, some-one would have already picked it up.

This humorous example of economiclogic gone awry strikes dangerously close tohome for students of the Efficient MarketsHypothesis (EMH), one of the most con-troversial and well-studied propositions inall the social sciences. Briefly, the EMHstates that in an efficient market, all avail-able information is fully reflected in currentmarket prices.7 Therefore, any attempt toforecast future price movements is futileany information on which the forecast isbased has already been impounded into thecurrent price.

The EMH is disarmingly simple tostate, has far-reaching consequences for aca-demic pursuits and business practice, andyet is surprisingly resilient to empiricalproof or refutation. Even after threedecades of research and literally thousandsof journal articles, economists have not yetreached a consensus about whether mar-ketsparticularly financial marketsareefficient or not.

One of the reasons for this state of affairsis the fact that the EMH, by itself, is not awell-defined and empirically refutable hypothesis. To make it operational, onemust specify additional structure, e.g., in-vestors preferences, information structure,etc. But then a test of the EMH becomes atest of several auxiliary hypotheses as well,and a rejection of such a joint hypothesistells us little about which aspect of the jointhypothesis is inconsistent with the data.For example, academics in the 1960s equat-ed the EMH with the RWH, but more re-cent studies by LeRoy [1973] and Lucas[1978] have shown that the RWH may beviolated in a perfectly efficient market.

More important, tests of the EMH maynot be the most informative means ofgauging the efficiency of a given market.What is often of more consequence is therelative efficiency of a particular market, rel-ative to other markets, e.g., futures vs. spotmarkets, auction vs. dealer markets, etc.The advantages of the concept of relative ef-ficiency, as opposed to the all-or-nothingnotion of absolute efficiency, are easy tospot by way of an analogy. Physical systemsare often given an efficiency rating based onthe relative proportion of energy or fuelconverted to useful work. Therefore, a pis-

Research Dialogues Page 5

ton engine may be rated at 60 percent effi-ciency, meaning that on average, 60 per-cent of the energy contained in the enginesfuel is used to turn the crankshaft, with theremaining 40 percent lost to other forms ofwork, e.g., heat, light, noise, etc.

Few engineers would ever consider per-forming a statistical test to determinewhether or not a given engine is perfectlyefficientsuch an engine exists only in theidealized frictionless world of the imagina-tion. But measuring relative efficiencyrelative to the frictionless idealiscommonplace. Indeed, we have come toexpect such measurements for many house-hold products: air conditioners, hot waterheaters, refrigerators, etc. Therefore, from apractical point of view, and in light ofGrossman and Stiglitz [1980], the EMH isan idealization that is economically unreal-izable, but serves as a useful benchmark formeasuring relative efficiency.

A Modern View of Efficient Markets

A more practical version of the EMH issuggested by another analogy, one involv-ing the notion of thermal equilibrium instatistical mechanics. Despite the occasion-al excess profit opportunity, on averageand over time, it is not possible to earn suchprofits consistently without some type ofcompetitive advantage, e.g., superior infor-mation, superior technology, financial in-novation, etc. Alternatively, in an efficientmarket, the only way to earn positive prof-its consistently is to develop a competitiveadvantage, in which case the profits may beviewed as the economic rents that accrue tothis competitive advantage. The consisten-cy of such profits is an important qualifica-tionin this version of the EMH, anoccasional free lunch is permitted, but freelunch plans are ruled out.

To see why such an interpretation of theEMH is a more practical one, consider for amoment applying the classical version ofthe EMH to a nonfinancial marketsay,the market for biotechnology. Consider, forexample, the goal of developing a vaccinefor the AIDS virus. If the market forbiotechnology is efficient in the classicalsense, such a vaccine can never be devel-opedif it could, someone would have al-ready done it! This is clearly a ludicrous

presumption since it ignores the difficultyand gestation lags of research and develop-ment in biotechnology. Moreover, if apharmaceutical company does succeed indeveloping such a vaccine, the profitsearned would be measured in the billions ofdollars. Would this be considered excessprofits, or rather the fair economic returnthat accrues to biotechnology patents?

Financial markets are no different inprinciple, only in degrees. Consequently,the profits that accrue to an investmentprofessional need not be a market inefficien-cy, but may simply be the fair reward tobreakthroughs in financial technology.After all, few analysts would regard thehefty profits of Amgen over the past fewyears as evidence of an inefficient market forpharmaceuticalsAmgens recent prof-itability is readily identified with the devel-opment of several new drugs (Epogen, forexample, a drug that stimulates the pro-duction of red blood cells), some consideredbreakthroughs in biotechnology. Similarly,even in efficient financial markets there arevery handsome returns to breakthroughs infinancial technology.

Of course, barriers to entry are typicallylower, the degree of competition is muchhigher, and most financial technologies arenot patentable (though this may soonchange); hence the half life of the prof-itability of financial innovation is consider-ably smaller. These features imply thatfinancial markets should be relatively moreefficient, and indeed they are. The marketfor used securities is considerably more effi-cient than the market for used cars. But toargue that financial markets must be per-fectly efficient is tantamount to the claimthat an AIDS vaccine cannot be found. Inan EMH, it is difficult to earn a good liv-ing, but not impossible.

Practical Considerations

These recent research findings have sev-eral implications for both long-term in-vestors in defined-contribution pensionplans and for plan sponsors. The fact thatthe RWH hypothesis can be rejected for re-cent U.S. equity returns suggests the pres-ence of predictable components in the stockmarket. This opens the door to superiorlong-term investment returns through dis-

ciplined active investment management.In much the same way that innovations inbiotechnology can garner superior returnsfor venture capitalists, innovations in finan-cial technology can garner equally superiorreturns for investors.

However, several qualifications must bekept in mind when assessing which of themany active strategies being touted is ap-propriate for a particular investor. First, theriskiness of active strategies can be very dif-ferent from that of passive strategies, andsuch risks do not necessarily average outover time. In particular, the investors risktolerance must be taken into account in se-lecting the long-term investment strategythat will best match his or her goals. Thisis no simple task, since many investors havelittle understanding of their own risk pref-erences. Consumer education is thereforeperhaps the most pressing need in the nearterm. Fortunately, computer technologycan play a major role in this challenge, pro-viding scenario analyses, graphical displaysof potential losses and gains, and realisticsimulations of long-term investment per-formance that are user-friendly and easilyincorporated into an investors worldview.Nevertheless, a good understanding of theinvestors understanding of the nature of fi-nancial risks and rewards is the naturalstarting point for the investment process.

Second, there are a plethora of activemanagers vying for the privilege of manag-ing pension assets, but they cannot all out-perform the market every year (nor shouldwe necessarily expect them to). Thoughoften judged against a common bench-mark, e.g., the S&P 500, active strategiescan have very diverse risk characteristics,and these must be weighed in assessingtheir performance. An active strategy in-volving high-risk venture-capital invest-ments will tend to outperform the S&P500 more often than a less aggressive en-hanced indexing strategy, yet one is notnecessarily better than the other.

In particular, past performance shouldnot be the sole or even the major criterion bywhich investment managers are judged.This statement often surprises investorsand finance professionalsafter all, isntthis the bottom line? Put another way, Ifit works, who cares why? Selecting an in-

Page 6 Research Dialogues

vestment manager solely by past perfor-mance is one of the surest paths to financialdisaster. Unlike the experimental sciencessuch as physics and biology, financial eco-nomics (and most other social sciences) re-lies primarily on statistical inference to testits theories. Therefore, we can never knowwith perfect certainty that a particular in-vestment strategy is successful, since eventhe most successful strategy can always beexplained by pure luck (see Lo [1994] andLo and MacKinlay [1990] for some con-crete illustrations).

Of course, some kinds of success are eas-ier to attribute to luck than others, and it isprecisely this kind of attribution that mustbe performed in deciding on a particularactive investment style. Is it luck, or is itgenuine?

While statistical inference can be veryhelpful in tackling this question, in thefinal analysis the question is not aboutstatistics, but rather about economics andfinancial innovation. Under the practicalversion of the EMH, it is difficult (but notimpossible) to provide investors with con-sistently superior investment returns. Sowhat are the sources of superior perfor-mance promised by an active manager, andwhy have other competing managers notrecognized these opportunities? Is it bettermathematical models of financial markets?Or more accurate statistical methods foridentifying investment opportunities? Ormore timely data in a market where minutedelays can mean the difference betweenprofits and losses? Without a compellingargument for where an active managersvalue-added is coming from, one must bevery skeptical about the prospects for futureperformance. In particular, the concept of ablack boxa device that performs aknown function reliably but obscurelymay make sense in engineering applica-tions, where repeated experiments canvalidate the reliability of the boxs perfor-mance, but it has no counterpart in invest-ment management, where performanceattribution is considerably more difficult.For analyzing investment strategies, itmatters a great deal why a strategy is sup-posed to work.

Finally, despite the caveats concerningperformance attribution and proper moti-

vation, we can make some educated guessesabout where the likely sources of value-added might be for active investment man-agement in the near future.

The revolution in computing technolo-gy and data sources suggests that highlycomputation-intensive strategiesonesthat could not have been implementedfive years agowhich exploit certainregularities in securities prices, e.g.,clientele biases, tax opportunities, infor-mation lags, can add value.

Many studies have demonstrated theenormous impact that transaction costscan have on long-term investment per-formance. More sophisticated methodsfor measuring and controlling transac-tion costsmethods that employ high-frequency data, economic models ofprice impact, and advanced optimiza-tion techniquescan add value. Also,the introduction of financial instru-ments that reduce transaction costs, e.g.,swaps, options, and other derivative se-curities, can add value.

Recent research in psychological biasesinherent in human cognition suggestthat investment strategies exploitingthese biases can add value. However,contrary to the recently popular behav-ioral approach to investments, whichproposes to take advantage of individualirrationality, I suggest that value-added comes from creating investmentswith more attractive risk-sharing char-acteristics suggested by psychologicalmodels. Though the difference mayseem academic, it has far-reaching con-sequences for the long-run performanceof such strategies: taking advantage ofindividual irrationality cannot be arecipe for long-term success, but pro-viding a better set of opportunities thatmore closely match what investors de-sire seems more promising.

Of course, forecasting the sources of fu-ture innovations in financial technology isa treacherous business, fraught with manyhalf-baked successes and some embarrass-ing failures. Perhaps the only reliable pre-diction is that the innovations of thefuture are likely to come from unexpected

and underappreciated sources. No one hasillustrated this principle so well as HarryMarkowitz, the father of modern portfoliotheory and a winner of the 1990 NobelPrize in economics. In describing his ex-perience as a Ph.D. student on the eve ofhis graduation in the following way, hewrote in his Nobel address: [W]hen I de-fended my dissertation as a student in theEconomics Department of the Universityof Chicago, Professor Milton Friedman ar-gued that portfolio theory was notEconomics, and that they could not awardme a Ph.D. degree in Economics for a dis-sertation which was not Economics. I as-sume that he was only half serious, sincethey did award me the degree withoutlong debate. As to the merits of his argu-ments, at this point I am quite willing toconcede: at the time I defended my dis-sertation, portfolio theory was not part ofEconomics. But now it is.8

References

Bodie, Z., 1996, Risks in the Long Run, Finan-cial Analysts Journal 52, 18_22.

Campbell, J., A. Lo, and C. MacKinlay, 1997, TheEconometrics of Financial Markets. Princeton, NJ:Princeton University Press.

Cox, J., and S. Ross, 1976, The Valuation of Op-tions for Alternative Stochastic Processes, Jour-nal of Financial Economics 3, 145_166.

Fama, E., 1970, Efficient Capital Markets: A Re-view of Theory and Empirical Work, Journal ofFinance 25, 383_417.

Grossman, S., and J. Stiglitz, 1980, On the Im-possibility of Informationally Efficient Mar-kets, American Economic Review 70, 393_408.

Hald, A., 1990, A History of Probability and Statis-tics and Their Applications Before 1750. NewYork: John Wiley & Sons.

Harrison, J., and D. Kreps, 1979, Martingalesand Arbitrage in Multi-period Securities Mar-kets, Journal of Economic Theory 20, 381_408.

Huang, C., and R. Litzenberger, 1988, Founda-tions for Financial Economics. New York: NorthHolland.

LeRoy, S., 1973, Risk Aversion and the Martin-gale Property of Stock Returns, InternationalEconomic Review 14, 436_446.

Lo, A., 1994, Data-Snooping Biases in FinancialAnalysis, in H. Russell Fogler, ed.: BlendingQuantitative and Traditional Equity Analysis.Charlottesville, VA: Association for InvestmentManagement and Research.

Research Dialogues Page 7

Lo, A., and C. MacKinlay, 1988, Stock MarketPrices Do Not Follow Random Walks: Evi-dence from a Simple Specification Test, Reviewof Financial Studies 1, 41_66.

Lo, A., and C. MacKinlay, 1990, Data SnoopingBiases in Tests of Financial Asset Pricing Mod-els, Review of Financial Studies 3, 431_468.

Lucas, R. E., 1978, Asset Prices in an ExchangeEconomy, Econometrica 46, 1429_1446.

Roberts, H., May 1967, Statistical versus Clini-cal Prediction of the Stock Market, unpub-lished manuscript, Center for Research inSecurity Prices, University of Chicago.

Samuelson, P., 1965, Proof That Properly Antic-ipated Prices Fluctuate Randomly, IndustrialManagement Review 6, 41_49.

Endnotes1 The etymology of martingale as a mathematical

term is unclear. Its French root has two mean-ings: a leather strap tied to a horses bit andreins to ensure that they stay in place, and agambling system involving doubling the betwhen one is losing.

2 See Hald (1990, Chapter 4) for further details. 3 See Campbell, Lo, and MacKinlay (1997,

Chapter 2) for a more detailed discussion of thevarious versions of the RWH.

4 An equal-weighted index is one in which allstocks are weighted equally in computing theindex, e.g., the Value-Line Index. A value-weighted index is one in which all stocks areweighted by their market capitalization; hencelarger-capitalization stocks are more influen-

tial in determining the behavior of the index,e.g., the S&P 500 index.

5 Lo and MacKinlays (1988) original sampleperiod was 1962 to 1985; it has been extendedto 1992 in Table 1, and the qualitative featuresremain unchanged.

6 Specifically, the parenthetical entries are z-statistics, which are approximately normallydistributed with zero mean and unit variance.

7 Although the EMH has a long and illustrioushistory, three authors are usually credited withits development: Fama (1970), Roberts(1967), and Samuelson (1965).

8 Tore Frngsmyr, ed., Les Prix Nobel (Stock-holm: Norstedts Tryckeri AB, 1990), 302.

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