which price changes are linearly correlated with priorchanges, at various lag intervals.”’ These studies have confirmed that pricechanges (i.e., returns) are indeed linearly independent. This means that alinear function of current and past returns cannot be used to predict fu-ture returns.” Based on these findings, it was concluded by EMH advo-cates, that security returns are an unpredictable random walk.
However, autocorrelation studies are relatively weak tests in thesense that they can only detect linear dependencies. Searching for lin-ear structure is merely one way to determine if a time series is behavingin a nonrandom fashion. Edgar Peters* and Andrew Lo and A. CraigMacKinlay*’ have shown that alternative data analysis methods indicatethat financial market time series do not behave like random walks. ForB42 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
example, the test statistic used by Lo and McKinlay, called the varianceratio, can detect more complex (nonlinear) nonrandom behaviors thatwould be invisible autocorrelation studies.
CHALLENGING EMH
 
A good theory is consistent in two ways. Its logic is internally consistentand it is consistent with observed evidence. Thus a theory can be chal-lenged either by showing that it contradicts itself or that it is contradictedby evidence.
A theory is self-contradicting if it implies or predicts something thatwould contradict the theory. An example was given earlier in this chapter:I showed that a cornerstone premise of popular TA, which asserts thatprice perfectly reflects all information, contradicts another of its centralpremises, that price contains predictive information.
The Smart versus Dumb Paradox
One implication of market efficiency is that knowledgeable investorsshould not be able to earn higher returns than investors who are lessknowledgeable. This follows from the premise that market efficiencymeans that whatever information is known or knowable has already beenreflected in security prices. In an efficient market, there is no competitiveadvantage to being smart or disadvantage to being dumb.
However, this implication conflicts with another of EMH’s assump-tions—that the arbitrage activities of rational investors are able to driveprices toward rational levels. (See the heading titled “The Assumptions ofEMH” later in this chapter.) Arbitrage can only act as an enforcer of ratio-nal prices if arbitrageurs have more trading capital and, thus, greaterprice-moving power than irrational, dumb investors. Having more tradingcapital implies that smart arbitrageurs must have earned higher returns inthe past than less well informed (dumb) investors. Either market pricesare set by the smartest, richest participants or they are not. EMH impliesboth. Paradoxical, isn’t it!
The Cost of Information Paradox
Another logical inconsistency of EMH has to do with the cost of informa-tion. It is reasonable to assume that it costs time, money, and intelligenceto gather information and process it into useful investing strategies. At thesame time EMH contends that such information cannot earn incrementalTheories of Nonrandom Price Motion 343
returns for investors who incur these costs. Remember, EMH contendsthat information is instantly reflected in prices. This implies that no mat-ter how wide or deep the research effort, whatever is discovered will be ofno value.
However, if EMH is correct that there is no payoff for informationgathering and processing, then investors would lack the motivation toincur the costs of doing so. With no one to dig out the information andact on it, it would not get reflected in price. In other words, if it is costlyto make markets informationally efficient, investors would be moti-vated to do it only if they were compensated with excess risk-adjustedreturns. Thus the contradiction—EMH requires that information seek-ers be compensated for their efforts and simultaneously denies thatthey will be.
This paradox is argued persuasively by Grossman and Stiglitz intheir article “On the Impossibility of Informationally Efficient Markets.”””They contend that inefficiencies are necessary to motivate rational in-vestors to engage in information gathering and processing. The returnsthey earn from the market’s pricing errors are compensation for their ef-forts, which, in turn, have the effect of moving prices toward rational lev-els. The gains of these rational investors are financed by the losses ofnoise traders and liquidity traders. Noise traders are investors who buyand sell based on signals that they think are informative but that are not.Rational investors also earn profits from the losses of investors who tradeto increase their cash reserves (liquidity traders). One way for the rationalinvestor to gain would be if there were a delay between the time informa-tion is discovered and the time it is reflected in prices, but EMH denies thepossibility of gradual price adjustments. This is yet another logical incon-sistency of EMH.
A similar logic applies to the costs of acting on information (e.g., com-missions, slippage, bid-asked spreads). Unless investors were compen-sated for incurring trading costs there would be no point to their tradingactivities, which are required by EMH to move the price to its rationallevel. The bottom line is that any factor that limits trading—costs to trade,costs to generate information, the rule that impairs short-selling, and soforth—limits the ability of the market to attain efficiency. It simply doesnot hold logically that there would be no compensation to those engagedin trading.
The Assumptions of EMH
To appreciate the arguments made by EMH’s critics, it is necessary tounderstand that EMH rests on three progressively weaker assumptions:(1) investors are rational, (2) investors’ pricing errors are random, and344 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
(3) there are always rational arbitrage investors to catch any pricing er-rors. Let’s examine each of these in a bit more detail.
First is EMH’s contention that investors are, by and large, rational. Torecap, rational investors, in aggregate, are purported to value securitiescorrectly. This means prices will reflect, as accurately as possible, the pre-sent discounted value of a security's future cash flows and risk character-istics. As rational investors learn new information, they respond quickly,bidding up prices when news is good and letting the price fall when newsis bad. As a consequence, security prices adjust, almost instantly, to newinformation.”*
Even if this assumption were incorrect, EMH advocates still insistthat prices adjust quickly to rational levels anyway because of their sec-ond assumption: The valuation mistakes of individual investors are uncor-related. This means that if one investor erroneously values a security toohigh, that error will be offset by another investor's error of valuing it toolow. Taken in aggregate, these valuation errors are self-canceling and havean average value of zero. That is to say pricing errors are unbiased. This ispresumed to be true because the error-prone investors are likely to be us-ing different, though useless, investment strategies. Therefore, their ac-tions should be uncorrelated. To put it bluntly, as one foolish investor getsan uninformative signal to buy, another investment fool is equally likely toget an uninformative signal to sell. In effect they wind up trading witheach other, leaving prices very close to rational levels.
Moreover, even if this second assumption fails to keep prices at ratio-nal levels, EMH invokes yet a third assumption. That is, if the valuationmistakes of irrational investors turn out to be biased (i.e., have an aver-age value that is greater than or less than zero), arbitrage investors willcome to the rescue. They will notice that prices have systematically di-verged from rational values. The arbitrageurs will buy when prices aretoo low or sell when they are too high, thus forcing prices back to wherethey should be.
In the EMH world, arbitrage is as close as it gets to a free lunch. An ar-bitrage transaction incurs no risk, requires no capital, and earns a guaran-teed return. As envisioned by efficient market advocates, an arbitragetrade goes something like this: Consider two financial assets, stocks X andY, which sell at equal prices and which are equally risky. However, theyhave different expected future returns. Obviously, one of the two assets isimproperly priced. If asset X has a higher future return, then to take advan-tage of the mispricing, arbitrageurs would buy asset X while short-selling Y.With the activities of like-minded arbitrageurs, the price of each stock willconverge to its proper fundamental value.”® Market efficiency attained inthis manner assumes there are always arbitrageurs ready, willing, and ableto jump on these opportunities. The better ones become very wealthy,Theories of Nonrandom Price Motion 345,
thereby enhancing their ability to drive prices to proper levels, while theirrational investors eventually go broke losing their ability to push pricesaway from equilibrium levels. The uninformed, irrational investors are dri-ven out of the market the way a weak species is driven from an ecosys-tem, while the rational, well-informed arbitrageurs thrive.
Flaws in EMH Assumptions
This section considers each of the assumptions of EMH and how theymiss the mark.
Investors Are Rational. Investors do not appear to be as rational asEMH assumes. Many investors react to irrelevant information, what notedeconomist Fischer Black calls “noise signals.”®* Though they think theyare acting intelligently, these investors can expect to earn the same returnas an investor who buys and sells based on a coin flip. Investors who fol-low the advice of financial gurus who base their advice on noise signalsare noise traders by proxy.
In fact, investors are guilty of numerous departures from rationality.For example, they fail to diversify, they trade too actively, they increasetheir tax liabilities by selling appreciated stocks but hold onto losing posi-tions, and they trade mutual funds with high fees. Moreover, their failuresare recurring. “Investors’ deviations from the maxims of economic ratio-nality turn out to be highly pervasive and systematic.”®! These departuresfrom rationality can be classified into three areas: inaccurate risk assess-ments, poor probability judgments, and irrational decision framing. I dis-cuss each of these in turn.
Investors typically do not assess risks in conformity with the norma-tive ideal put forward by Neumann and Morgenstern, known as “expectedutility theory.” In a perfectly rational world, an individual faced withchoosing among several options selects the one with the highest expectedvalue. The expected value of a particular choice is equal to a sum of prod-ucts, where each product is the probability of each possible outcome mul-tiplied by the value or utility of that outcome to the decision maker. Theproblem is people do not actually behave this way. Research has shownthat investors make numerous systematic errors when assessing risks andmaking choices.
These mistakes have been incorporated into a framework calledProspect Theory, which was proposed by Kahneman and Tversky (1979).”It explains how people actually make decisions under conditions of uncer-tainty. For example, it explains that investors hold onto losing stocks butsell profitable positions to avoid the psychic pain of realizing a loss. It alsoexplains why investors overvalue low-probability long-shot speculations.346 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The second way investors depart from the rational ideal of EMH is intheir judgments of probability. EMH assumes that, as investors receivenew information, they update their probability assessments in accordancewith Bayes’ theorem, a formula for combining probabilities in a theoreti-cally correct way. However, to their detriment, investors do not behavethis way. One common error, discussed in Chapter 2, is the crime of smallnumbers—drawing grand conclusions from small samples of data. Thisexplains why investors will rashly conclude that a corporation with ashort string of successful quarterly earnings reports is likely to continueto grow rapidly. Their overreaction to this small sample of positive earn-ings changes causes the stock to become overpriced.
Lastly, investors’ decisions can be strongly impacted by how choicesare described (framed). By incorrectly framing a decision situation, in-vestors tend to misperceive the true expected value of a choice. For ex-ample, when choices are framed in terms of potential gains, investors tendto choose the option most likely to earn a gain, even if it is insignificant insize. However, when the same choices are framed in terms of potentiallosses, investors will assume the risk of a very significant loss just to avoidthe certainty of a small loss. This error, called the “disposition effect,” isthought to explain why investors sell winners quickly, so as to be sure toearn a gain, even if it’s small, but hold on to losers even if it means there isa chance the loss will turn into a much larger one.
Investor Errors Are Uncorrelated. The assumption that investors’errors are uncorrelated is contradicted by psychological research whichshows people do not deviate from rationality randomly in situations char-acterized by uncertainty. In reality, most people tend to make similar mis-takes in such situations and hence their deviations from rationality arecorrelated. Many investors will be tempted to buy the same stock becausethe stock appeals to a common heuristic rule of judgment that makes itlook like a candidate for further appreciation. For example, a companythat has three positive earning quarters can be perceived by many in-vestors to be a growth stock that warrants a high price-to-earnings ratio orP/E. This problem is made worse by social interactions, or herding, be-tween investors. “They follow each other's mistakes listening to rumorsand imitating the actions of their fellow traders.”**
Money managers, who should know better, make these mistakes aswell. They are guilty of creating portfolios that are excessively close tothe benchmarks against which they are measured, all in an effort to re-duce the chance they will underperform. Professional money managersalso engage in imitative behavior and move herd-like into the samestocks, for fear of falling behind the pack. They dress up their portfoliosTheories of Nonrandom Price Motion 347
by adding stocks that have done well and eliminate those that have not,so year-end portfolio reports show the fund invested in the highest per-forming stocks.
Arbitrage Forces Prices to Rational Levels. This assumptionfails because the power of arbitrage activities to push prices toward ratio-nal levels is limited. First, no one rings a bell when securities become mis-priced. The rational price is the discounted value of a stream of futurecash flows, which is, by definition, uncertain. Investors try to estimate fu-ture earnings, but their forecasts are prone to significant error.
Second, arbitrageurs do not have unlimited tolerance for adverseprice movement—for example, when an underpriced stock that hasbeen purchased continues to go lower, or an overpriced security thathas been sold short continues to soar. The actions of noise traders caneasily push prices further away from rational levels before they returnto them. Therefore, even if an arbitrageur spots a truly mispriced secu-rity, the pricing error may grow larger before it is finally eradicated.Should this adverse price movement become too large, the arbitrageurmay have to close the position with a loss. If this happens often enough,the noise traders can drive rational investors out of business. This is re-ferred to as noise trader risk*‘ and it limits the motivation and commit-ments of arbitrage traders. Behavioral finance expert Andre Shleifersays even an arbitrage trade that looks nearly perfect from the outsideis in reality quite risky so the number of investors who go after it will belimited. The bottom line is arbitrage activities cannot always enforcerational pricing.
Noise trader risk was a factor in the blow-up of the Long Term CapitalManagement (LTCM) hedge fund in the fall of 1998. The fund’s crashnearly took the entire financial market with it. Ultimately, the mispricingsthat LTCM had identified were corrected, but because they had overlever-aged their positions, the fund lacked the staying power to hold its posi-tions through a short-term period of even greater mispricing.
Improper use of leverage is yet another factor that can impair therole arbitrage plays in driving markets to efficiency. Thus, even if arbi-trageurs can accurately identify over- and under-priced securities, ifthey use too much leverage they can get wiped out. There is an optimalleverage for favorable bets (i.e., speculations with a positive ex-pectancy).®° If this level is exceeded, the probability of ruin rises de-spite the positive expectation.
I show this to my students during a class I call Casino Night. We play agame in which everyone starts off with an imaginary $100. I have a friendcome in to act as coin flipper. Before each flip, the students determine what348 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
fraction of their capital to bet on the next coin toss. If a head results, thepayoff is twice the amount of the bet. If a tail results, only the amount of thebet is lost. We play the game for 75 flips. This game has a very favorable ex-pectation.** However, even in a game with such a favorable expectancy,many students wind up losing money because they bet too aggressively(ie., the fraction of capital wagered on a bet is too large). A formula workedout by Kelly, an electrical engineer at Bell Labs in the 1950s, now known asthe Kelly Criterion, specifies the optimal fraction to bet on each coin flip soas to maximize the growth rate of the bettor’s capital. The optimal fractiondepends on the probability of a win and the ratio of the average win to aver-age loss. In this particular game, the optimal fraction to wager on each betis 0.25. If this level is exceeded, the bettor faces greater risk without thebenefit of a faster growth of capital. If one were to employ a bet fraction of0.58 it is likely all funds would be lost, despite the favorable expectation.This is what happens to an arbitrageur with good information who uses toomuch leverage.
Another constraint on an arbitrage’s ability to enforce efficient pric-ing is the lack of perfect substitute securities. An ideal (riskless) arbi-trage transaction involves the simultaneous purchase and sale of a pairof securities with identical future cash flows and identical risk charac-teristics. An arbitrage transaction based on securities that do not con-form to this ideal necessarily involves risk. And it is risk that limits thedegree to which arbitrage activity can force prices to efficient levels.When a broad class of assets, such as all stocks, become overpriced, asthey did in the spring of 2000, there is no substitute security to use asthe long-side hedge to a short sale of the entire stock market. Even inthe case where the securities in an arbitrage transaction are close sub-stitutes, there can be substantial risks. Each stock has its own specificor idiosyncratic risks, and this makes arbitrageurs wary. For example, ifGM were undervalued and it were purchased against an offsetting shortsale in Ford, there would be the risk that some bullish event unique toFord or a bearish event unique to GM would create a loss for the arbi-trage trader.
There are still other constraints that prevent arbitrage from playingthe price-policing role envisioned by EMH. Arbitrageurs do not have un-limited funds to correct pricing errors nor do they have total freedom topursue any and all opportunities. Most arbitrage investors manage moneyfor other investors in the form of hedge funds. The management contractsunder which the fund managers operate typically constrain their actionsto some degree. Without a completely free hand and unlimited funds,some mispricings will remain unarbitraged.
As a result of these limits, the EMH assumption that all arbitrage op-portunities will be eradicated appears to be an oversimplification.Theories of Nonrandom Price Motion 349
Empirical Challenges to EMH
The EMH is not only riddled with logical inconsistencies, its predictionsare contradicted by a growing body of empirical evidence. This sectionsummarizes these findings.
Excessive Price Volatility. If security prices were as tightly con-nected to fundamental values as EMH asserts, then the magnitude of pricechanges should be similar to the magnitude of changes in the underlyingfundamentals. However, studies show prices are far more volatile thanfundamentals. For example, when fundamental value is defined as the netpresent value of future dividends,*’ changes in fundamental value are un-able to explain the high volatility of prices. The technology stock bubblethat ruptured in the spring of 2000 and the bubble in Japanese stockprices in the late 1980s are examples of price movements that cannot beexplained by changes in fundamental value.
EMH also predicts that large price changes should occur only whensignificant new information enters the market. The evidence does notagree. For example, the stock market crash of October 1987 was not ac-companied by news that would have justified a price drop that exceeded20 percent. A 1991 study by Cutler cited by Shleifer examined the 50largest one-day price movements since the end of World War IL Many ofthese price events were not associated with significant news announce-ments. In a similar study, Roll showed that fluctuations in the price offrozen orange juice futures often occurred without any developments inthe weather, the major fundamental influence on that market. Roll alsoshowed that individual stock movements are often not associated withcorporate news events.
Evidence of Price Predictability with Stale Information. Theevidence most damning to EMH are studies showing that price move-ments can be predicted to a meaningful degree with publicly known(stale) information. In other words, strategies based on stale informationcan generate risk-adjusted returns that beat the market. If it were true thatprices quickly incorporate all known information, as EMH asserts, thisshould not be possible.
How Cross-Sectional Predictability Studies Are Performed. TheApril 2001 issue of Journal of Finance notes that many predictabilitystudies show that publicly available information is not fully reflected instock prices and that numerous strategies based on this information areprofitable.”” These studies measure the degree to which indicators basedon public information are able to forecast the relative performance of350° METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
stocks."' Indicators tested included a stock’s price-to-earnings ratio,its price-to-book-value ratio, its recent relative price performance, andso forth.
Predictability studies employ a cross-sectional design. That is tosay, they examine a large cross section of stocks at a given point intime, for example, all stocks in the S&P 500 Index as of December 31,1999. For that date, the stocks are ranked on the basis of an indicator”that is being examined for its predictive power, such as a stock’s rate ofreturn over the past six months (price momentum). With this done, thestocks are arranged into a number of portfolios on the basis of rank,with each portfolio containing an equal number of stocks. Ten portfo-lios is a common number. Thus portfolio 1 would contain the top 10percent of all stocks ranked by their prior six-month rate of return.That is to say, the portfolio is composed of those stocks whose priorsix-month rate of return was in greater than the ninetieth percentile. Asecond portfolio is formed containing stocks ranked from the eightiethpercentile to the eighty-ninth percentile, and so on until a final portfoliois formed from the 10 percent of stocks with the worst prior six-monthperformance.
To determine if six-month momentum has predictive power, the fu-ture performance of the top decile portfolio (1) is compared to thefuture performance of the bottom decile portfolio (10). The forwardprediction horizon is typically one time period. Therefore, usingmonthly data, it would be one month.” Typically these studies quantifythe indicator’s predictive power as the return earned by a long portfolioversus a Short portfolio. In other words, a long position is assumed tobe taken in all portfolio 1 stocks and a short position in all portfolio 10stocks. For example, if in a given time period, the long portfolio earned7 percent while the short portfolio lost 4 percent (e.g., the stocks soldshort went up 4 percent), the long-versus-short strategy would haveearned 3 percent. Although in this example the indicator used to rankstocks was the six-month price momentum, any item of informationthat was known at the time the portfolios are constructed could beused. I illustrate this concept in Figure 7.6, where the indicator used iseach stock’s P/E ratio.
I just described how a cross-sectional study is carried out for a singlemonth (December 1999). However, cross-sectional studies are carried outover many months (cross-sectional time series). Thus, the predictivepower of an indicator is measured as the average return on portfolio 1 mi-nus the average return on portfolio 10 over an extended period of time.Such studies often examine a number of candidate predictor variables.This idea is illustrated in Figure 7.7.Theories of Nonrandom Price Motion 351
     
 
N StocksRanked byPE 10 Rankedfor Month | PortfoliosFormed Future1. Lowest PE PerformanceDifferential
   
2. 2nd Lowest PE 1. Lowest PE3. 3rd Lowest PE 2. 2nd Lowest PE
    
    
Return Port. #1
1
1 vs. 10 Diff.
J
Return Port. #10
      
  
UniverseNStocks
 
    
    
 
 
 
      
 
10. Highest PE
  
N. Highest PE
FIGURE 7.6 Cross-sectional study to determine the predictive power of P/E ratio.
Stock 1Stock 2
 
sock [| TTPe
 
PredictorVariables
FIGURE 7.7 Cross-sectional time series study.
Predictability Studies Contradicting Semistrong EMH. The semi-strong form of EMH is the boldest testable version of EMH." It assertsthat no information in the public domain, fundamental or technical, canbe used to generate risk-adjusted returns in excess of the market index.The bottom line of numerous well-conducted cross-sectional time seriesstudies is this: Price movements are predictable to some degree withB3S2_ METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
stale public information, and excess risk-adjusted returns are possible.Here, I summarize some of these key findings:
¢ Small capitalization effect: A stock’s total market capitalization,defined as the number of shares outstanding multiplied by its priceper share, is predictive of future returns.” Stocks in a portfolio com-posed of the lowest decile portfolio of market capitalization earnedabout 9 percent per year more than stocks in the highest decile port-folio.*’ This effect is most pronounced in the month of January. Re-cent studies show this indicator’s predictive power has disappearedsince the mid to late 1980s.
e Price-to-earnings ratio effect: Stocks with low P/E ratios outper-form stocks with high P/E ratios.”
¢ Price-to-book-value effect: Stocks with low price to book value ra-tios outperform stocks with high price to book value ratios.'* Thecheapest stocks, in terms of price to book, outperformed the most ex-pensive stocks by almost 20 percent per year.
e Earnings surprise with technical confirmation: Stocks reportingunexpected earnings or giving earnings guidance that is confirmed bystrong price and volume action on the day after the news is an-nounced earn an annualized return spread (longs — shorts) over thenext month of over 30 percent.” This strategy is a marriage of funda-mental and technical information.
Predictability Studies Contradicting the Weak Form of EMH.The weak form of EMH is the least bold version of the theory. It claimsthat only a subset of public information, past prices, and price returns” isunhelpful in earning excess returns. The following studies show that staleprices and other data used in technical indicators are indeed useful. Thisis very good news for TA and very bad news for EMH. The narrowest,most timid, and most difficult to falsify version of EMH has been contra-dicted with evidence.
¢ Momentum persistence: Jegadeesh and Titman (1993)*! showedthat price momentum measured over the past six to twelve monthspersists. In other words, the stocks that have been strongest over thepast 6 months, 7 months, 8 months, and so on, up to 12 months, tendto outperform over the following 6 to 12 months. Their study simu-lated a strategy of holding long positions in stocks with the highest re-turns over the prior 6 months (top decile) and holding short positionsin stocks with the worst performance (lowest decile). The portfolio oflong and short positions was then held for 6 months. This strategyTheories of Nonrandom Price Motion 35
eared an annualized return of 10 percent. In light of this evidence,even one of the high priests of EMH, Eugene Fama, had to admit thatpast stock returns can predict future stock returns.” Score a big onefor TA!
¢ Momentum reversal: Although stocks with strong trends over thepast 6 to 12 months tend to maintain those trends over the follow-ing 6 to 12 months, something different is observed when momen-tum is measured over longer time spans. Strong trends measuredover the prior three to five years display a tendency to reverse. DeBondt and Thaler tested a strategy of buying stocks with the mostnegative five-year trends (losers) and selling short stocks with themost positive five-year trends (winners). The long-versus-shortportfolio averaged an 8 percent annualized return over the nextthree years,” and most importantly, this return difference was notattributable to risk. The prior losers (future winners) were notmore risky than the prior winners (future losers).>! This contradictsa central proposition of EMH that higher returns can only be earnedby assuming higher risks. Additionally, it bolsters the notion that avery simplistic form of TA is useful.
e Nonreversing momentum: When a stock’s momentum is measuredby its proximity to its 52-week high, rather than its prior rate of re-turn, profits are greater and momentum does not reverse.” The au-thor of this study speculates that investors become mentallyanchored to prior 52-week price highs. Anchoring is known to pre-vent people from making appropriate adjustments to new informa-tion. The author of this study, Michael Cooper, conjectured that thisprevents stocks near their 52-week highs from responding to newfundamental developments as rapidly as they should. Retarded newsresponse engenders systemic price trends (momentum) that correctthe mispricing.
¢ Momentum confirmed by trading volume: Further support for thevalidity of TA comes from studies showing that, when trading volumeis used conjointly with price momentum, even higher returns can beearned. That is to say, a synergism can be attained by combining priceand volume indicators. The return of the combination is 2 to 7 percenthigher than the return can be earned using price momentum alone.Stocks with high volume and positive price momentum do better go-ing forward than stocks with positive price momentum alone. More-over, stocks with high volume and negative price momentum doworse going forward than stocks that merely have negative price mo-mentum. Said differently, the discrimination power of price momen-tum is greater for high-volume stocks.354 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
EMH Digs for a Defense
When an established theory is contradicted with empirical evidence, itssupporters do not simply roll over and say never mind. The cognitivemechanisms of belief persistence (see