.
With the sampling distribution now in hand, the p-value can becomputed.
The p-value would simply be the fraction of the 500 values obtainedat step 7 that exceed the average return of the tested rule. (See Chap-ter 5 for the procedure.)
The example described above was intentionally highly simplified. In a
more realistic case the data miner would examine a much larger numberof rules over a much longer time period. But the procedure for generatingData-Mining Bias: The Fool's Gold of Objective TA 327
the sampling distribution would be the same. All this is done automati-cally by the WRC software, once it has been provided with the interval re-turns, (e.g., daily) of all rules tested. This set of data contains all theinformation WRC needs to derive the sampling distribution that is appro-priate for a particular data-mining venture. When many rules are testedthis can be a considerable amount of data. Currently, few data miners ordata-mining systems save this valuable information.
In Part Two of this book I will perform a case study of 6,402 rules fortrading the S&P 500 index. A version of WRC that incorporates some re-cent enhancements, which are described later, will serve as one method totest the statistical significance of the rules’ observed performances.
The Monte Carlo Permutation Method. The Monte Carlo permu-tation method (MC) can also be used to generate the sampling distributionrequired to evaluate the statistical significance of rules found by data min-ing. As noted in Chapter 5, it uses different data than the bootstrap and ittests a different formulation of the null hypothesis, or H,.
In terms of the data, MC uses the historical times series of a rule’s out-put values (i.e., +1, —1) as well as the market's raw returns. In contrast, thebootstrap uses the rule’s interval (e.g., daily) returns. In terms of the H,,both WRC and MC test the notion that all rules examined during data min-ing have no predictive power. However, MC formulates H, somewhat dif-ferently. To simulate the performance of a rule devoid of predictive power,MC randomly pairs rule output values with daily market price changes. Incontrast to WRC, MC’s random coupling of output values and marketchanges is done without replacement. Presumably, if rule output valuesare randomly assigned to market changes, the performance would be con-sistent with the null hypothesis that the rule is worthless. The returnearned by the random pairings becomes the benchmark against which theactual rule returns are compared. If a rule has genuine predictive power,then its informed pairing of output values and market changes should gen-erate significantly better performance.
The performance of the random pairing is simply the rule’s value(+1 or -1) multiplied by the market change randomly assigned to that day.Thus, if a rule output of +1 gets paired with a day when the market rose,the rule earns the market’s price change. Likewise, if a —1 rule output getsrandomly paired with a day on which the market fell, it earns that positiveamount that day. Losses occur on days when the sign of the rule’s outputvalue is opposite to that of the market’s price change.
After the full history of a rule’s output values have been paired with amarket price change, the mean return is computed. This is done for eachrule in the universe of N rules giving N mean returns. The maximum meanreturn is selected, and this becomes the first value used to construct the328 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
MC sampling distribution. This entire process is repeated many times(>500) with different random pairings each time. The sampling distribu-tion is generated from this large number of values.
Note that there is no need to reposition each rule’s return distributionto be centered over zero as is done with WRC because it assumes that allrules have an expected return of zero. In contrast, the MC sampling distri-bution’s mean is the expected return of a useless rule in a data-miningventure. If, after randomly assigning rule values to market returns, thesampling distribution is situated at a value greater than zero, so be it. p-values can be computed directly from the MC generated sampling distrib-ution, just as they would be with a sampling distribution generated byalternative methods. The p-value is the area in the right tail of the distribu-tion that lies at or beyond the back-tested rule’s mean return.
A limitation of the MC method compared to WRC is that it cannot beused to generate confidence intervals because it does not test a hypothe-sis about the rule’s mean return. MC’s null hypothesis is simply that allrules tested have output values that are randomly correlated with futuremarket behavior.
To recap, the steps by which the MC permutation method generatesthe sampling distribution for a data miner are:
1. Obtain the daily rule output states for all N rules examined during thedata-mining venture.
2. Each rule’s output values are randomly paired with a scrambled ver-sion of the actual future market price changes. Note that it is impor-tant the same pairings be used for all rules. Thus, if a rule’s outputvalue for day 7 is paired with the market return for day 15, this samepairing must be done for all competing rules. This is done to preservecorrelation structure that may be present in the rules, which is one ofthe five factors impacting the data-mining bias.
3. Determine the mean rate of return for each rule.
4. Out of these N rules, select the highest mean return. This value be-comes the first value for the sampling distribution of the mean for thebest mean among N useless rules.
Repeat steps 2, 3, and 4, M times (where M = 500 or some largenumber).
gl
6. Form the sampling distribution from the M values obtained in steps 2through 5.
7. The p-value for a back-tested rules can be determined by determiningthe fraction of the values obtained by step 6 that are equal to orgreater than its mean return.Data-Mining Bias: The Fool’s Gold of Objective TA 329
Potential Flaws in Initial WRC and MCP Methods. Both WRCand MC test the null hypothesis that all rules in the data-mined universeare useless. The rule miner hopes to reject this hypothesis in favor ofthe alternative hypothesis: that not all the rules examined are useless.As pointed out earlier, the meaning of the term useless depends on therandomization method used. In the context of WRC, a useless rule hasan expected return equal to zero. In the context of the MC, uselessrefers to a rule whose output values are randomly paired with the mar-ket’s future change.
As was discussed in Chapter 5, a hypothesis test can err in two ways.A type-I error occurs when the null hypothesis is true (all rules tested re-ally are useless) is rejected in error. This occurs when a rule that is in factuseless managed to earning a high mean return and a low p-value by luck.This is the data miner’s fool’s gold.
A type-II error occurs when the null hypothesis is in fact false andshould be rejected, but the rule’s performance is too low to do so. That isto say, the rule really does have predictive power, but its virtue remainsundetected because it experienced bad luck during the back test. The dataminer winds up leaving real TA gold in the ground.
The ability of a hypothesis test to avoid making a type-II error isreferred to as the test’s power, not to be confused with a rule’s predic-tive power. Here, we are speaking of the power of a statistical test todetect a false H,. So a hypothesis test is characterized by two measuresof goodness: its significance (probability of making a type-I error) andits power (probability of avoiding a type-II error). It is with respect tothe issue of power that initial versions of WRC and MCP are open tocriticism.
As pointed out by economist Peter Hansen, WRC and, by extension,the MCP would both suffer a loss of power (increased likelihood of mak-ing a type-II error) when the data-mined universe contains rules that areworse than the benchmark. This refers to a situation in which one or morerules are actually worse than useless—they have expected returns thatare less than zero. This could occur, for example, if one were to reversethe output value of a rule that has an expected return that is truly greaterthan zero. Because approximately half of the rules tested in Part Two ofthis book are obtained in this fashion (i.e., inverse rules), the researchpresented in Part Two of this book is vulnerable to the problem discussedby Hansen.
To evaluate Hansen’s criticism, the power of both WRC and MCP wasevaluated by Dr. Timothy Masters, on an ATR universe that containedrules that were both better than and worse than the benchmark. In otherwords, the evaluation simulated exactly the case that troubles Hansen.These tests showed that his concerns are justified for a situation in which330 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
a rule with negative expected returns has an extremely large variance inreturns. This can drastically reduce the power of both WRC and MCP.However, in cases that one is more likely to encounter in TA rule data min-ing, both methods are reasonably resistant to this problem. Therefore,when there is one or more superior rules in the universe of examinedrules, both WRC and the MCP method have a reasonable chance of detect-ing them.
Recent Enhancement to WRC and MCP. Despite the reasonablepower of the initial versions of WRC and MCP methods, a recent paper byRomano and Wolf** recommends a modification that enhances the powerof WRC and that also appears to enhance the power of MCP. Thus the Ro-mano and Wolf enhancement reduces the probability of a Type-II error.This modification was introduced to the versions of WRC and MC used inPart Two's case study. However, at this time, there is no commercial ver-sion of WRC with this enhancement. The MCP version with the enhance-ment is being placed in the public domain and codes for it will be madeavailable on a web site, www.evidencebasedta.com.Theories of
NonrandomPrice Motion
 
 
pletely random, TA would be pointless. TA is a justifiable endeavor
if and only if price movements are nonrandom to some degreesome portion of the time. This chapter offers several theories explainingwhy episodes of nonrandom price movements ought to occur in financialmarket prices.
Although the occurrence of nonrandom price motion is necessaryto justify TA, this alone is not sufficient to justify any specific TAmethod. Each method must demonstrate, by objective evidence, itsability to capture some part of the nonrandom price motion. Part Twowill evaluate a large number of TA rules with respect to their ability todo just that.
A t the risk of stating the obvious, if market fluctuations were com-
THE IMPORTANCE OF THEORY
 
Several new theories from the field of behavioral finance explain whyprice movements are nonrandom to some degree and therefore poten-tially predictable . Thus, these novel theories take a position that is con-trary to the efficient markets hypothesis (EMH), a cornerstone of financetheory for over 40 years. EMH contends that price changes in financialmarkets are random and, therefore, unpredictable. Therefore, these newtheories hold out hope for TA.
331B32 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The reader may wonder why theoretical support for nonrandomnessis even necessary. If a TA method has a profitable back test, isn’t that allthat should be needed? It could be asserted that a significantly profitableback test not only establishes that markets are nonrandom, it also estab-lishes that the method is able to exploit some portion of the market’s non-randomness.
This view misses the importance of theoretical support. Even whenall statistical precautions have been taken, a profitable back test that isnot supported by sound theory is an isolated result and possibly still alucky one. A successful back test always provokes the question: Will therule continue to work in the future? Theory can be helpful here because aback test that is consistent with sound theory is less likely to be a statisti-cal fluke. When a back test has theoretical foundation, it is no longer anisolated fact, but part of a larger cohesive picture in which theory explainsfact and fact confirms theory.
For example, the profitability of technical trend-following systems incommodity futures can be explained as compensation (i.e., a risk pre-mium) for providing a valuable service to commercial hedgers, that of risktransference. In other words, economic theory predicts that futures mar-kets should manifest enough profitable trends to motivate trend followersto accept the price risks hedgers wish to shed.! This is discussed later inthis chapter.
SCIENTIFIC THEORIES
 
In everyday speech, a theory is a speculative conjecture about why some-thing is the way it is. As explained in Chapter 3, a scientific theory is some-thing different. First, it offers a succinct explanation for a broad range ofprior observations. Second, and most importantly, it makes specific pre-dictions that are later confirmed by new observations.
Kepler's laws of planetary motion’ concisely explained a largenumber of prior astronomical observations and made specific predic-tions that were subsequently confirmed by additional observations.However, as good as Kepler's laws were, Newton's theory of gravitationwas better because it was broader in scope. It not only explained whyKepler’s laws worked but explained a far wider variety of phenomena.Theories of nonrandom price motion need not predict with the accu-racy of physical theories. However, to be useful, they must not only suc-cinctly describe a wide variety of previously observed market behavior,but must also make testable predictions confirmed by subsequentobservations.Theories of Nonrandom Price Motion 333
WHAT IS WRONG WITH POPULAR TA THEORY?
 
Many TA texts offer no explanation about why their proposed methodswork. The statement of John Magee, author of one of TA’s seminal works?is typical. He said, “We can never hope to know why the market behavesas it does, we can only aspire to understand how. History obviously hasrepetitive tendencies and that’s good enough.”
Some TA texts do offer explanations, but these are typically ad-hoc ra-tionales that generate no testable predictions. According to author JohnMurphy, the cornerstone premise of TA is “anything that can possibly af-fect the price—fundamentally, politically, psychologically, or otherwise—is actually reflected in the price of that market.”* One would be hardpressed to extract testable predictions from such a vague statement.
Actually, this statement, which purports to explain why TA works,contains a logical contradiction. For, if it were true that price did reflect(i.e., discount) all possible information, it would imply that price was de-void of any predictive information. To understand why, assume a hypo-thetical price pattern has just occurred in stock XYZ, which is currently at$50, and based on the pattern a move to $60 is implied. Then, by defini-tion, when the pattern occurs its predictive implication has yet to be re-flected in prices. However, if the premise that price reflects all informationwere true, the price would already be at the level predicted by the pattern,thus negating the pattern’s forecasting ability.
This logical contradiction is even more apparent when it is pointedout that EMH, a school of thought that rejects the efficacy of TA, rests onthe very same premise; “prices fully reflect all available information.”Technical analysis cannot be based on the same premise as its mortal en-emy. This contradiction is an example of cloudy uncritical thinking that isall too common in the popular version of TA.
Fortunately for TA, its cornerstone premise that price reflects all in-formation appears to be contradicted by fact. One example is the so-called underreaction effect, which has been postulated by behavioralfinance. It says that, because prices sometimes fail to respond to new in-formation as rapidly as EMH theorists contend, a systematic price move-ment, or trend, toward a price level that does reflect the new informationoccurs. The failure of prices to respond rapidly is caused by a several cog-nitive errors that afflict investors, such as the conservatism bias and theanchoring effect. These are discussed later in this chapter.
Another popular justification of TA is based on pop psychology. Bypop psychology, I mean principles of human behavior that seem plausiblebut lack scientific support. According to noted economist and authorityin the field of behavioral finance, Robert Shiller, “In considering lessonsfrom psychology, it must be noted that the many popular accounts of the334 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
psychology of investing are simply not credible. Investors are said to beeuphoric or frenzied during booms or panic-stricken during marketcrashes. In both booms and crashes, investors are descried as blindly fol-lowing the herd like so many sheep, with no minds of their own.”® Thefact is, people are more rational than these pop-psychology theories sug-gest. “During the most significant financial events, most people are preoc-cupied with other personal matters, not with the financial markets at all.So it is hard to imagine that the market as a whole reflects the emotionsdescribed by these psychological theories.”” We will need to look beyondthe platitudes of popular texts for TA’s justification. Fortunately, theoriesdeveloped in the field of behavioral finance and elsewhere are beginningto offer the theoretical support TA needs.
THE ENEMYS POSITION: EFFICIENT MARKETSAND RANDOM WALKS
Before discussing theories that explain why nonrandom price movementsshould exist, we need to consider the enemy’s position, the EMH. Re-cently, some have argued that EMH does not necessarily imply that pricesfollow unpredictable random walks,* and that efficient markets and pricepredictability can coexist. However, the pioneers of EMH asserted thatrandom walks were a necessary consequence of efficient markets. Thissection states their case and examines its weaknesses.
What Is an Efficient Market?
An efficient market is a market that cannot be beaten. In such a market,no fundamental or technical analysis strategy, formula, or system can earna risk-adjusted rate of return that beats the market defined by a bench-mark index. If the market is indeed efficient, the risk-adjusted returnearned by buying and holding the market index is the best one can hopefor. This is so because prices in an efficient market properly reflect allknown and knowable information. Therefore, the current price providesthe best estimate of each security's value.
According to EMH, markets achieve a state of efficient pricing be-cause of the vigorous efforts of numerous rational investors attempting tomaximize their wealth. In their pursuit of true value, these investors areconstantly updating their beliefs with the latest information in a proba-bilistically correct manner’ so as to project each security’s future cashflows. Although no single investor is all knowing, collectively they knowas much as can possibly be known. This knowledge motivates investors toTheories of Nonrandom Price Motion 335
buy and sell in such a way that prices settle at the equilibrium or rationalprice level.
In such a world, prices change only when new information arrives.When it does, prices change almost instantly to a new rational price thatproperly reflects the news. Thus, prices do not gradually trend from onerational price level to the next, giving the trend analyst a chance to get onboard. Not at all. In the world posited by EMH, prices trace a step functionas they move almost instantly from one rational level to the next. If thenews is favorable, prices rise, and if it’s unfavorable, prices fall. Because itis not predictable whether the news will be favorable or unfavorable (itwouldn't be news if it was), price changes will be unpredictable as well.This is illustrated in Figure 7.1.
The Consequences of Market Efficiency:Good and Bad
Market efficiency has good and bad implications. They are good for theeconomy as a whole but bad—very bad—for TA. They are good for theeconomy because rational prices send vital signals of asset values that, inturn, encourage the efficient allocation of scarce resources, such as capi-tal and labor. This fosters economic growth.!”
However, prices in an efficient market are unpredictable rendering allforms of TA useless. According to Paul Samuelson, financial market prices
Price
 
Negative News Event
 
 
 
1| Rational:Price |
 
Time
 
Positive News Event
FIGURE 7.1 Efficient market's response to positive and negative news.336 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
follow a random walk because of the actions of many intelligent/rationalinvestors. In seeking to maximize wealth, they buy undervalued assetspushing their prices higher and sell overvalued assets pushing priceslower.'! “Taken to its logical extreme, it means that a blindfolded monkeyselecting stocks by throwing darts at a newspaper's financial pages coulddo just as well as one carefully selected by the experts.””
“EMH rules out the possibility of trading systems, based on availableinformation, that have expected profits or returns in excess of equilibriumexpected profit or return.”” “In plain English, an average investor—whether an individual, pension fund, or a mutual fund—cannot hope toconsistently beat the market, and the vast resources that such investorsdedicate to analyzing, picking and trading securities are wasted.”"* Al-though, under EMH, it is still possible to generate positive returns from aninvestment strategy, when those returns are adjusted for risk, they will notbe superior to the return of buying and holding the market index portfolio.
The efficient markets hypothesis also declares that when there is nonews entering the market, prices tend to oscillate in a random and unbi-ased fashion above and below the rational price level. See Figure 7.2. Be-cause this level is itself subject to uncertainty, no technical orfundamental indicator can reliably indicate when prices are above or be-low it. This means, for example, that in an efficient market stocks with alow price to book ratio, a well known fundamental indicator, are no morelikely to appreciate than stocks with a high price to book ratio. This is acold world for anyone looking for an edge.
prcctcce 1: Rational «|' Price
 
Time
FIGURE 7.2 Efficient market hypothesis (random and unbiased pricing errors).Theories of Nonrandom Price Motion 337
False Notions of Market Efficiency
There are a number of commonly held but false notions about market ef-ficiency. First is the idea that efficiency requires the market price to beequal to rational value at all times. In fact, market efficiency simply re-quires that price deviates from rational value in an unbiased fashion.Therefore, positive deviations from rational value are just as likely asnegative deviations, and at any point in time there is a roughly equalchance that the asset’s price will be above its rational value as below it.Moreover, these deviations are random. Thus the time series of pricingerrors in an efficient market is a random variable whose probability dis-tribution is centered at the rational price and is approximately symmet-rical about it.
A second false notion about market efficiency is that it implies thatno one can beat the market. Actually, in any given time period, about 50percent of all investors will outperform the benchmark index, while theremaining 50 percent underperform. The notion that no single investoror money manager can beat the market over the long term is equallyfalse. Given enough players, a small number are likely to have lengthystreaks of market beating returns even if their strategies are totally with-out merit. Nassim Taleb! shows that even if we assume money man-agers are no better than a blind monkey throwing darts'* (probability ofbeating the market = 0.5) and the universe of managers is large enough,say 10,000, after five years there is likely to be about 312 firms who havebeaten the market five years in a row. These lucky folks are the oneswho will send salesmen calling. The other 9,682 are less likely to knockon your door.
The Evidence in Favor of EMH
As previously discussed, a scientific hypothesis plays a dual role: expla-nation and prediction. Its veracity is tested by comparing its predictionswith new observations. As discussed in Chapter 3, predictions are mean-ingful only if they are specific enough to offer the possibility of empiricalfalsification. If new observations do contradict a hypothesis’s predic-tions, the hypothesis is either reformulated and tested anew or thrownout. However, what should be inferred when observations and predic-tions agree?
On this issue there is debate. Philosophers in the camp of David Humecontend that no amount of confirmatory evidence is ever sufficient toprove a theory, but in the practical world of science, confirmation doesadd strength to a hypothesis. If test after test yields observations that areconsistent with its predictions, that means something to most scientists.338 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
So EMH advocates have put forward a roster of supporting evidence.Their evidence comes in two flavors because EMH comes in two testableflavors: semistrong and weak.'” The semistrong form asserts it is impossi-ble to beat the market with public information. Because this includes allfundamental and technical data, the semistrong form predicts that neitherfundamental nor technical analysis can beat the market. This informalprediction is not sufficiently specific to be testable, but it is in agreementwith the observation that people have great difficulty profiting consis-tently from market fluctuations—and a lot try.
The semistrong form also makes several specific predictions that aretestable. One is that a security’s price will react quickly and accurately toany news that bears on its value. The proper response of an efficient mar-ket to news is illustrated in Figure 7.3.
This prediction implies prices should neither overreact nor underre-act to news. This is testable in the following way. Imagine for a momentthat prices did not behave efficiently and did systematically over- or un-derreact to new information. If this were the case, it would imply thatprice movements would be predictable. To see why, consider what wouldhappen if a stock overreacted to news either by going up too much in re-sponse to good news or down too much in response to bad. Because EMHsays prices must stay close to rational values, overshooting rational valuewould necessarily lead to a corrective movement back toward rationalvalue. This correction would not be random meandering but rather a pur-
"Rational:1 Price |
   
 
Time
Bullish News Event
 
 
 
FIGURE 7.3 Efficient market response to bullish news.Theories of Nonrandom Price Motion 339
poseful movement, as if the price were being magnetically drawn to therational level. Such a movement would be, to some degree, predictable.Because EMH denies predictability, it must also deny the possibility ofoverreactions to news. A hypothetical overreaction to bullish news and asubsequent systematic movement back to rational levels is illustrated inFigure 7.4.
By the same logic, EMH must also deny the possibility of underreac-tion to news, where prices move less than the news justifies. In this case, asystematic price movement would also develop as prices continued totrend (drift) toward the new rational level implied by the news. Underre-action to bullish and bearish news events and the resultant nonrandommovement toward rational value are illustrated in Figure 7.5.
Evidence supporting EMH’s prediction that overreactions and under-reactions do not occur is presented in the event studies of Eugene Fama.!®He examined all types of corporate news events such as earnings and div-idend announcements, takeovers, mergers, and so forth and found that af-ter an initial, almost instantaneous, nonexploitable price movementtriggered by the news, there was no additional movement. These observa-tions are consistent with EMH’s prediction that the markets quickly andaccurately discount news events.!”
A second prediction of EMH is that prices should change only whennews arrives. It follows then, that prices should not change dramaticallyin the absence of news or in response to noninformative events.2° These
[Price
| Nonrandom Price Movement Back to Rational Price Level
|
Overreaction
 
 
 
 
 
 
‘ Rational :
' Price
 
 
Time
 
 
Bullish News Event
 
FIGURE 7.4 Overreaction to bullish news (implies nonrandom price movements).340 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
Price
 
 
 
Negative News
 
' Rational 1i Pricey
 
Trend: A Gradual Adjustment to NewRational Price Level
Positive News
 
Time
 
 
 
FIGURE 7.5  Underreaction to news can explain nonrandom trends.
two predictions suggest yet a third that is most crucial to TA. EMH im-plies that stale information, information already in the public domain,should have no predictive power and be of no value in making invest-ment profits. Clearly, all information used by TA qualifies as stale. Thus,EMH predicts that all TA methods should fail. If this were to be con-firmed, it’s lights out for TA.
The prediction that all stale information strategies should have nopredictive power seems cut and dried until one tries to test it. Recall,EMH says an investment strategy based on stale information should notbe able to generate excess profits after risk adjustment. So the mere factthat a strategy based on stale information makes gains is not sufficient torebut EMH. To contradict EMH, it must be demonstrated that the gainsare excessive after adjusting for the strategy’s risk.
The notion of judging investment strategies on the basis of risk-adjusted returns is entirely reasonable. For example, if a strategy makes20 percent per year and the benchmark makes 10 percent, but the strategyexposes the investor to three times the risk, the strategy has not beatenthe index after risk adjustment. The question is: How does one define andquantify risk?
Quantifying risk requires a risk model. The most well known is thecapital asset pricing model”! (CAPM), which explains systematic differ-ences in the returns of securities in terms of a single risk factor, the secu-rity’s relative volatility. This is to say, the risk of a stock is quantified by itsTheories of Nonrandom Price Motion 341
volatility relative to the volatility of the market as a whole. Thus, if a stockis twice as volatile as the market index, its returns should be twice that ofthe market. Such a stock is said to earn excess returns when it earns morethan twice the market return. This approach works well when measuringthe risk of a single stock or a portfolio of long stock positions. However,CAPM cannot quantify the risk exposures of more complex strategies. Inresponse to this limitation, capital market theorists have proposed otherrisk models. One of the best known is APT (arbitrage pricing theory),which attributes risk to several independent risk factors.”
However, EMH advocates have tacitly given themselves the liberty ofcooking up new risk factors whenever they wish. This makes it nearly im-possible to refute their claim that stale information strategies cannotbeat the market. For, it is always possible to propose a new risk modelthat explains away a strategy’s excess returns as compensation for risk.As explained in Chapter 3, this is not a scientific sin if the risk factor(s)were identified before the stale information strategy earning excess re-turns was discovered. However, proposing a new risk factor(s) after amarket-beating strategy has been discovered is nothing more than an adhoc hypothesis. This is an explanation cooked up after the fact for thespecific purpose of immunizing a theory, in this case EMH, from falsifica-tion. This practice is frowned upon in science for good reason. Also, asdiscussed in Chapter 3, the information content of a scientific theory isroughly equivalent to the opportunities it presents for falsification. Theunbridled ability to explain away any and all dissonant evidence effec-tively drains the theory of its information content. Thus, the freedom toconcoct new risk factors to explain each and every investment strategythat beats the market with stale information effectively reduces EMH toameaningless theory. .
The evidence confirming the weak form of EMH, which states thatstale prices and indicators derived from them—such as price momen-tum—are without value, is based on auto-correlation studies. They mea-sure the degree to