Tilburg University

What's causing overreaction?

Offerman, T.J.S.; Sonnemans, J.H.

Publication date:1997

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Citation for published version (APA):Offerman, T. J. S., & Sonnemans, J. H. (1997). What's causing overreaction? An experimental investigation ofrecency and the hot hand effect. (CentER Discussion Paper; Vol. 1997-36). CentER.

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~ ~~ Discussion

IIIAJIIII I.I IInIUIN II IIII II IIIII IIIII IIIIIN I

,,,

Centerfor

Economic Research

No. 9736

WHAT'S CAUSING OVERREACTION' ANEXPERIMENTAL INVESTIGATION OF

RECENCY AND THE HOT HAND EFFECT

By Theo Offerman and Joep Sonnemans

April 1997

ISSN 0924-7815

What's Causing Overreaction?An Experimental Investigation of Recency and

the Hot Hand Effect~

Theo Offerman"

Jcep Sonnemans"'

AbstractA substantial twdy of empirical literature provides evidence for overreaction in markets.Past losers outperform pas[ winners in stock markets as well as in sports markets. Twohypotheses are consistent with this observation. First, the recency hypothesis states that[radcrs overweigh recent information. Thus, they are too optimistic about winners and toopessimistic about losers. Second, the hot hand hypothesis states that traders try todiscover trends in the past record of a firm or a team, and thereby overestimate theautocorrelation in the series. An experimental design allows us to distinguish betweenthesc hypotheses. "Phe eviderxe is consistent with the hot hand hypothesis.

JEL codes: H41, C91.Key-words: overreaction, recency, hot hand, experiments.

February, 1997

~~` 'I'ilburg UnivcrsilyDcparhncnt uf ccunomicsPO Box 901535000 LE TilburgNetherlandse-mail: offermanQkub.nl

"' University of AmsterdamIkpartment of ec;onomicsRoetersstraat I11018 WB AmsterdamNetherlandse-mail: joeps~fee.uva.nl

~` We would like to thank Uri Gneezy, Jan Potters, Arthur Schram, Randolph Sloof andJtirgen Wit for useful comments.

I. Introductinn

In the economics profession the proposition that markets yield efficient outcomes has beenconsidered a truism for a long time. For financial markets efficiency implies (amongothers) that prices resemble intrinsic values of stocks and that the development of theprice of a stock over time is not distinguishable from a random walk with a positive drift.It is assumed that if the development of prices were predictable, arbitrators would detectthe trends and make money. Their actions would immediately drive stock prices back tointrinsic values.

The view that financial markets are efficient has been seriously challenged inrecent empirical work. De Bondt and Thaler (1985) report that prices in the New YorkStock Exchange overreact in the period between 1926 and 1982. Stocks of firms that weredoing (extremely) badly for the last 3 years are undervalued and stocks of firms that weredoing (extremely) well are overvalued. Prior losers provide higher returns than priorwinners in the following years, contradicting the random walk hypothesis. Subsequentempirical studies support this result (e.g., De Bondt and Thaler, 1987; Chan, 1988; Famaand French, 1988; Chopra, Lakonishok and Ritter, 1992; see also the survey by Forbes,1996). Often this phenomenon of overreaction is even more pronounced in stock marketsoutside the USA (cj. Poterba and Summers, 1988; Alonso and Rubio, 1990; Stock, 1990;da Costa, 1994). It may be tempting to think that it is only the misguided behavior of asmall group of noise traders that is causing overreaction in stock markets. However, DeBondt and Thaler (1990) present evidence that even the judgments of professional securityanalysts are affected by overreaction.

A rational (efficiency preserving) explanation for the phenomenon is provided byrisk aversion. L.osing firms are more likely the riskier firms. Therefore, rational traderswould need an extra premium in order to buy their stocks. Although there is evidence thatstocks of' lusing firms are riskier than stocks of winning firms, the majority of theaforementioned authors feels that the difference in risk is not large enough to explain the

difference in expected returns.'

~It hati alui twxn suggested U~at the effext of ovcrreaction is confimiwlcd with Uie small fimi effect.SmJI fimis exrn relatively high returni. However, De Binxlt xnd Thaler (t989) rctxirt that the k„ers of theoverccaction effixa are iKit exactly the samc smalt firms acvx;iatecl with die small fim~ effect. Chopra er al.

I

Instead, a boundedly rational explanation is offered by De Bondt and Thaler(1985, 1987). They attribute overreaction to the psychological phenomenon of recency.

When processing information, people tend to overweigh recent information comparedwilh thcir prior bclicl. 'I'hus, traders who are not sure of the intrinsic value of a stockwill be tai optimistic about its value when the firm is winning and too pessimistic when itis losing. Recency may thus cause a temporary wedge between stock prices and intrinsic

values.

A related literature on judgmental biases in sports markets is inspired by the article ofGilovich, Vallone and Tversky (1985). They show that both basketball players and fansbelieve that a player is more likely to hit a shot if his previous shot was a hit instead of amiss. However, they do not find a positive correlation between the actual outcomes ofsuccessive shots. Although Gilovich et a[. use a different terminology, this bias is inprinciple similar to the phenomenon of overreaction in stock markets.

Camerer (1989) investigates whether a false belief in autocorrelation is alsorevealed in the betting market for basketball teams. Consistent with Gilovich et a[., hefinds that winning teams are overvalued and that losing teams are undervalued in theNBA games between 1983 and 1986. However, the bias is too small to provide incentivesfor arbitration (due to transaction costs).2 Overreaction may be more common in othersports markets. Badarinathi and Kochman (1994) report results that betting againstwinning teams was broadly profitable for the NFL 1983-1992 football games. Their resultis partly supported by the analysis of Tassoni (1996). He reports overreaction for theNFL football games in the periods 1956-1965 and 1976-1979, but not in the period 1980-1985.

In sports markets the phenomenon of overreaction is usually attributed to amistaken belief in a'hot hand'. Bettors believe that the performance of a winning (losing)team during a particular period is better (worse) than its overall record. They conclude

(1942) fincl an cY:onumically impnrtan[ overrraction effect even after adjusting for risk ane! size.

zBruwn antl Sauer (t993) nl.ui elulyze the Jate of NBA gemes. Their resutt.i show tlut hettors helicvein ~ISitivr auawurrelatiun. Howevrr, they culxluJe that the Ja[a are nut sufticiently informxtive toJetemlinr whrdler an nctual currela[iun hetween te:un~s sulceSilVr performaltres Joes or Joes not exist, soit is not clear whether this belief is a bias or not.

2

too easily that there are trends in a team's past record by overestimating the

autocorrelation in the results of a team's successive games. A similar judgmental bias isuflcn fuuncl in thc bcliefs of gamblers in a casino. Knowing that the probability of red isequal to 0.5, they expect more alternations between red and black than would statistically

be expected on the basis of pure chance (the gambler's fallacy is discussed by Tversky

and Kahneman, 1982). Both gamblers falling prey to the gamblers' fallacy and bettorsmislccl hy Ihc hiN hanel eflcct havc the tendency ti, expect lex, many runs in a series given

a certain amount u( aulocorrelation.

In stock markets stocks of winning tirms are overvalued and stocks of losing firms areundervalued. In sports markets winning teams are overvalued and losing teams areundervalued. However, overreaction is explained differently in stock markets than insports markets. Note that the explanation for overreaction in stock markets (recency) canalso be used to explain overreaction in sports markets: it could be that bettors in a sportsmarket, uncertain of the strength of their team, overweigh recent information about theperformance of the team. In that case, they would be too optimistic about the value ofwinning teams and too pessimistic about the value of losing teams. On the other hand, theexplanation of overreaction in sports markets (hot hand) can also be used to explainoverreaction in stock markets: it could be that traders try to discover trends in the pastrecord of a firm, to see whether it is in a good shape or not. In doing so, they couldoverestimate the amount of autocorrelation, thus putting too much value on winning firmsand too little value on losing firms.

These [wo, conceptually different, explanations for overreaction can obviously notbe separated using either real world data of sports markets or of stock markets, since theyboth yield the same bias. It is possible to distinguish between these hypotheses in anexperimental setting, however. The main goal of this paper is to determine experimentallywhich of the two gives a bctter explanation of overreaction.

Consider the following experimental setup. A coin is selected randomly from anurn containing an equal number of false and fair coins (the prior probability of a false

coin - 0.5). A fair coin has no memory: each toss of the coin will be head (tail) wíth

probability 0.5 (0.5). A false coin has the property that the previous outcome is repeated

with probability 0.7. If the previous outcome was head, the new outcome will be head

3

with probability O.7 and it will be lail with probability U.3. '1'hus, the outcome of the tossof a false coin is only dependent on the outcome of the previous toss. The outcome of thefirst toss with a false coin is head (tail) with probability 0.5 (0.5).

"I'he decision maker is not told whether the randomly selected coin is fair or false.The coin is tossed twenty times yielding a series of heads and tails. The decision makerobserves the series and predicts the probability that the series was generated by a falsecoin. The payoff of an incentive compatible mechanism (the quadratic scoring rule, cf.Murphy and Winklcr, 1970) cncourages the decision maker to take the task seriously.

How would a Bayesian observer handle this problem? In the following, let 8deno[e the Bayesian posterior probability that the coin is false and let y denote the numberof alternations in the series. Then,

B - P[data~jalsecoin]P[data ~f'aLrecoin] tP[data ~faircoin]

(t)- 0.5~0.7~-r-'.0.3y

,~10096 - 100~

0.5~0.7~y'~0.3yt0.5~ tt(7)19~(3)y .

Note that a Bayesian observer only needs to know the number of alternations in theseries. This number directly determines the Bayesian posterior probability that a coin isfalse.

The hot hand effect would induce a decision maker to overestimate the autocor-relation in the series. Therefore, (s)he would report a higher than Bayesian posteriorprobability that the coin is false. Recency occurs if a decision maker overweighs recentinformation (the series of coin tosses) and underweighs the prior information. The effectof recency depends on the number of alternations in the series of heads and tailsgenerated by the coin. If this number is such that a Bayesian observer would report ahigher probability than SOI, then neglect of the prior distribution would induce a

decision maker lo overestimate lhe probability that the coin is false. On the other hand, if

tlie number of alternations leads a Bayesian observer to predict a probability smaller than

50~, then neglect of the prior distribution would induce a decision maker to

undcrestimate thc probability that the coin is false. Thus, series that scem to be generated

by a fair coin can bc used to separate recency from hot hand.

Two other systematic biases in decision makers' judgments are possible. First, the

4

decision maker could underestimate the autocorrelation in the series. Such a decisionmaker would fall prey to the so-called cold hand effect, and would make errors oppositeto the errors predicted by the hot hand effect. Second, a decision maker could underweighnew evidence compared with the prior belief. Such a decision maker would be affected byconservatism, and tnake errors in the opposite direction of the errors implied by recency.The design allows to discriminate between these four hypotheses. Together they (almost)exhaust the possible systematic errors that rould be made by a decision maker. Table isummarizes the predictions.

hypothesis B c SO Io B 150~

hot hand R 1 B R) g

recency R G B R 1 Bcold hand R c B R c B

conservatism B c R c 50 "!0 50 qo C R c B

Table l: predictions. 'B' denotes the Bayesian posterior probabiliry that the coin is false;'R' denotes the de~ision maker's reported posterior probabi[iry that the coin is false.

The remainder of this paper is organized as follows: section 2 describes the experimentaldesign in more detail. Section 3 provides the experimental results. Section 4 contains aconcluding discussion.

2. Design

The instructions and the experiment itself are computerized.' The experimental situation

is explained as follows:'Therc is an urn containing fxir atxl false cointi. One coin will he drawn from this urn and this cuin

will ne tossed repea[etlly. You will onxrve the outcomes anc! we will atik you to rstimate [he

prnnenility Inxt tne coin is felse. Tlte fair ;uul tlte false coitu differ in the following sense: if the

coin is fair, the prunxnility of 'head' (H) ancl the pronxnility of 'uil' (T) is 509ó for each toss. A

'The progr:un is develoPtxl in TurMi Pau:al using die Ratlmage Iinrery (iee Annitilt and Sadrieh, 1995tiir dexumentation of this linrxry). Tlte progr:un is availanle from the auWors.

5

fnir cuin does nul h.we a'memury', A false coin does IIaVC a mentury. The finl u~cs with a falsecuin will yicld uutcumc H with a prubability uf 5096 xnd uutcumc T with a prohabiliry uf 50~.Af[er dte fint tuss, the outcome of the previuus toss will he repeeted wiUt e probxbility of 7096.Su, if the cuin is false end the previous ro~s yielded uutcome T, the next to~ witl yielJ outcome Twith a probnhility uf 70~ etxl outcomc H with a probahility uf 30`Yo. Likewitie, if the previous tossyieWed nutcumc H, the nezt toati will yield ouu:omc H with a pn,banilily of 70`A6 etxl outcome Twith a prnbxbility uf 30X.

T7te urn coutaitu 50 fxlsc atx! 50 fair coittti. The cvin will be drewn ranllomly from thisunt. Thux, the prohebility tha[ an :ubi[rary coin is false is 50`;B. With the help of the computer thiscuin will he tussec! 20 times. Yuu will see the outcontes on yuur cumputer kreen. Then we willa~k yuu ~i estimete the prohxhility Utat thi~ coin is fàlse.

This pnxedure will be repeettxl 20 times, ut for 20 scries uf uutcomes you IInVC loestintxte Ute prubability that the series is tossed with a False coin. Eech tinte the coin is Jrawn fromxn urn wi[h 50 felse attd 50 fair coiac. You will ntH see tlte urn. The cuntputer witl teke wre of thedrewing uf tlle coin and the tossing of that coín.'

Then it is explained how subjects make money. For each estirnate they receive a payoffdetermined by a yuadratic scoring rule. Let F denote the reported probability of a falsecoin in percentages, then the payoff is 10000-F' points if the coin is fair and 200'F-F'points if the coin is false. A quadratic scoring rule is an incentive compatible mechanismto measure expectations. [t has been successfully used in Offerman, Sonnemans andSchrarn (1996) and Sonnemalu, Schram and Offerman (1996) to elicit subjects' beliefs inpublic good games.

Subjects do not know the formula, but retxive a payoff table based on the formulaon paper. The table displays the payoff for each (integer) estima[e between Ol and 100~,when the coin is fair and when the coin is false. The instructions explain that it is in thebest interest of subjects to report their true beliefs. Subjects answer some questions tocheck their understanding. At the end of the experiment the points are exchanged formoney (8000 points - 1 Dutch guilder).

All subjects observe the same 20 series generated by 20 coins (see the appendix).The whole series of 20 outcomes is displayed at the top of the screen. At the bottom ofthe screen a window appears asking the subject to report the probability that the coin isfalse. The subject confirms her or his percentage and has to wait a few seconds, before(s)he receives the outcomes generated by the subsequent coin. Only after the last (20th)

6

coin the truc state of cach coin and the carnings are communicated lo the subjects.' Atthc cnil i~l thc cxpcriincnl subjcctx fill in a yucstionnairc bcfurc lhcy are paid privalcly.'fhe coins and the series generated by each coin have been produced wi[h the help of arandom number generator. i l of the 20 coins are fair coins. Details of the series of thecoins are presented in the appendix.

To investigate whether our results are affected by the order in which the series ofoutcomes generated by the coins are presented, we use a different order of the coins inthe two sessions. In the second session coins I and 11, 2 and 12, etc, of the first sessionare swapped.

Subjects and the order of the coins

A total of 39 subjects participated in two sessions. 25 of the 39 undergraduates arestudents of economics and l4 are students of other departments; 9 are female and 30 aremale. An average of 19.60 guilders (about US~ 11.50) was earned by subjects in about45 minutes. Only one subject states in the questionnaire that he did not report his truebeliefs in the experiment: for the first 10 coins he reports 50~ each time and for thesecond 10 coins he reports al[ernately 0~ and 100~. The data of this subject areexcluded from the analyses. This decision does not have an (important) impact on theresults.

The difference in the order of the coins between the two sessions does not affectsubjects' judgments. We could not find any (systematic) difference in the judgmentsreported in the two sessions. Therefore, we abstrac[ from the order of the coins in theremainder of this paper: the data of the two sessions are simply combined.

3. Results

Subjects tend to estimate the probability that a coin is false higher than a Bayesianobserver would (on average 59.6q versus 45.9~). To see whether the difference issigniticant, we counted for each subject the number of times that (s)he reports a higher

4Wc reveal the states of the coiac o~ily at the enJ of the experiment, t~ause we want to avuid thut dteresults are conf'uunded with aspec~ts of le:trning.

7

than Bayesian probability that the coin is false (Jlplus) and the number of times that (s)hereporLS a smaller or equal probability (1lminus-20-JJplus). A two-tailed Wilcoxon ranktest clearly rejects the hypothesis that the ranks of A~plus are equal to the ranks of llminus,in favor of the hypothesis that the ranks of llplus are higher (n-38; Z--5.02; p-0.00).Although judgments are biased, there is a clear positive correlation between reported andBayesian probabilities (the Spearman rank correlation coefficient is equal to 0.62,p-0.001). Figure 1 plots the mean reported probabilities as function of the Bayesianprobabilities. The figure shows that the difference between the reported and Bayesianprobabilities increases when the Bayesian probability of a false coin decreases.

100

90fi

60t'

70t

1-i--I } 1 I i } I-~

0 [0 20 30 40 50 60 70 g0 9p lpB

Figure l: ntean reported probabilities (R: vertica[ aris) as function of the Bayesianprobabilities (B:horizontal aris). The straight [ine R-B is added as a benchmark.

A pair-wise comparison of the four hypotheses is made to assess which hypothesis takesbest account of the biases in subjects' judgments. The results are summarized in table 2.For some comparisons we focus on a subset of the results. In those cases the hypotheses

~

predict a similar bias for some coins. These coins are excluded from such a comparison.For example, in the comparison between hot hand and recency, we focus on coins thatseem fair (B~SO~), because both hypotheses predict that subjects will overestimate theprobability uf a false coin when the coin seems false (B1S0~). For each subject it iscounted how often (s)he judges in accordance with each hypothesis. Thus, for eachcomparison each subject yields one pair-wise data-point, and a Wilcoxon rank test is usedto test the null that both hypotheses explain the biases equally well. The hot handhypothesis beats all other hypotheses.

H 1 versus H2Whichcoins?

consistentfirst

consistentsecond

WilcoxonZ-statistic

hot hand versus recency B c S0~ 9.3 I.3 -5.27"

hot hand versus cold hand OY6 C B c 100~ 14.0 S.3 -5.10"hot hand versus conservatism B~ SO ~ 4.7 3.1 -2.11'

recency versus cold hand B~ SO?b 4.7 4.0 -0.9l

recency versus conservatism Oo6 G B C 100~ 6.0 8.6 -2.25'

cold hand versus conservatism B C S09b I.3 S.5 -4.61"

Table 2: pair-wise comparison of the four hypotheses. The second column indicates whichcoins are used to test the hypotheses in the first column; the third (fourth) co[umnindicates how often a subject made a judgment in accordance with the first (second)hypothesis of the row; the last column shows the Wílcoxon rank test statistic (n-38 for alltests; ' indicates significance at the S~b [evel and " at the I~ level).

The biases are best explained by the hot hand hypothesis. However, close examination offigure 1 reveals that the evidence is more clear-cut for coins that seem fair than for coinsthat seem false. This might be explained by the presence of white noise: it is more likelythat the positive bias caused by a hot hand effect is offset by a negative bias caused bywhite noise for coins with a high Bayesian probability of being false. To formalize the

idea that the data are generated by the combination of a systematic error component

provided by either of the four hypotheses and a random component provided by white

noise, we estimate five models using maximum likelihood techniques. The base model

maintains the hypothesis that subjects are Bayesian and that all errors are white noise:

9

R-BtE. (Z)

Recall that R represents the reported and B the Bayesian posterior probability that a coinis false. For each model proposed it is assumed that all random error terms e areindependently drawn from the same truncated N(O,o2) distribution. The distribution of theerror terms is truncated, because subjecis never report probabilities smaller than 096 orgreater than 100~.

First, the hut hand model proposes:

R- B t a~(100-8) t E. (3)

If a is estimated to be equal to a value between 0 and 1, the equation implies that subjectsoverestimate the probability of a false coin for all coins. This would only be expected onthe basis of the hot hand hypothesis.

Second, the recency model proposes:

R B;(1-~) t E ij B~5096- B} p~(lOO-B) t E if B~SO96 .

(4)

With a,B between 0 and l, the above equation implies that subjects overestimate theprobability of a false coin for coins that seem false, but underestimate this probability forcoins that seem fair, as proposed by the recency hypothesis.

Third, the cold hand model assumes:

R - B~(1-y) t E . (5)

If y lies between 0 and I, this equation implies that subjects always underestimate theprobability of a false coin, whieh is consistent with the cold hand hypothesis.

And finally, the conservatism model predicts:

R- B} d~(50-8) t E. (6)

With a ó between 0 and I, this eyuation implies that subjects make errors biasing theirpredictions towards SO~b as predicted by eonservatism. The base model is nested in eachof the four models, by setting the parameter of that model (a, ~, y or ó) equal to 0.

Table 3 summarizes the results of the estimation procedure. The hot hand model

10

explains the data better than the base model. Not only is the likelihood of the hot handmodel better, its estimate of the white noise component a is also considerably better (less)than that of the base model. The other general models do not explain the data better thanthe base modeL It is concluded that hot hand plus white noise provides the best explana-tion of the data.

Model parameter a -IogLbase XX 38.7 358.0

hot hand ~-0.39 22.7 341.0"recency 5-0.00 38.7 358.0

cold hand ry-0.00 38.7 358.0

conservatism 5-0.00 38.7 358.0

Table 3.~ matimum likelihood estimates. " indicates significance at the 1~ of the[ikelihood ratio test.

Tlie foregoing analysis has been inspired by hypotheses suggested by the literature.However, one may wonder whether other factors or biases also play a role in determininga subject's reported probability of a false coin. We consider two possibilities: theposterior subjective probability of a false coin may be affected by the length of themaximal run in the series generated by the coin; the posterior subjective probability maybe affected by a bias in the relative frequency of heads and tails in the series.

The number of alternations in the series is a sufficient statistic for a Bayesianobserver (cf. equation 1). Thus, a Bayesian observer should allocate equal probabilities tocoins with equal numbers of alternations. On the other hand, for non statisticians a seriesmay provide stronger evidence for a false coin if the length of the maximal run is higher.This seems to be the case. Twelve times a comparison can be made between two coinstha[ generated an equal number of alternations but an unequal length of the maximal run.For 10 (2) of the 12 comparisons, subjects estimate the probability higher (lower) if thelength of the maximal run is higher.

The other factor considered is the bias in relative frequency. Given a number of

alternations, a series may provide a subject with stronger evidence for a false coin if the

ll

overall relative frequency of tails is further removed from 0.5. This factor dces not seem

to play a role. Of the 9 times that a comparison can be made between two coins with

equal number of alternations but unequal relative frequency, only 5 predictions are in line

wilh thc dircclion prcdicted by this factor.

4. Concluding discussion

Two psychological hypotheses potentially account for overreaction in stock and sports

markets. Trading data of real markets cannot be used to separate these hypotheses. The

simple experimental design in this paper provides an opportunity to differentiate between

the two explanations. The data generated with this design aze clearly better explained by

the hypothesis stating that biases consist of a systematic par[ caused by hot hand and a

random part caused by white noise. Recency cannot explain our data. In fact, the results

reported in table 2 suggest that if a bias comes up in the weighing of new information, it

is that people tend to put insufficient value to new information.

The psychological líterature does not propose that people always underweigh or

always overweigh new information. Hogarth and Einhorn (1992) classify a multitude of

studies on order effects in belief learning. They propose that the interaction between the

response mode (either a judgment is made after each piece of information, or a judgment

is made after a series of information pieces), the complexity of the task (simple or

complex) and the number of pieces of information (short or long series) determines

whether recency or conservatism will be observed. Recency may not provide such a

stable basis to predict biases in markets.

Both the recency explanation of overreaction in stock markets and the hot hand

explanation of overreaction in predicting sports events were originally attributed to the

more general phenomenon of representativeness (by De Bondt and Thaler, 1985 and by

Gilovich et al., 1986, respectively). According to Tversky and Kahneman (1982, p. 24),

'people view a sample randomly drawn from a population as highly representative, that

is, similar to the population in all essential characteristics. Consequently, they expect any

two samples drawn from a particular population to be more similar to one another and to

the popula[ion than sampling [heory predicts, at least for small samples.' The representa-

12

tivcncss hcuristics Iriggen dífferent judgmental biases. For example, besides the recencyeffect (or insensitivity to prior probabilities) and the hot hand effect, representativenessalso prcdicts judgments to be insensitive to sample size. This paper suggests thatrepresentativeness may be a too broad concept, in the sense that it allows for countervail-ing forces. In the present design, the hot hand effect and recency can work in oppositedirections, and it is not clear what should be expected on the basis of representativeness.

The goal of this paper is to find the cause of overreaction in markets. In doing so,it turns out that individual judgmental biases in this design are considerable: on averagesubjects estimate the posterior probabilities of a false coin 14~ above Bayesian probabili-ties. One may question whether overreaction is less pronounced in markets than inenvironments without interaction between decision makers. Biased traders may learn fromunbiased traders via the signals provided by market prices. Or vigorous trading byunbiased investors might to some extent neutralize the effect of trading of biased traderson the aggregate price level. These are interesting topics for future experimental work.

Knowledge about the cause of overreaction is of scientific interest because itimproves the understanding of what we observe in markets. But it is also of practicalrelevance. Consider the case that a trader tries to form a belief about the value of a stockthat was previously unknown to him or her. This paper suggests that (s)he should not betoo concerned that (s)he overweighs recently revealed information about the stock. Itsuggests that (s)he should not conclude too easily that the stock is in a good or a badshape on the basis of trends in the past record of the stock. More generally, the trainingof traders should focus more on the pitfall of perceiving trends too easily than on themistake of overweighing recent information.

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Forbes, W.P., 1996: ' Picking Winners? A Survey of the Mean Reversion and Overreac-tion of Stock Prices Literature', Journal of Economic Surveys 10, 123-158.

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Appendix

Coin Series

THTHTHHHT'I'ITPHTTITTH

HHTTTHHTHHT'I'I'I'fHHHTH

TTTI'HHTTHHFiTTTHTTTHH

TTHHHHHHTI'ITTTHHTTHH

THHTHHHHHHTHTHZTHHTT

TTHTTTHHHHHHHZTTHTFIT

TTTTTHHTTTHHHHTHHTHH

HHTTHTTHTTHHTHHHTHHT

THHHHTTHTHHTTHHHHHTH

HHTHHTTHHHHHHHZTHHTT

HHHHHHTHHHTZTITITHTH

HHHHH

HHTTTHTHHHHTHTTfHHHH

HTHHTTHTHHHT"I'I'I'ITHTH

TTTTTHHH

HTHHHHTHTHHHHHHTTHHTHHTTHTTTITTHHHHT'ITHHHHHT

Bayesian Mean reportedprobability probability Type of win

23 60.7 fair

4(1 S3.S fair

61 64.6 fals~e

90 82.1 faiti~

I I 39. I fair

40 á14.ó falf

79 87.6 fal~

61 SS.3 fal,ve

S ~ 22.1 fair

23 47.3 Fair

ÓI 70.1 f'dlr

S S I .6 fair

79 83.5 fals~e

95 83.9 false

40 40.3 fair

II 44.7 faise

79 80.5 false

2 23.3 fair

23 54.6 Fdir

90 82.1 Palse

45.9 59.6

No. Author(s)

9GG I U. Gncery and 1. Potlcrs

9GG2 H.1. Bicrcns

9GG3 J.P.C. Blanc

9G(~1 M.J. Lcc

9GG5 C. Fcmándc h J. Osícwalskiand M.F.J. Slcel

9GGG X. Han and H. Wcbcrs

96G7 R. Kollmann

9GG8 R.C.H. Chcng and1.P.C. Klcijncn

9GG9 E.van Hcck andP.M.A. Ribbers

9670 F.Y. Kumah

'X~71 J.Janscn

9672 Y.H. Farzin, K.J.M. Huismanand P.M. Kort

9673 J.R. Magnus and' F.1.G.M. Klaassen

9G74 J. Fidrmuc

9G75 M. Das and A. van Socst

9G76 A.M. Lcjour andH.A.A. Vcrbon

9G77 B. van Aarlc andS.-E. Hcwgaard Jcnscn

9678 Th.E. Nijman, F.A. dc Roonand C.Vcld

Titk

An Expcrimenl on Risk Taking and Evaluation Pcriods

Nonparamclric Nonlinear Co-Trcnding Analysis, wilh anApplication lo Interest and In(lation in thc U.S.

Optimization of Pcriodic Polling Systems wilh Non-Precmptivc,Time-Limited Scrvice

A Rool-N Consislcnl ScmiparamcUic Estimalor for Fixcd EffcclBinary Rcsponse Pancl Data

Robust Bayesian Inference on Scale Paramclers

A Commcnt on Shakcd and Sutlon's Modcl of Vcrtical ProduclDiffcrentiation

The Exchangc Rale in a Dynamic-Optimizing Currcnl AccountModel wilh Nominal Rigiditics: A Quantitalivc Invcsligalion

Improvod Design of Queucing Simulation Experimenls wilhHighly Hctcrosccdastic Rcsponscs

Ecawmic E(rocts of Elcetronic Markcts

The Effect of Monelary Policy on Exchange Rates: How to Solvclhe Puzzles

On lhc First Enlrancc Timc Dislribulion of lhc MIDIa Qucuc: aCombinalorial Approach

Optimal Timing ofTcehnology Adoption

Testing Somc Common Tennis Hypothcses: Four Ycars atWimbledon

Political Suslninabilily of Economic Rcforms: Dynamics andAnalysis of Regional Economic Factors

A Panel Daw Modcl for Subjective Information on HouseholdIncomc Growth

Fiscal Policics and Endogcnous Growth in Intcgatcd CapitalMarkcts

Output Slabiliralion in EMU: Is Thcrc a Casc for an EFTS?

Pricing Term Slructurc Risk in Fulures Markcts

No. Author(s) Title

9G79 M. Dufwenberg and U. Gneczy Efficicncy, Reciprocity, and Expectations in an ExperimentalGame

9680 P. Bolton andE.-L. von Thaddcn

9681 T. tcn Raa and P. Mohncn

9G82 S.Hochguertclandvan Soest

9683 F.A. de Roon, Th.E. Nijmanand B.J.M. Werkcr

9G84 F.Y. Kumah

9G85 U.Gneery and M. Das

9G8G B. von Stcngcl,A. van dcn Elzcn andD. Talman

9G87 S.Tijs and M. Koslcr

9G88 S.C.W. Eijffingcr,H.P. Huizinga andJ.J.G. Lcmmen

9689 T. ten Raa and E.N. Wolff

9G90 J. Suijs

9G91 C. Scidl and S.Traub

9692 C. Scidl and S.Traub

9G93 R.M.W.J. Bcctsma andH.Jcnscn

9G94 M. Voorncvcld

9G95 F.B.S.L.P.Jansscn andA.G.de Kok

9G96 L. Ljungqvist and H. Uhlig

9G97 A. Rustichini

Blocks, Liquidity, and Corporate Conlrol

The Localion oC Comparativc Advanlagcs on lhe Basis ofFundamentals only

The Relation betwecn Financialand Housing Wealth ofDutch A.Houscholds

Testing for Spanning with Futures Contracls and NonlradcdAssets: A General Approach

Common Stochastic Trcnds in thc Cun-ent Accounl

Experimental Investigalion of Pcrccivcd Risk in Finite RandomWalk Processes

Tracing Equilibria in E.Klensivc Gamcs by ComplemcntaryPivoling

Gcneral Aggrcgalion of Dcmand and Cosl Sharing Mcthods

Shorl-Tcrm and Long-Tcrm Govcrnmcnl Dcbl andNonresident Interest Withholding Taxcs

Outsourcing oC Services and the Productivity Rocovery in U.S.Manufacturing in the 1980s

A Nuclcolus for Stochastic Coopcrativc Games

Rational Choicc and lhc Rclcvancc of Irrclcvant Altcmatives

Tesling Decision Rulcs for Multiatlribute Decision Making

InOation Targcts and Contracts with Unccrtain CcntralBankcr Prcfcrcnccs

Equilibria and Approximatc Equilibria in Infinile PotcntialGames

A Two-Supplier Invenlory Modcl

Catching up with thc Kcyncsians

Dynamic Programming Solution of Incentivc ConslrainedProblcros

No. Aulhor(s)

9698 G.Gurkan and A.Y. Gzge

9699 H. Huiringa

96100 H. Huiunga

961 O I H. Norde, F. Patrone andS. Tijs

96102 M. Bcrg, A. De Waegcnacreand J. Wielhouwcr

96103 G. van dcr Laan, D. Talmanand Z. Yang

96104 H. Hui~rnga and S.B. Nielsen

9G I OS H. Dcgrysc

96106 H. Huizinga and S.B. Nielsen

96107 T. Dicckmann

96108 F. de long andM.W.M. Donders

9G 109 F. Vcrboven

96110 D. Granot, H. Hamersand S. Tijs

961 I I P. Aghion, P. Bolton andS. Frics

9G I 12 A. Dc Wacgcnacrc, R. Kastand A. Lapicd

96113 R. van den Brink andP.H.M. Ruys

96114 F. Palomino

961 I S E. van Damme andS. Hurkcns

9GIIG E.Canlon

Tille

Sample-Path Optimization of Buffer Allocations in a TandemQueue - Part I: Theoretical Issucs

The Dual Role of Moncy and Oplimal Financial Taxes

The Taxation Implicit in Two-Ticred Exchange Rale Systems

Characterizing Propcrties of Approximatc Solutions forAptimization Problems

Optimal Tax Reduction by Dcpreciation: A Stochastic Model

Existencc and Approximation ofRobust Stalionary Points onPolytopes

The Coordination of Capital Incomc and Profit Taxation withCross-Owncrship of Firms

The Total Cost of Trading Bclgian Shares: Brusscls VersusLondon

Thc Political Economy of Capilal Incomc and Profit Taxation ina Small Open Economy

The Evolution oCConventions with Endogcnous Interaclions

InVaday Lead-Lag Rclalionships Bctwecnthe Futures-,Options and Stock Markct

Brand Rivalry, Market Scgmcntation, and thc Pricing ofOptional Engine Powcr on Aulomobilcs

Weakly Cyclic Graphs and Dclivcry Gamcs

Financial Rcslnucturing in Transilion Economics

Non-linear Assct Valualion on Markcts with Frictions

The Internal Organi~.ation of lhc Firm and its ExtemalEnvironmcnl

Conflicting Trading Objcclivcs and Markct Efficicncy

Endogenous Stackelbcrg Lcadcrship

Busirtess Cyclcs in a Two-Scctor Modcl of Endogcnous Growth

9701 J.P.J.F. Scheepens Collusion and Hicrarchy in Banking

No. Author(s) Títle

9702 H.G. Blocmcn and Individual Wcallh, Rcscrvation Wagcs and Transitions intoE.G.F. Stancanclli Employmcnt

9703 P.J.J. Hcrings and Refinemenls of RationaliTability for Normal-Form GamesV.J. Vannetclbosch

9704 F. dc 1ong, F.C. Drost Exchange Ratc Targct Zoncs: A Ncw Approachand B.J.M. Werker

9705 C. Fernándcz and M.F.J. Steel On the Dangers of Modclling Through Continuous Distribulions:A Baycsian Pcrspcctivc

970G M.A. Odijk, P.1. Zwancvcld, Decision Support Syslcros Hclp Railncd to Scarch for 'Win-J.S. Hooghicroslra, L.G. Kroon Win' Solutions in Railway Nclworl: Dcsignand M. Salomon

9707 G. Bckacri, R.J. Hodrick andD.A. Marshall

9708 C. Fernández and M.F.J. Stecl

9709 H. Huizinga and S.B. Niclsen

9710 S. Eijffingcr, E. Schaling andM. Hocberichts

971 I H. Uhlig

9712 M. Dufwcnberg and W. Guth

9713 H. Uhlig

9714 E. Charlicr, B. Mclenbcrg andA. van Socsl

9715 E. Charlier, B. Melenberg andA. van Soesl

9716 1.P. Choi and S.-S. Yi

9717 J.P. Choi

9718 H.Dcgrysc and A. Irmcn

9719 A. Possajcnnikov

9720 1. Janscn

9721 J. tcr Horst and M. Vcrbeck

Thc Implications ofFirst-Ordcr Risk Avcrsion for AssetMarket Risk Prcmiums

Multivariale Sludcnt-i Regession Modcls: Pitfalls and Infcrence

PrivatiTation, Public Invcslment, and Capilal Income Taxalion

Central Bank Independcnce: a Scnsitivity Analysis

Capital Incomc Taxation and thc Suslainability of PermancnlPrimary Deficils

Indirect Evolution Vcrsus Stratcgic Dclcgation: A ComparisonofTwo Approaches to Explaining Economic Institutions

Long Term Dcbt and thc Political Support for a Monetary Union

An Analysis of Housing Expcndilurc Using ScmiparamclricModels and Pancl Data

An Analysis of Housing Expcndilurc Using ScmiparamctricCross-Section Madcls

Vertical Foreclosure with lhe Choicc of Input Spceifications

Patent Litigation as an Infortnation Transmission Mechanism

Altribulc Dcpcndcncc and thc Provision of Qualily

An Analysis oC a Simplc Rcinforcing Dynamics: Lcarning toPlay an "Egalitarian" Equilibrium

Rcgulaling Complcmcntary Inpul Supply: Cost Corrclalion andLimitcd Liabilíty

Estimating Short-Run Pcrsistcncc in Mutual Fund Performance

No. Author(s)

9722 G. Bekacrt and S.F. Gray

9723 M. Slikker andA. van den Nouweland

9724 T. tcn Raa

9725 R. Euwals, B. Mclcnbcrg andA. van Socst

972G C. Fcrshtman and U. Gncezy

9727 J. Pouers, R. Sloof andF. van Windcn

9728 F.H. Pagc,lr.

9729 M. Bcrlianl and F.H. Page, Jr.

9734 S.C.W. Eijffinger andWillcm H. Vcrhagcn

973 I A. Riddcr, E. van der Laanand M. Salomon

9732 K. Kultti

9733 J. Ashaycri, R. Hculs andB. Tammel

9734 M. Dufwcnbcrg, H. Nordc,H. Rcijnicrsc, ar~d S. Tijs

9735 P.P. Wakkcr, R.H. Thalerand A. Tvcrsky

9736 T. Offcrman and ]. Sonnemans

Titk

Target Zones and Exchange Rales: An Empirical Investigation

A One-Stage Model of Link Formation and Payoff Division

Club Efficicncy and Lindahl Equilibrium

Testing the Predictive Vnluc of Subjective Labour Supply Data

Stratcgic Delcgation: An Expcrimcnl

Campaign Expcndilures, Contributions and DireclEndorsements: The Strategic Usc of Information and Moncy toInfiucncc Voler Bchavior

Existcncc of Oplimal Auclions in Gcncral Environmcnts

Optimal Budget Bnlancing Incomc Tax Mechanisms and thcProvision of Public Goods

The Advantage of Hiding Bolh Hands: Foreign ExchangeIntervention, Ambiguity and Private Infonnation

How Larger Demand Variability may Lead to Lower Coslsin the Newsvcndor Problem

A Model of Random Malching and Pricc Formation

Applicalions ofP-Median Tcchniqucs to Facilitics DcsignProblems: an Improvcd Hcuristic

Thc Consistcncy Principlc for Sct-valucd Solutions and aNew Direction for the Thcory of Equilibrium Refincments

Probabilistic Insurancc

What's Causing Overrcaclion? An Expcrimental Invcstigation ofRccency and thc Hot Hand Effcct

r1I1V AAJ~I1 rAAA 1 r TII Pf11rll'1 Tl ir ~IrT11rnLANDSBibliotheek K. U. Brabant

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