Overconfidence in Investment Decisions

Overconfidence in Investment Decisions - An Experimental Approach -* Dennis Dittrich‡, Werner Güth‡, Boris Maciejovsky‡ August, 2001 Abstract The purpose of this paper is to develop a formal model that allows to test – in a controlled experimental setting – whether participants exhibit overconfidence in their investment behavior. Participants’ decisions are contrasted with (i) the optimal investment solution, (ii) with a “risk averse” investment decision, and (iii) with a “risk loving” investment decision. We employ a conservative approach by defining overconfidence as the systematic and consistent deviation of one’s decisions for all three investment alternatives. Our results indicate that nearly twothirds of the participants exhibit overconfidence in their investment behavior, and in addition those who perform weakly at the investment task are the most likely to be overconfident. Keywords: Investment decisions; Overconfidence; Endowment effect; Willingness to accept; Willingness to pay JEL-Classification: C910; D800; D840; G110

*

Financial support by the Deutsche Forschungsgemeinschaft (SFB-373, C5) is gratefully acknowledged. We are also indebted to Silke Meiner, Sylvia Schikora, and Volker Zieman for their research assistance. ‡ Max-Planck-Institute for Research into Economic Systems, Strategic Interaction Unit, Kahlaische Straße 10, D07745 Jena, Germany. Tel.: +49/3641/686-620, Fax: +49/3641/686-622, e-mail: [email protected] ‡ Max-Planck-Institute for Research into Economic Systems, Strategic Interaction Unit, Kahlaische Straße 10, D07745 Jena, Germany. ‡ Max-Planck-Institute for Research into Economic Systems, Strategic Interaction Unit, Kahlaische Straße 10, D07745 Jena, Germany.

Contents

1. Introduction

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2. The basic model

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3. Solution behavior and behavioral hypotheses

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4. The experiment

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4.1. The general course . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2. The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5. Discussion

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References

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A. Handout

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1. Introduction

Psychological evidence on decision biases and heuristics challenges the prescriptive predictions of standard finance theory (Rabin, 1998; Shiller, 1997) which is still the dominant paradigm in modern finance. Particularly, it doubts the validity of the rationality axiom. One violation of standard finance theory is, for instance, the overconfidence bias, which refers to the systematic overestimation of the accuracy of one’s decisions and to the overestimation of the precision of one’s knowledge. The overconfidence bias has been observed in many professionals, for instance, in clinical psychologists (Oskamp, 1965), physicians and nurses (Christensen-Szalanski and Bushyhead, 1981), lawyers (Wagenaar and Keren, 1986), negotiators (Neale and Bazerman, 1990), engineers (Kidd, 1970), entrepreneurs (Cooper et al., 1988), investment bankers (Stael von Holstein, 1972) and managers (Russo and Schoemaker, 1992). Alba and Hutchinson (2000) showed that – since information used in consumer decision making is seldom complete or errorless – moderate levels of calibration that include some degree of systematic bias – usually overconfidence, but sometimes underconfidence – are the norm whereas high levels of calibration are achieved rarely. In particular, individuals were found to overestimate the precision of their knowledge (Alpert and Raiffa, 1982; Brenner et al., 1996; Lichtenstein et al., 1982). “We see that when people should be right 70 % of the time, their ‘hit rate’ is only 60 %; when they are 90 % certain, they are only 75 % right; and so on” (Fischhoff et al., 1977, p. 552). Most of the psychological evidence supporting the overconfidence bias is based on questionnaire results involving hypothetical decision tasks. Overconfidence was found to be strongest for questions of moderate to extreme difficulty (Griffin and Tversky, 1992; Pulford and Colman, 1997; Yates, 1990), and seems to increase with the personal importance of the task (Frank, 1935). People were also found to be more confident of their predictions in fields where they have self-declared expertise (Heath and Tversky, 1991).

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Overconfidence has been explained by selective information searching strategies (e.g., Hoch, 1985; Klayman, 1995; Koriat et al., 1980), by motivational factors (e.g., Babad, 1987; Kunda, 1990; Langer, 1975; Larrick, 1993), by imperfections in learning (e.g., Erev et al., 1994; Ferrell, 1994), and, for instance, by the experimenters’ tendency to choose harder-than-normal questions (e.g., Gigerenzer et al., 1991; Juslin, 1993, 1994). Hvide (2000) introduced the notion of pragmatic beliefs and showed that overconfidence can emerge as an equilibrium phenomenon, in that the pragmatic beliefs in a simple job market example were shown to be overconfident. There are also studies which challenge the validity of the conclusion that individuals are generally overconfident (e.g., Erev et al., 1994). Maciejovsky and Kirchler (2001) investigated overconfidence within the context of an experimental asset market and found, for instance, that the existence of overconfidence depends on how it is operationalized. Klayman et al. (1999) emphasize that overconfidence depends on (i) how the experimenter asks his/her questions, (ii) what (s)he asks, and (iii) whom (s)he asks. Additionally, consistent individual differences in the degree of overconfidence were found, indicating that individuals generally differ in their proneness to biased responses (e.g., Soll, 1996). Exceptions to overconfidence are reported (i) for tasks where predictability is high, (ii) for tasks where swift and precise feedback about the accuracy of the judgments is provided, and (iii) for highly repetitive tasks (Kahneman and Riepe, 1998). Correspondingly, expert bridge players (Keren, 1987), race-track bettors (Dowie, 1976; Hausch and Ziemba, 1995), and meteorologists (Murphy and Winkler, 1984) were found to be well-calibrated in their predictions. Recently, the behavioral concept of overconfidence has also been applied to financial decisions, was analytically (e.g., Barber and Odean, 1999; Benos, 1998; Caballé and Sákovics, 2000) and experimentally (e.g., Adams et al., 1995; Benos and Tzafestas, 1997; Camerer and Lovallo, 1999; Nöth et al., 2001) studied and confirmed for field data (e.g., Barber and Odean, 2000; Kim and Nofsinger, 2000; Statman and Thorley, 1999). Overconfident investors trade too much (Biais et al., 2000; Odean, 1998, 1999), deviate from Bayes’ rule when aggregating information (Nöth and Weber, 2000) and overreact to private signals and underreact to public signals (Daniel et al., 1998; Yue et al., 2000). Though overconfident agents could thus be exploited by other market participants and driven out of the market, there are studies that show that overconfidence can persist nevertheless (e.g., Bernardo and Welch, 2001;

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Daniel et al., 2000; Kyle and Wang, 1997; Wang, 2001). The process of becoming wealthy can make successful investors overconfident. “[But,] a particular trader’s overconfidence will not flourish indefinitely; time and experience gradually rid him of it. However, in a market in which new traders are born every minute, overconfidence will flourish” (Gervais and Odean, 2000, p. 31). Bloomfield et al. (1998) showed experimentally that alerting less-informed investors – who suffer from the above mentioned traits of overconfidence – to the extent of their informational disadvantage can eliminate overconfidence and thereby welfare losses. Likewise, Zacharakis and Shepherd (1999) recommend to try to reduce overconfidence by improving knowledge and thereby the decision quality of venture capitalists. The purpose of this paper is to develop a formal model that allows to test – in a controlled experimental setting – whether participants exhibit overconfidence in their investment behavior. Participants’ decisions are contrasted with (i) the optimal investment solution, (ii) with a “risk averse” investment decision, and (iii) with a “risk loving” investment decision. We employ a conservative approach by defining overconfidence on the systematic and consistent deviation of one’s decisions for all three investment alternatives. In the next section, the basic model is introduced, in section 3 the optimal investment solution is derived and our hypotheses are introduced. In section 4, the participants, the design and the experimental procedure are discussed and also the results are presented. Eventually, in section 5 we will discuss the results.

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2. The basic model

We apply the mechanism to control the decision makers’ risk preferences described by Berg et al. (1986) in order to derive the optimal investment behavior. We want to induce risk averseness. Since Holt and Laury (2000) showed in spite of Rabin (2000) that most decision makers are risk averse even with ‘normal’ laboratory payoffs this should not counteract the decision makers’ true risk preferences and thus not add only additional noise (Selten et al., 1995). The decision maker can either win a low (M ) or a high monetary (M ) prize with 0 0 ∀x ∈ [x; x¯] ϕ(x) = = 0 otherwise. The decision maker chooses his/her limit l in the sense that whenever x ≤ l (s)he will pay x probability points to obtain his/her own investment i instead of î, whereas for x > l (s)he will pay nothing but obtain the alternative investment î. Thus, his/her cardinal utility now depends on i, î, l and x as follows:   W (i) − x for x ≤ l ˆ W = W (i, i, l, x) =  W (î) for x > l.

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One of the most robust findings in experimental analysis in economics is that decision makers often display a large discrepancy between their willingness to accept (wta) in order to sell an item and their willingness to pay (wtp) to purchase it (e.g., Bateman et al., 1997; Kahneman et al., 1990). Thus we will ask for both willingness to pay and willingness to accept in order to test for correlation between levels of confidence and the wta/wtp disparity. Of course, the decision maker will not want to switch from i to î if (s)he considers i as better than î. In such a case (s)he will want to be rewarded for giving up i. We will classify such decision makers as confident and, if î is the optimal choice i , even as overconfident. On the other hand, a decision maker might regret his/her choice and prefer î over i. In such a case (s)he would be even willing to pay for switching from i to î. We will speak then of nonconfidence. The above classification is a conservative but intuitive approach to define overconfidence in the context of our experiment. Since we will ask the decision makers not only to invest just once in one risky asset but to successively invest several times in a different risky asset each time without any feedback between his/her decisions we will suggest a more statistically motivated definition of overconfidence as well. If l (i, î) is the optimal switching limit we classify a decision maker as persistently overconfident when l is significantly larger than l (i, î). If l is significantly smaller than l (i, î) we will speak of persistent underconfidence. In case we should observe simultaneous under- and overconfidence when comparing the willingness to pay and to accept we also want to introduce a third concept of overconfidence. We will talk of consistent overconfidence if and only if the decision maker is classified in both cases as overconfident when asked for his/her willingness to pay and willingness to accept. This completes the description of the basic model according to which the decision maker first chooses an investment i and then for a given pair i and î, namely his/her own choice i and a predetermined alternative î, his/her limit l expressing his/her willingness to switch from î to i. In the following section we will determine the optimal investment i by disregarding the possibility of switching later before turning attention to the overall optimal behavior.

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3. Solution behavior and behavioral hypotheses

Let us explore the conditions for an interior solution based on W (i) = 0 and W < 0 that requires

w 1−w

1/1−α d−r (P0 − 1)r + id = ¯ r−d (P0 − i)r + id¯

since W < 0 holds due to 0 < α < 1. With the help of R=

w 1−w

1/1−α d−r r − d¯

the optimal investment level i can then be described as i =

(1 − R)rP0 . ¯ Rd − d + (1 − R)r

(3.1)

Proposition 2 Under assumptions (2.1) to (2.9) the optimal investment level i is given by equation (3.1). Let us now consider the overall game situation where one first chooses i then is confronted with an alternative investment level î which one can exchange for i depending on the probability points x which one pays (x > 0) or obtains (x < 0) for switching from î to i. Since one should switch whenever W (î) ≤ W (i) − x, the dominant limit l is determined by l (i, î) = W (i) − W (î).

(3.2)

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Proposition 3 Rational switching in the sense of a unique weakly undominated strategy l requires l (i, î) = W (i) − W (î). If one has chosen optimally before, i.e. i = i , and if î = i one consequently will choose a positive limit l(i , î). But also in case of i = i we expect positive limits even for î = i as expressed by our behavioral Hypothesis 1 Even for î = i participants in the experiment will often choose positive limits l(i, î) regardless of whether i is optimal or not. The obvious reasons for this hypothesis are that • most participants will not select i = i and thus violate the rationality hypothesis predicting i = i and l(i, î) = l (i, î), • many participants feel committed to their own choice i and thus will be reluctant to substitute it by î even when î is unambiguously better in view of the rationality hypothesis. Participants will not only be confronted with the optimal alternative i but also with the alternative investment levels î = i− and î = i+ satisfying 0 < i− < i < i+ < ¯i. Our test of confidence will be performed for Hypothesis 2 All three limits l(i, i− ), l(i, i ) and l(i, i+ ) are positive. Thus, overconfidence requires consistently positive limits and not just l(i, i ) < 0. Diagnosing overconfidence in this sense avoids the problem that overconfidence is just a result of a more or less stochastic deliberation which will hardly ever provide such consistency of overconfidence in the sense of positive limits. We will also test the more sophisticated Hypothesis 3 Participants will choose persistently all three limits l(i, i− ), l(i, i ) and l(i, i+ ) such that they are greater than the corresponding optimal limits l (i, i− ), l (i, i ) and l (i, i+ ). Regarding the investment behavior we do not expect participants to engage in the proper (probability) calculus leading to i but rather to form directly aspiration

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levels on how much to guarantee, e.g. by stating a lower bound for (P0 − i) or for the sure interest (P0 − i)r which can be used to cover (hedge) the risk from positive investments i. More specifically, we conjecture Hypothesis 4 Most investment levels i, chosen by participants, will be prominent shares of P0 . By making P0 itself a prominent number, e.g. P0 = 100, one can rely on the usual prominence of the decimal system as it is, for instance, expressed by most monetary systems whose coins and bills are mostly specified by the numbers 1, 2, 5, 10, 20 or 25, 50 and 100. To avoid that prominence supports the rationality hypothesis for the wrong reasons the parameters of the basic model should be specified in such a way that i is not a prominent number itself. Additionally, we expect participants to only estimate a lower and upper bound of the differences between the true values of one’s investment decisions and the alternatives instead of applying the proper calculus. Therefore, these differences will be uncertain. As Mueser and Dow (1997) argue this will lead to a disparity between wta and wtp. We therefore want to test also Hypothesis 5 There will be a substantial wta/wtp disparity. This disparity increases as the value of an object is less certain (Mueser and Dow, 1997). Thus, the wta/wtp disparity is an indicator for the degree of uncertainty of the differences of the true values of one’s own investments and the alternative investment levels. As being less certain about something implies a lower level of confidence we finally conjecture Hypothesis 6 The wta/wtp disparity is negatively correlated with the level of confidence.

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4. The experiment

The experiment was conducted at the Humboldt-University of Berlin’s experimental economics computer lab in June 2001 on three consecutive days. We had six sessions of about 12 participants each, 72 participants in total. 28 of them were female and 44 male participants. They were mostly students of business administration and economics with an average age of 23.2 years, the youngest being 19 years old while the oldest was 31. They were recruited from a pool of students who stated their general willingness to participate in experiments before. The low monetary prize M was 15 DM and the high monetary prize M was 40 DM leading to an average payment of well above 25 DM. Each session lasted for about 70 minutes.

4.1.

The general course

After registration each participant gets a handout including the instructions and an introductory calculus problem (see Appendix). While reading the instructions participants have the opportunity to ask questions. Those are answered privately. Afterwards they are asked to solve two problems1 related to their task in the experiment without making use of pocket calculators which are prohibited during the whole experiment. Thus, they have to estimate the solution or calculate it using pen and paper. After a few minutes the problems are solved by one of the experimenters in public. This ensures that every participant understands how to calculate the probability of earning the high monetary prize in general. During the experiment we talk about lottery tickets instead of probability. Therefore, we transform the probability of earning the high monetary prize W (i) to 1

These problems are essentially the following two. How many lottery tickets do you get if you ¯ How many lottery tickets do you invest P0 in the risky asset and it yields the high interest d? get if you invest nothing in the risky asset?

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Table 4.1.: Parameters for the four different investment decisions r 0.0010 0.0010 0.0007 0.0010

d −0.0001 −0.0001 −0.0001 −0.0001

d¯

w

α

i

W (i )

i−

W (i− )

i+

W (i+ )

0.006 0.006 0.006 0.007

0.65 0.67 0.65 0.70

0.5 0.5 0.5 0.5

43 38 53 37

0.346 0.340 0.315 0.341

23 21 29 19

0.340 0.330 0.306 0.336

71 63 77 74

0.332 0.335 0.302 0.317

number of lottery tickets by multiplying by 1000. Thus, each lottery ticket has a value of a 0.1 % chance to earn the high monetary prize M . The actual experiment is conducted using zTree (Fischbacher, 1999). Successively, we ask the participants for four investment decisions for different risky assets (see table 4.1). Their endowment for each investment is P0 = 100. The upper limit for investments ¯i is set to 80 so that P > 0 holds for all possible investments i in our experiment. After each investment decision the participants are confronted with the alternative investment levels î− , î and î+ one after another in a randomized order. They do not know that one of the three alternative investment levels for each investment decision is the optimal one. Each time we ask them: “How many lottery tickets are you willing to pay in order not to have to switch to the alternative investment level?” and “How many lottery tickets do we have to pay you so that you are willing to switch to the alternative investment level?” Due to the possible variation in the expected values of the investment levels we set the interval for the random price mechanism to [−49; 50]. It is common knowledge that only one but not which one of these decisions will be relevant for the individual lottery afterwards. After all investment decisions are taken the participants are told which of their decisions will be the relevant one. Then they have to answer a short questionnaire. Finally, we determine whether the relevant risky asset yields a high or low interest by throwing a ten sided die. Afterwards, we conduct the random price mechanism for each participant individually by letting her/him throw two ten sided dice2 and thus determine the number of lottery tickets (s)he has. Last, by throwing three ten sided dice, the winning lottery ticket and final payment for each participant is determined. (S)he earns the high monetary prize if the number of points is less or equal to the number of lottery tickets otherwise (s)he earns the low monetary prize. 2

We have to subtract 50 from the number of points to get the interval [−49; 50].

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50 40 30 20

frequency

10 0

0

20

40

60

80

investment levels

Figure 4.1.: Participant’s investment levels for all decisions

4.2.

The data

Let us first look at the investments. As is obvious from figure 4.1. most investment levels i are prominent shares of 100, namely multiples of 10 or at least 5. Only 20 out of 288 investment decisions do not fall into these two categories. This confirms our fourth hypothesis. The average investments are larger than the optimal ones (pairwise Wilcoxon rank sum test3 , p < 0.001) with 7.5 as the mean of the differences. This is not true for each risky asset itself. Indeed, investment in risky asset number 3 is not significant different from the optimal one, the 95 % confidence interval4 for the difference between actual and optimal investment ranges from −8.30 to 7.80. Both boundaries are positive for the other three investment decisions. However, testing for each participant individually – due to the small sample size at the 5 % level we cannot reject the null of optimal investment, i.e. i = i , for any participant – at the 10 % level we have to reject the null of optimal investment for only 11 out of the 72 3

The t test provides virtually the same result. We are, however, reluctant to assume normality. Indeed, the Shapiro-Wilk test for normality rejects this assumption at p 0.001. Thus we will use only distribution free / nonparametric tests throughout our analysis even in cases when we could assume asymptotic normality due to sample size. All computations are done with R (Ihaka and Gentleman, 1996). 4 This exact nonparametric confidence interval is obtained by the algorithm described in Bauer (1972).

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Table 4.2.: Number of participants classified as over- or nonconfident times

overconfident 4 3 2 1

participants (wtp)a participants (wta)b

8 12 12 13 20 3 0 1 41 11 10 6 3 0 0 0

0

nonconfident 1 2 3 4 0 0

a

Two participants were classified as once both over- and nonconfident. One participant was classified as twice overconfident and once nonconfident. b One participant was once classified as nonconfident and three times as overconfident.

participants. Thus, we can assume that most participants indeed tried to maximize the expected number of lottery tickets and thereby W (i). This leads us to the optimal limits l . The average optimal limit l equals −3.78, indicating that most times investments i were not as good in terms of W (i) as the alternatives. The pairwise Wilcoxon test reveals that, indeed, W (i) < W (î− ) with p < 0.001 and of course W (i) < W (î ) with p 0.001 but W (i) > W (î+ ) with p < 0.001. Our participants, however, valued their investments quite differently. First, we observe a significant wta/wtp disparity (p 0.001) which confirms our fifth hypothesis. The mean limit resulting from the wta question lwta = 29.34 is well above the mean limit resulting from the wtp question lwtp = 10.29. Second, the mean limit for each of the three alternative investments is positive. We will now focus on individual decisions and apply our confidence classifications. Eventually, we will see whether there is even simultaneous under- and overconfidence when comparing lwtp and lwta . A participant is classified as overconfident if all three limits are positive according to our hypothesis 2, or as nonconfident if all three limits are negative. Table 4.2 shows the distribution of the number of participants who were classified as either one. To yield a statistically significant classification at the 10 % level a participant has to be classified at least three times as either overconfident or nonconfident. Therefore, we can call 20 out of our 72 participants overconfident in the sense of consistently overvaluing their own investment decision when looking at their limits lwtp . Using lwta for classification we can call 52 participants overconfident. Even the one we classified first as nonconfident is now to be classified as overconfident.

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Now let us apply the more sophisticated second approach of classification we introduced in section 2. We have to look at the differences between limits l and optimal limits l for each investment and participant and to apply the pairwise Wilcoxon rank sum test for each participant in order to classify him/her. If his/her limits l are significantly larger at the 5 % level than the optimal l we classify him/her as persistently overconfident and if his/her limits l are significantly smaller than the optimal l we call him/her persistently underconfident. Applying this approach yields the following results. For the limits lwtp we classify 2 participants as persistently underconfident, 46 participants as persistently overconfident and 24 as neither one. For the limits lwta we call only 1 participant persistently underconfident which surprisingly we before classified as persistently overconfident. 69 participants are classified as persistently overconfident including the two we called persistently underconfident before, and 2 are not classified in either category. Since the two approaches result in different numbers of overconfidence classifications – at least if we insist on statistically significant classifications – we have to ask whether the heuristic approach classifies the subjects correctly in the sense that they are classified into the same category by our second, statistically motivated, approach, too. Unfortunately it does not. Using the wtp data we find that 1 out of 20 participants is classified as overconfident by the heuristic approach but not by our second method. And an additional one is classified as nonconfident but not as persistently underconfident. The differences between the two approaches become more distinct if we drop our insistence on statistically significant classifications. This is where we finally want to apply our definition of consistent under- and overconfidence. Only those participants who are classified into the same category by both wtp and wta data are called consistently under- respectively overconfident. This reduces the disparity between our two approaches. If a participant is classified as consistently overconfident by the heuristic approach – the above mentioned insistence on statistically significant classifications still has to hold – (s)he remains consistently overconfident as well in our second approach, but not vice versa. Finally we want to know which features characterize a participant who is classified as overconfident. To answer this question, we conduct a binary probit regression. The dependent variable is the vector of consistent classifications by our second approach, i.e. a vector of “1s” for persistently overconfident participants and “0s” otherwise. The covariates are the age of the participant, his/her sex (“1”: male,“0”:

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Table 4.3.: Probit Regression Dependent Variable: consistent overconfidence classification Method: ML - Binary Probit QML (Huber/White) standard errors and covariance Variable

Coefficient

Std. Error

z-Statistic

Prob.

constant age sex math mark self-assessment wta/wtp mean absolute i − i time invest time alternative FKK-PC FKK-SKI

4.369724 −0.042747 −0.455834 0.019182 −0.057818 −0.045660 0.080693 0.004832 −0.001150 −0.039070 −0.023244

2.563155 0.092929 0.380899 0.233441 0.222621 0.012669 0.023463 0.007868 0.009010 0.019111 0.017858

1.704822 −0.459996 −1.196732 0.082170 −0.259715 −3.604188 3.439224 0.614159 −0.127642 −2.044395 −1.301640

0.0882 0.6455 0.2314 0.9345 0.7951 0.0003 0.0006 0.5391 0.8984 0.0409 0.1930

Mean dependent var S.E. of regression Sum squared resid Log likelihood Restr. log likelihood LR statistic (10 df) Probability(LR stat)

0.625000 0.434260 11.50346 -34.96441 -47.63255 25.33629 0.004743

S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Avg. log likelihood McFadden R-squared

0.487520 1.276789 1.624613 1.415259 -0.485617 0.265956

female), his/her math mark at his/her university entrance qualification / school leaving exam and his/her self-assessment of whether (s)he is a good student. Since our questionnaire consists of a psychological test for conviction of competence and control (Krampen, 1989) resulting in 2 scales: generalized self-effectiveness (FKK-SKI) and generalized beliefs in external control (FKK-PC), these scales will be covariates, too. Additionally, we include a vector of the wta/wtp differences, a vector of the mean absolute differences of investments and optimal investments and a vector of the average amount of time for investment decisions and valuing the alternatives respectively. As the likelihood ratio statistic shows, our regression model is indeed a significant improvement to the na¨ıve assumption of constant probability of being classified as overconfident. Neither age, math mark nor self-assessment are significant. This is true for both time variables and the scale of generalized self-effectiveness. Since our regression shows that sex has no significant influence on overconfidence classifications, we cannot confirm the existence of a gender difference (e.g., Barber and Odean, 2001; Huberman and Rubinstein, 2000; Lundeberg et al., 1994).

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The significant covariates are the wta/wtp disparity, the mean deviation of optimal and actual investment and the scale of generalized beliefs in external control. First, a larger wta/wtp difference leads to a smaller probability of being classified as overconfident. This confirms our sixth hypothesis. With the wta/wtp disparity being an indicator for the degree of uncertainty about the difference of the true values of one’s own investments and the alternatives, the participants are less likely to be overconfident the more uncertain about the true values they are. Second, the larger the mean deviation of optimal and actual investment the more likely is the overconfidence classification of the participant. This confirms the intuition that those who performed poorly at the investment task are unable to recognize their non-competence and thus are supremely confident of their abilities (Kruger and Dunning, 1999). And, finally, decision makers who are more prone to believe that their life is controlled by external factors are less likely classified as overconfident. Since those decision makers asses their failures and successes rather to external factors than to their own abilities we could classify them as generally nonconfident. In our investment decision context this nonconfidence is confirmed by a less likely overconfidence classification.

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5. Discussion

We conducted an experiment to test the participants for overconfidence in an investment decision context. For classification we applied two different approaches. The first is based on a simple heuristic classifying a decision maker as overconfident if and only if (s)he prefers his/her investment decision i to the optimal one (î ) and a more ‘risk averse’ (î− ) and a more ‘risk loving’ (î+ ) investment level. We asked for both willingness to pay and willingness to accept for (not) switching to the alternatives while the decision maker did not know their true nature. The second approach demands a statistically significant overvaluation of one’s own investment decisions when contrasted to the three alternatives and thus allows for overconfidence classifications even if the decision maker does not prefer his/her own investment decisions to the alternatives, i.e. in cases when W (i) < W (î). The two approaches do not yield the same results which is mainly due to the fact that the heuristic approach does not use all available information and thus is not efficient. More specifically, it does not take account of the following two cases. First, if W (i) < W (î) and 0 > l(i, î) > W (i) − W (î) a participant is classified as nonconfident although (s)he really is more fond of his/her investment than (s)he should be. And second, if W (i) > W (î) and W (i) − W (î) > l(i, î) > 0 a participant is classified as confident although his/her investment decision is better than (s)he believes. Additionally, the heuristic approach has less selectivity power and is more conservative than our second method of classification. There are, however, some advantages. First, it does not need cumbersome calculations as we just have to count positive or negative limits. Second, it does not depend on the knowledge of the exact optimal limits and thereby the decision maker’s exact utility function as long as we know at least his/her optimal investment level. Even if we do not know his/her exact optimal investment level this heuristic can serve as a first approximation to a method that incorporates such uncertainties.

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In our experiment we observed that nearly two third of our participants are prone to overconfidence. Overconfidence is correlated to a larger wta/wtp difference that is an indicator for the degree of uncertainty of the value of the investments. Additionally, we observed that those participants who performed badly at the investment task are more likely to be overconfident. The skills required for competence are the same skills necessary to recognize competence. Finally, participants who are prone to underconfidence in a more general sense, i.e. beliefs in external control are dominant features of these participants, are indeed less likely overconfident in our investment decision context. This last finding strengthens the validity of our test. Psychological diagnosis and overconfidence classification in our investment decision context are coincident. A possible extension of our basic model is, for instance, the simultaneous investment in at least two risky assets which resembles actual portfolio decisions more than the investment in just one risky asset. Furthermore one could explore the theoretical statistical properties of investments and switching limits and thus derive an improved method of classification from the underlying distributions. A direct intra-individual comparison using additional different psychological tests would be interesting, too. These ideas will be left for further research.

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A. Handout

Herzlichen Dank f¨ ur Ihre Bereitschaft an unserem Experiment teilzunehmen! Das Experiment dient der Erforschung individueller Entscheidungsfindung. Alle Angaben werden streng anonym behandelt und keinesfalls an Dritte weitergegeben. Die Bearbeitungszeit beträgt etwa 1 Stunde und 10 Minuten. In diesem Experiment treffen Sie Ihre Entscheidungen unabh¨ angig von den anderen Teilnehmern. Ihre abschließende Auszahlung h¨ angt nicht von dem Verhalten der anderen ab. Sie wird f¨ ur jeden Teilnehmer individuell allein aufgrund seiner eigenen Entscheidungen ermittelt. Sie werden in diesem Experiment aufgefordert, insgesamt vier Investitionsentscheidungen bez¨ uglich jeweils einer unsicheren (Aktie) und einer sicheren Anlage (Sparbuch) zu treffen. Die unsichere Anlage kann zu einer negativen oder positiven Rendite f¨ uhren. Die jeweiligen Wahrscheinlichkeiten hierf¨ ur werden wir Ihnen mitteilen. Die positive Rendite der unsicheren Anlage ist gr¨ oßer als die Rendite der sicheren Anlage. Sie erhalten f¨ ur jede Investition 100 Gulden, von denen Sie jeweils maximal 80 Gulden in die unsichere Anlage investieren k¨ onnen. Gulden, die Sie nicht in die unsichere Anlage investieren, werden automatisch in die sichere Anlage investiert. Anschließend werden wir Ihnen verschiedene andere Investitionsniveaus vorschlagen, und Sie bitten uns mitzuteilen, unter welchen Bedingungen Sie zu einem Wechsel bereit sind. Ob Sie auf das vorgeschlagene Investitionsniveau wechseln m¨ ussen, wird vor der Auszahlung durch einen W¨ urfelwurf bestimmt. Wenn L die Anzahl der Lose ist, die Sie bereit sind, an uns zu zahlen, um nicht wechseln zu m¨ ussen, so m¨ ussen Sie nicht wechseln, wenn wir eine Zahl kleiner oder gleich L w¨ urfeln. Sie zahlen an uns dann jedoch W¨ urfelwurf Lose. W¨ urfeln wir eine Zahl gr¨ oßer L, so m¨ ussen Sie auf das angebotene Investitionsniveau wechseln. Falls Sie wechseln wollen, können Sie auch einen negativen Betrag angeben. Die Seiten des W¨ urfels sind von -49 bis 50 durchnummeriert. Dieser Mechanismus gilt umgekehrt f¨ ur die Frage, wieviel Lose wir Ihnen f¨ ur einen

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Wechsel zahlen m¨ ussen. Aus Ihren so getroffenen Entscheidungen resultieren jeweils zwei verschiedene m¨ ogliche Auszahlungen, eine niedrige und eine hohe, deren Wahrscheinlichkeiten jenen der unsicheren Anlage f¨ ur negative und positive Renditen entspricht. Die Auszahlung der Rendite wird jedoch nicht direkt in Geld, sondern in Form von Lotterielosen erfolgen. Insgesamt gibt es in jeder individuellen Lotterie 1000 Lose. Eines der Lose in jeder Lotterie gewinnt 40 DM. Sollten Sie dieses Los nicht besitzen, erhalten Sie eine Auszahlung von nur 15 DM. Nur eine Ihrer Investitionsentscheidungen wird auszahlungsrelevant sein. Diese haben wir bereits vorher festgelegt. Sie wird Ihnen am Ende des Experiments mitgeteilt. Beachten Sie bitte, daß jede Ihrer getroffenen Entscheidungen auszahlungsrelevant sein k¨ onnte. Zum Abschluß dieses Experiments werden wir durch W¨ urfelwurf bestimmen, ob die unsichere Anlage zu einer hohen oder niedrigen Rendite f¨ uhrt und somit bestimmen, wieviel Lose Sie erhalten. Anschließend werden wir mit Ihnen ausw¨ urfeln, welches der Lose aus Ihrer Lotterie den großen Preis gewinnt. Schließlich erhalten Sie Ihre Auszahlung.

27

Teilnehmerbogen Teilnehmernummer:

Datum:

Uhrzeit:

P sei die von Ihnen bei dieser Investitionsm¨ oglichkeit erzielbare Rendite in Gulden. Sie √ erhalten dann 1000 ∗ P Lose. Die unsichere Anlage hat mit einer Warscheinlichkeit von 35% eine Rendite von 0, 006 und mit einer Wahrscheinlichkeit von 65% eine Rendite von −0, 0001. Die sichere Anlage hat eine Rendite von 0, 001. Die mögliche Anzahl an Losen ist dann, wenn Sie i Gulden investieren: 1000 ∗ (100 − i) ∗ 0, 001 − i ∗ 0, 0001 oder 1000 ∗

(100 − i) ∗ 0, 001 + i ∗ 0, 006

Wieviele Lose erhalten Sie, wenn Sie 100 Gulden in die unsichere Anlage investieren und sie schließlich die hohe Rendite von 0,006 erzielt? Wieviele Lose erhalten Sie, wenn Sie keinen Gulden in die unsichere Anlage investieren und sie schließlich die negative Rendite von -0,0001 erzielt?

Bitte erst nach Aufforderung ausf¨ ullen!

Die auszahlungsrelevante Entscheidung Ich habe

Gulden in die unsichere Anlage investiert.

Aus dieser Investition resultieren mit und mit

% Wahrscheinlichkeit

% Wahrscheinlichkeit Lose.

Gulden resultieren mit

Aus dem alternativen Investitionsniveau von Wahrscheinlichkeit Ich bin bereit,

Lose und mit

Lose

% Wahrscheinlichkeit

% Lose.

Lose f¨ ur mein eigenes Investitionsniveau zu zahlen. Ich verlange

Lose f¨ ur den Wechsel zum alternativen Investitionsniveau. Ich habe eine

gew¨ urfelt. Ich erhalte also

Lose.

Es wurde Los

gezogen. Ich erhalte 15,- / 40,- DM.

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