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Why inexperienced investors do not learn: They do not know their past portfolio performance
Finance Research Letters 4 (2007) 203–216 www.elsevier.com/locate/frl
Why inexperienced investors do not learn: They do not know their past portfolio performance Markus Glaser a,∗ , Martin Weber a,b a Lehrstuhl für Bankbetriebslehre at the Business School, Universität Mannheim, L 5, 2, 68131 Mannheim, Germany b CEPR, London, UK
Received 21 July 2007; accepted 18 October 2007 Available online 26 October 2007
Abstract Recently, researchers have gone a step further from just documenting biases of individual investors. More and more studies analyze how experience affects decisions and whether biases are eliminated by trading experience and learning. A necessary condition to learn is that investors actually know what happened in the past and that the views of the past are not biased. We contribute to the above mentioned literature by showing why learning and experience go hand in hand. Inexperienced investors are not able to give a reasonable self-assessment of their own past realized stock portfolio performance which impedes investors’ learning ability. Based on the answers of 215 online broker investors to an Internet questionnaire, we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. We show that investors are hardly able to give a correct estimate of their own past realized stock portfolio performance and that experienced investors are better able to do so. In general, we can conclude that we find evidence that investor experience lessens the simple mathematical error of estimating portfolio returns, but seems not to influence their “behavioral” mistakes pertaining to how good (in absolute sense or relative to other investors) they are. © 2007 Elsevier Inc. All rights reserved. JEL classification: C93; D8; D10; D14; G1; G10; G11 Keywords: Return estimation; Portfolio return; Perceived returns; Self-assessment; Better than average effect; Overconfidence; Financial education; Financial literacy; Learning; Experience
* Corresponding author.
E-mail addresses: [email protected] (M. Glaser), [email protected] (M. Weber). 1544-6123/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2007.10.001
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1. Introduction Recently, researchers have gone a step further from just documenting biases of individual investors. More and more studies analyze how experience affects decisions and whether biases are eliminated by trading experience and learning. Consider, for example, one of the most extensively studied biases of individual investors, the disposition effect. Feng and Seasholes (2005) analyze the disposition effect, the investor’s reluctance to realize losses and his propensity to realize gains, and find that experience eliminates the reluctance to realize losses. Seru et al. (2007) analyze 22 million trades from more than one million individuals in Finland from 1995 to 2003 and also find that the disposition effect falls, and performance improves, as investors become more experienced. Dhar and Zhu (2006) use demographic and socioeconomic variables as proxies for investor literacy, and find empirical evidence that wealthier individuals exhibit a lower disposition effect. Weber and Welfens (2007) present empirical and experimental evidence that learning attenuates the magnitude of the disposition effect. Consistent with the studies above, trading frequency also tends to reduce the disposition effect. Kaustia and Knüpfer (2007) document a strong link between personal experience with IPOs and future subscriptions. Greenwood and Nagel (2007) find that around the peak of the stock market bubble in the year 2000, mutual funds run by inexperienced managers were more heavily invested in technology stocks. Nicolosi et al. (2007) also present evidence that individual investors learn from past trading experience. A necessary condition to learn is that investors actually know what happened in the past and that the views of the past are not biased. We contribute to the above mentioned literature by showing why learning and experience go hand in hand. Inexperienced investors are not able to give a reasonable self-assessment of their own past realized stock portfolio performance which impedes investors’ learning ability. Based on the answers of 215 online broker investors to an Internet questionnaire we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. Portfolio returns are calculated with the help of the stock portfolio positions of this investor group over the years preceding the questionnaire. Furthermore, we compare their perceived performance percentile with the actual performance percentile. Moreover, we analyze determinants of the cross-sectional heterogeneity in a regression analysis. The first focus of our paper is on the absolute difference between estimated and realized performance. A potential difference is presumably mainly driven by lack of knowledge or mathematical skills. No behavioral factors (should) come into play in this mathematical exercise. Thus, it is intuitive that expertise might play a role in explaining potential heterogeneity across investors. Furthermore, we analyze whether investors overestimate their past realized performance and their performance relative to other investors. We thus also contribute to the literature on overconfidence. The facets of overconfidence usually studied in the literature are (see Glaser et al., 2004; Glaser and Weber, 2007; or Moore and Healy, 2007): (1) overestimation of one’s actual performance, (2) overplacement of one’s performance relative to others, also called the better than average effect, and (3) excessive precision in one’s belief, also called miscalibration. Empirical and experimental studies show that these facets of overconfidence are hardly correlated (see Glaser and Weber, 2007 and Moore and Healy, 2007 and the references cited therein).
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The first two facets of overconfidence can be regarded as a psychological foundation of differences of opinion models in finance (see Hong and Stein, 2007) while the last facet resembles the way overconfidence is modeled in finance with investors inferring a higher signal-to-noise ratio in market news than is statistically appropriate with the consequence of too tight prediction intervals (see, for example, the models by Odean, 1998 and Gervais and Odean, 2001, and the survey by Glaser et al., 2004). By analyzing the determinants of the first two out of the three above mentioned facets of overconfidence, we contribute to the still scarce literature on the demographics of overconfidence in the spirit of Bhandari and Deaves (2006). Our main results can be summarized as follows. Investors are hardly able to give a correct estimate of their own past realized stock portfolio performance over the past four years. The correlation coefficient between return estimates and realized returns is not distinguishable from zero. Furthermore, people overrate themselves. On average, investors think, that they are better than others. The correlation between self ratings and actual performance is also not distinguishable from zero. High past realized stock portfolio performance does not make investors overconfident in the sense that they rate themselves as better than other investors. In other words, investors who think that they had above average performance actually did not have above average performance in the past. Investors with higher stock market investment experience and higher past portfolio returns are better able to estimate their past realized stock portfolio performance. The rest of the paper is organized as follows. In Section 2, we present the data sets analyzed and the design of the study. In Section 3, we analyze the correlation between return estimates and actual past realized portfolio returns. Results on the correlation between perceived performance percentile and actual performance percentile are presented in Section 4. Section 5 contains regression results on the determinants of cross-sectional heterogeneity in the answers provided. The last section summarizes and discusses the results and concludes. 2. Data sets and the design of the study This study is based on the combination of several data sets. The main data set consists of 563,104 buy and sell transactions of 3079 individual investors from a German online broker in the period from January 1997 to mid-April 2001. We considered all investors who trade via the Internet, had opened their account prior to January 1997, had at least one transaction in 1997, and have an e-mail address. The second data set consists of several demographic and other self-reported information (age, gender, investment strategy, investment experience), that was collected by the online broker at the time each investor opened her or his account. The third data set consists of the answers to an online questionnaire (see Glaser and Weber, 2005 and the next section for details). Data on the securities traded are obtained from Datastream, our fourth data source. In August and September 2001, our investor sample received an email from the online broker with a link to an online questionnaire. 215 investors answered the questionnaire.1 Glaser and Weber (2007) show that there is no indication of a sample selection bias. The results of this paper are based on parts of this questionnaire and will be discussed in the following sections. We calculate the monthly gross portfolio performance of each investor making the following simplifying assumptions: We assume that all stocks are bought and sold at the end of the month and we ignore intra-month trading. Barber and Odean (2000) show that these simplifying as1 See Glaser and Weber (2005) for details about this questionnaire.
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Table 1 Cross-sectional distribution of percentage monthly gross portfolio returns All investors Mean Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum DAX (arithmetic monthly return) Number of households
Respondents to the questionnaire
0.54%
0.30%
−16.02% −5.83% −2.99% −1.90% −0.49% 0.57% 1.50% 2.75% 3.92% 7.80% 23.81%
−10.73% −8.15% −3.96% −2.11% −0.58% 0.53% 1.40% 2.52% 3.42% 6.06% 7.09%
2.02% 2793 (91% of 3079)
2.02% 195 (91% of 215)
sumptions do not bias the measurement of portfolio performance. The gross portfolio return Rht of investor h in month t is calculated as follows: Rht =
Sht i=1
wiht Rit
Pit niht with wiht = S , ht i=1 Pit niht
(1)
Rit is the return of stock i in month t , Sht is the number of type of stocks held by individual h in month t , Pit is the price of stock i at the beginning of month t , and niht is the number of stocks of company i held by investor h in month t . wiht is the beginning-of-month-t market value of the holding of stock i of investor h divided by the beginning-of-month-t market value of the whole stock portfolio of investor h. Table 1 shows the results for all investors and the subgroup of respondents to the questionnaire. The cross-sectional distribution of the monthly gross returns is similar to the results in Barber and Odean (2000, Table IV, p. 791). We observe a large cross-sectional variation in the performance across investors. When we exclude investors with stock positions in 12 or fewer months, we find gross returns between −16% and +24% per month. On average, investors underperform relevant benchmarks. For example, the arithmetic average monthly return of the German blue chip index DAX from January 1997 to March 2001 is 2.02% whereas the mean gross monthly return of investors in our data set is 0.54%. Furthermore, parametric and nonparametric tests show that the distribution of monthly returns is not significantly different in the two groups. Thus, there is no indication of a sample selection bias.2 3. Do investors know their past portfolio returns? In this section, we present survey evidence on investors’ ability to give an estimate of their own past realized stock portfolio performance. We asked the investors to give an estimate of their portfolio performance in the past (from January 1997 to December 2000): 2 Glaser and Weber (2007) show that this is also true for all other variables used later in the present paper.
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Table 2 Return estimates Number of observations Mean Standard deviation Skewness Kurtosis Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum
210 14.93% 13.11% 2.01 24.33 −50% −15% 0% 5% 10% 15% 20% 27% 35% 41% 120%
Please try to estimate your past performance of your stock portfolio at your online broker. Please estimate the return of your stock portfolio from January 1997 to December 2000: [Answer] percent per year on average. Table 2 presents the results. 210 of 215 investors who answered at least one question answered the question presented above. The investors think, on average, that their own realized stock portfolio performance from January 1997 to December 2000 was about 15% per year. There is a large variation in the answers to this questions. The answers range from −50% to +120%. Figure 1 plots the realized portfolio returns versus return estimates of the individual investors who answered the questionnaire (variables are winsorized at the 10% level). The correlation coefficient between return estimates and realized returns is −0.0471 (p = 0.5203). This complete lack of correlation might seem extremely surprising. But another study that uses a design similar to ours documents exactly the same findings. Owhoso and Weickgenannt (2007) investigate the extent to which auditors’ ratings of self-perceived abilities correspond with their actual performance, and whether these perceptions are influenced by audit experience and effectiveness when conducting audits within their domain of specialization. 144 industry-specialized audit seniors and managers reviewed two sets of audit working paper cases. At the end of the review, the auditors rated their ability to perform an audit in their domain. One result is that there is no significant positive correlation between auditors’ self-perceived abilities and actual performance. The difference between return estimates and realized returns is positive (mean and median are higher than 10% points per year, see also Table 3). The difference is highly significantly positive (p < 0.0001). This finding is consistent with Fig. 1 which shows that most dots lie below the 45◦ line. Thus, many investors believe that they made money although they did not. This finding is consistent with psychological evidence that people overstate past performance in a variety of tasks (see Dunning et al., 2004; Moore and Healy, 2007; and Owhoso and Weickgenannt, 2007). Why is there no correlation between realized portfolio returns and return estimates? One interpretation is that investors do not have a good understanding of the concept “return.” Another explanation is the way the online broker presents returns. Usually, the online broker presents gains and losses (with the buying price as the reference point) for every stock in the portfolio
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Fig. 1. Return estimates and realized returns. This figure plots return estimates versus realized portfolio returns of the individual investors who answered the questionnaire. Furthermore, the figure shows a 45◦ line. Variables are winsorized at the 10% level.
separately which makes it difficult to estimate the monthly or yearly stock portfolio performance. The broker also presents the total value of the portfolio, day-by-day. However, still, it is hard to calculate the performance of the portfolio when investors are continuously buying and selling stocks. When stocks are bought every month with additional money from, say, a cash account the stock portfolio value can increase although the average stock had negative returns. The information that should be relevant to judge own stock selection ability, the own past realized stock portfolio performance, is not calculated by the online broker. The results in this subsection are related to the experimental literature which shows that individuals in general are poor at recalling price changes when compared to recalling prices. Andreassen (1988) finds in an experiment that errors recalling price changes were significantly larger than those made in recalling prices. He argues that subjects pay greater attention to prices than to price changes. This result is in line with Glaser et al. (2007) who show that a group of students has bigger problems stating return forecasts for financial time series when compared to price forecasts. Table 3 also shows that experienced investors are better able to estimate their past realized stock portfolio performance. The difference between the perceived return and the actual return is significantly lower for investors with more than 5 years of investment experience.3 Furthermore, the percentage of investors who estimate at least the right sign of their past realized portfolio performance is higher for experienced investors. Moreover, more experienced investors are reasonably close with their estimates (see the lines in the table which show the number of investors 3 We use a cutoff of 5 years as this is the median level of experience so that we obtain two groups of approximately equal size.
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Table 3 Return estimates, self-assessments, and experience All investors Low investment High investment p-value (with experience experience experience (Mann–Whitney) variable available) (less than 5 years) (more than 5 years) (difference in experience groups) Absolute return difference
0.098*
Mean Median Observations Different from 0 (Wilcoxon)
20.96 17.84 142 p < 0.0001***
23.68 21.01 64 p < 0.0001***
18.73 16.71 78 p < 0.0001***
Correct sign Wrong sign
87 55
37 27
50 28
Percent correct
61.27%
57.81%
64.10%
Less than 5% points wrong
35
13
22
Less than 10% points wrong
48
18
30
Perceived return– actual return
Mean Median Observations Different from 0 (Wilcoxon)
11.61 13.85 142 p < 0.0001***
13.18 14.13 64 p < 0.0001***
10.32 12.41 78 p < 0.0001***
0.42
Absolute percentile difference
Mean Median Observations Different from 0 (Wilcoxon)
25.33 26.00 140 p < 0.0001***
25.31 23.00 62 p < 0.0001***
25.35 27.00 78 p < 0.0001***
0.99
Actual percentile– perceived percentile
Mean Median Observations Different from 0 (Wilcoxon)
4.44 4.00 140 0.0485**
5.61 3.50 62 0.103
3.50 4.00 78 0.2328
0.73
Notes. This table presents mean, median, the number of observations as well as the p-value of a Wilcoxon test (null hypothesis: value is equal to 0) of the absolute return difference, the difference between the perceived return and the perceived return, the absolute performance percentile difference and the difference between actual performance percentile and the actual performance percentile for all investors (with stock market investment experience variable available) and investors with low (less than 5 years) and high (more than 5 years) stock market investment experience. 5 years is the median experience level in our data set so that we obtain two groups of approximately equal size. See Sections 3 and 4 for details. Furthermore, the table shows the number of cases and the percentage of cases in which the sign of the past return assessment was correct. Moreover, the table shows the number of investors who are reasonably close with their estimates (see the lines which show the number of investors who are less than 5% points or 10% points wrong). Variables are winsorized at the 10% level. * Indicates significance at 10%. ** Indicates significance at 5%. *** Indicates significance at 1%.
who are less than 5% points or 10% points wrong). These findings might explain why the studies mentioned in the Introduction find that experienced investors make better decisions.
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These results are supported by Amromin and Sharpe (2006). They examine answers to the following question: “Thinking about a diversified portfolio of stocks, what would you guess was the average annual return earned over the past 10 years?” from the Michigan Survey of Consumer Attitudes, conducted by the Survey Research Center (SRC) at the University of Michigan. In particular, they calculate the absolute value of the recall error, i.e. the difference between recalled and actual 10-year market returns, and regress this difference on demographic and stock ownership characteristics. They find that the accuracy of a respondent’s recall of past returns improves with both wealth and education, as well as other indicators of financial market knowledge. To summarize, the main result of this section is that investors are hardly able to give a correct estimate of their own past realized stock portfolio performance and that experienced investors are better able to do so. 4. Self-rating and actual performance Furthermore, we asked the following question to analyze investors’ self-ratings and their relation with actual performance: What percentage of customers of your discount brokerage house had higher returns than you in the four-year period from January 1997 to December 2000? (Please give a number between 0% and 100%) [Answer] percent of other customers had higher returns than I did. Table 4 presents the results. The mean is 46.99 indicating a slight better than average effect. This number is significantly different from 50 (p = 0.0335, Wilcoxon signed-rank test).4 We are thus able to confirm prior literature on the better than average effect (Taylor and Brown, 1988; Svenson, 1981). One reason for the finding that this number is so close to 50 might be that about 30% of all investors classify themselves as average, i.e. state 50 as an answer.5 Figure 2 plots the self-ratings in percentiles versus actual return percentiles of the individual investors who answered the questionnaire. Such a graph is often used in the literature (see for example Ackerman et al., 2002). The figure shows that there is no relation between the selfratings in percentiles and actual return percentiles. The correlation between the self-ratings and actual percentiles is −0.0110 (p = 0.8810) which is not significantly distinguishable from zero. We are thus able to confirm prior research which shows that a correlation between self-ratings in percentiles and objective measures in percentiles is not existent (see Larrick et al., 2007 for further references and Dunning et al., 2004 for a recent survey). Furthermore, the difference between the actual return percentile of the respective investor and the self-assessed percentile is positive on average (this difference is positive if an investor thinks, for example, that only 25% of the other investors had higher portfolio returns in the past even though 30% of the investors in the sample actually had higher returns). Thus, investors overestimate their relative position in terms of return percentiles. 4 Note that in Table 3 the results are slightly different as we show results for the subgroup of respondents for which we have data on investment experience in that table. 5 Furthermore, recent studies show that the better than average effect is not as universal as was previously documented in the literature (see Moore, 2007; Moore and Cain, 2007; and Moore and Small, 2007). Thus, our small better than average effect is not a puzzle.
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Table 4 Self-ratings Number of observations
212
Mean Standard deviation Skewness Kurtosis
46.99 19.33 0.04 2.87
Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum
2 5 15 20 30 50 60 70 80 90 95
Fig. 2. Self-ratings in percentiles and actual percentiles. This figure plots the self-ratings in percentiles versus actual percentiles of the individual investors who answered the questionnaire.
Moreover, high returns in the past do not lead to high overconfidence as measured by perceived percentile in our questionnaire at the end of the sample period. Thus, we do not find support for the learning-to-be-overconfident hypothesis (Gervais and Odean, 2001), i.e. a high degree of overconfidence as a result of past investment success. We argue, that one reason is, that investors do not know their past realized stock portfolio performance as was presented in the
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previous section.6 Note, however, that Gervais and Odean (2001) model the third of the manifestations of overconfidence mentioned in the Introduction while we are analyzing the first two facets in this paper. However, there is also a further interpretation of these findings. We find that the correlation between investors’ self-assessed absolute performance and their self-assessed relative performance is 0.2704 (with a p-value of 0.0002). Therefore, investors are somehow consistent in their answers. This raises the question “which” returns are actually relevant for overconfidence. It is possible that not the actual realized returns are relevant for the learning-to-be-overconfident hypothesis but the perceived realized returns. It is possible that investors “feel overconfident” even without knowing the true performance, by simply allowing their overblown beliefs of own realized portfolio returns to influence their view of returns relative to others. Thus, it is intriguing that actual returns are uncorrelated with the self-perceived ranking, but perceived returns are. To summarize, investors who believe they have done well in the absolute sense, also believe they have done better than others. Which returns are actually more relevant for overconfidence is a question for future research. 5. Which investors are able to correctly estimate their past realized portfolio performance? Table 5 presents cross-sectional regression results on the determinants of the absolute difference between return estimates and realized returns (Regressions (1) and (2)), the difference between return estimates and realized returns (Regressions (3) and (4)), the absolute difference between perceived and actual return percentile (Regressions (5) and (6)), and the difference between actual and perceived return percentile (Regressions (7) and (8)) as dependent variables and stock market investment experience, a gender dummy variable, age, a mutual fund investor dummy, a warrant trader dummy variable, a high risk dummy, the logarithm of mean monthly stock portfolio value, the time-series average of the monthly stock portfolio performance of an investor, the logarithm of the standard deviation of monthly stock portfolio performance as a measure of portfolio risk, and the logarithm of number of stocks in portfolio.7 Stock market investment experience, gender and the high risk dummy are based on a voluntary self-report made by investors at the time the respective account was opened. This information was not updated afterwards by the online broker. The dependent variables and the monthly stock portfolio performance are winsorized at the 10% level. The table reports standardized beta coefficients (except for the intercept). Robust p-values are in parentheses. Regression (1) shows that stock market investment experience has a significantly negative effect on the absolute difference between return estimates and realized returns at the 1% level. This finding can be interpreted in the way that investors learn how to better judge their own 6 These results do not contradict the studies of Statman et al. (2006) or Glaser and Weber (2008). These studies find that returns over the past 6 months positively influence trading activity which is consistent with the learning-tobe-overconfident hypothesis. Statman et al. (2006) find, however, that returns with lags larger than 6 do not influence trading volume anymore. In connection with the findings presented in this study, we can conclude that learning-to-beoverconfident stories are more appropriate for the effects of past returns over shorter horizons than the four year horizon which we analyze in the present study. 7 We use the natural logarithm of variables that are positively skewed. Tests show, that we thus avoid problems like nonnormality, nonlinearity, and heteroscedasticity in the cross-sectional regression analysis. See Spanos (1986, chapter 21, especially, pp. 455–456), Davidson and MacKinnon (1993, chapter 14), and Atkinson (1985, pp. 80–81).
Table 5 Determinants of the difference between return estimates and realized returns and between perceived and actual return percentile: cross-sectional regressions Absolute difference between return estimate and realized return
Mutual fund investor (Dummy) Warrant trader (Dummy) High risk investment strategy (based on self-report; dummy) ln(stock portfolio value) (in EUR; time-series average per investor) Stock portfolio performance (time-series average per investor) ln(portfolio risk) (standard deviation of monthly portfolio returns) ln(number of stocks in portfolio) (time-series average per investor) Constant Observations Adjusted R-squared
Absolute difference between perceived percentile and actual percentile
Difference between actual percentile and perceived percentile
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
−0.202 (0.010)*** −0.074 (0.523) −0.014 (0.854) −0.102 (0.197) −0.063 (0.434) 0.031 (0.717) 0.037 (0.771) −0.467 (0.000)*** 0.221 (0.063)* −0.151 (0.231) 55.606 (0.000)*** 121 0.325
−0.186 (0.029)** −0.056 (0.619) −0.060 (0.538) −0.034 (0.694) −0.029 (0.759) −0.054 (0.460) 0.062 (0.645)
−0.088 (0.051)* 0.011 (0.557) 0.038 (0.490) −0.0758 (0.076)* 0.031 (0.417) −0.036 (0.427) −0.025 (0.704) −0.919 (0.000)*** −0.048 (0.351) 0.012 (0.882) 14.800 (0.039)** 121 0.828
−0.057 (0.519) 0.047 (0.686) −0.051 (0.622) 0.058 (0.539) 0.099 (0.311) −0.201 (0.026)** 0.0241 (0.879)
−0.040 (0.646) −0.032 (0.722) −0.096 (0.403) −0.051 (0.579) 0.046 (0.647) 0.028 (0.780) −0.236 (0.136) −0.126 (0.232) −0.011 (0.918) 0.072 (0.628) 59.101 (0.000)*** 119 0.002
−0.036 (0.691) −0.028 (0.749) −0.107 (0.344) −0.033 (0.712) 0.057 (0.574) 0.005 (0.960) −0.226 (0.150)
−0.088 (0.179) 0.028 (0.225) 0.027 (0.737) −0.074 (0.196) −0.044 (0.447) 0.0158 (0.784) −0.018 (0.857) −0.813 (0.000)*** 0.057 (0.385) 0.146 (0.150) 14.235 (0.327) 119 0.629
−0.056 (0.543) 0.056 (0.596) −0.047 (0.637) 0.041 (0.676) 0.026 (0.785) −0.131 (0.189) 0.043 (0.800)
0.231 (0.044)** −0.175 (0.230) 52.042 (0.001)*** 121 0.110
−0.027 (0.839) −0.036 (0.825) 5.352 (0.820) 121 0.000
−0.008 (0.943) 0.065 (0.658) 57.772 (0.000)*** 119 0.000
0.079 (0.505) 0.100 (0.498) −0.679 (0.983) 119 0.000
213
Notes. This table presents cross-sectional regression results on the determinants of the absolute difference between return estimates and realized returns (Regressions (1) and (2)), the difference between return estimates and realized returns (Regressions (3) and (4)), the absolute difference between perceived and actual return percentile (Regressions (5) and (6)), and the difference between actual and perceived return percentile (Regressions (7) and (8)) as dependent variables and stock market investment experience, a gender dummy variable (the variable is set equal to 1 if the investor is male), age, a mutual fund investor dummy (the variable is set equal to 1 if the investor trades funds at least once in the time period from January 1997 until April 2001), a warrant trader dummy variable (the variable is set equal to 1 if the investor trades warrants at least once in the time period from January 1997 until April 2001), a high risk dummy (the variable is set equal to 1 if the investor classifies her or his investment strategy as high risk), the logarithm of mean monthly stock portfolio value, the time-series average of the monthly stock portfolio performance of an investor, the logarithm of the standard deviation of monthly stock portfolio performance as a measure of portfolio risk, and the logarithm of number of stocks in portfolio. Investment experience is reported within five ranges, where the top range is more than 15 years. In the regressions we use the midpoint of each range and 17.5 years for the top range. The dependent variables and the monthly stock portfolio performance are winsorized at the 10% level. The table reports standardized beta coefficients (except for the intercept). Robust p-values are in parentheses. * Indicates significance at 10%. ** Indicates significance at 5%. *** Indicates significance at 1%.
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Stock market investment experience (in years) Gender (Dummy; men = 1) Age
Difference between return estimate and realized return
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past realized stock portfolio performance over time. Stock portfolio performance is also negatively related to the absolute difference between return estimates and realized returns. In other words, the lower the returns the worse investors are when judging their realized returns. There are several interpretations of this result. On the one hand, investors may look at their portfolio less often when returns are negative and, as a consequence, they do not know how bad they have actually performed. On the other hand, it is possible, that investors do not want to admit that they have performed pretty badly. This is consistent with psychological studies showing that people often neglect bad outcomes or unfavorable experience (see Dunning et al., 2004 for a survey). Karlsson et al. (2005), for example, present related evidence that investors check the value of their portfolios more frequently in rising markets but “put their heads in the sand” when markets are flat or falling. This finding is therefore sometimes called the “Ostrich Effect.” Furthermore, Table 2 shows that only less than 5% of our investors think they had negative returns in the past while more than 25% actually had negative returns in the past. Thus, somehow mechanically, investors with high past returns are closer to their self-assessment on average. This is why we re-run the regression without stock portfolio performance as explanatory variable (see Regression (2)). The results are similar. Stock market experience remains highly significantly negative at the 5% level.8 Furthermore, portfolio risk has a positive effect on the absolute difference between return estimates and realized returns. This result is intuitive. The higher the standard deviation of returns, the more difficult is it to calculate the past realized stock portfolio performance. All the other variables are not robustly related to the dependent variable. Regression (3) shows that experienced investors and mutual fund investors are less likely to overestimate their past realized portfolio performance. However, this effect is not significant in Regression (4) anymore. Regressions (5) to (8) present the determinants of the (absolute) difference between perceived and actual percentile. Compared to Regressions (1) to (4), the adjusted R-squared values are quite low. Furthermore, we do not find a robust influence of our explanatory variables on the (absolute) difference between perceived and actual percentile. To summarize, we find that experience helps in calculating the own past realized portfolio performance. This task should be mainly driven by skills that are enhanced by investment experience. In contrast, the other measures analyzed in Regressions (3) to (8) are closely related to the manifestations of overconfidence mentioned in the Introduction, especially overestimation of one’s actual performance and overplacement of one’s performance relative to others. The regression analysis in this part is exploratory in the spirit of Bhandari and Deaves (2006) who analyze the demographics of overconfidence. We had no ex ante hypothesis of the effect of expertise (and the other variables) on these overconfidence measures. Our analysis shows that our explanatory variables are not related to these overconfidence measures. In general, we can conclude that we find evidence that investor experience lessens the simple mathematical error of estimating portfolio returns, but seems not to influence their “behavioral” mistakes pertaining to how good (in absolute or relative sense) they are.
8 All results are similar when we use a winsorization at the 2% or 5% level. For example, when variables are winsorized at the 5% level, the beta coefficient for experience is −0.185 with a p-value of 0.018 in Regression (1) and −0.171 (p-value = 0.041) in Regression (2). When we use quantile regressions, the significance of the experience variable in Regression (1) is even stronger (p-value = 0.003). In Regression (2), the experience variable remains significant at the 10% level.
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6. Summary, discussion, and conclusion Based on the answers of 215 online broker investors to an Internet questionnaire we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. Furthermore, we compare their perceived performance percentile with the actual performance percentile. Moreover, we analyze determinants of the cross-sectional heterogeneity in a regression analysis. The main findings can be summarized as follows. Investors are hardly able to give a correct estimate of their own past realized stock portfolio performance. Experienced investors are better able to do so. Furthermore, people overrate themselves. On average, investors think, that they are better than others. Moreover, the correlation between self ratings and actual performance is not distinguishable from zero. We find that investors do not have a good understanding of the concept “return.” This result is consistent with other studies. Parts of our results can be explained by psychological reasons (such as the negative influence of past portfolio performance on the absolute difference between return estimates and realized returns). However, this is only one part of the story. We also find that stock market investment experience has a positive influence on the quality of estimates of past realized stock portfolio returns. This is consistent with other studies that document a positive effect of financial education on behavior. As investors are increasingly encouraged or even forced to invest for their own retirement savings, a good understanding of returns is essential. Future research should further investigate why people have problems dealing with returns and how these problems can be mitigated. Acknowledgments We would like to thank an anonymous referee for helpful comments. This paper was in parts written while Markus Glaser was visiting the Swedish Institute for Financial Research (SIFR) in Stockholm whose support is gratefully acknowledged. Financial Support from the Deutsche Forschungsgemeinschaft (DFG) is also gratefully acknowledged. References Ackerman, P.L., Beier, M.E., Bowen, K.R., 2002. What we really know about our abilities and our knowledge. Personality and Individual Differences 33, 587–605. Amromin, G., Sharpe, S., 2006. From the horse’s mouth: Gauging conditional expected stock returns from investor surveys. Working paper, Federal Reserve Bank of Chicago. Andreassen, P.B., 1988. Explaining the price–volume relationship: The difference between price changes and changing prices. Organizational Behavior and Human Decision Processes 41, 371–389. Atkinson, A., 1985. Plots, Transformations, and Regression. Clarendon Press, Oxford. Barber, B.M., Odean, T., 2000. Trading is hazardous to your wealth: The common stock investment performance of individual investors. Journal of Finance 55, 773–806. Bhandari, G., Deaves, R., 2006. The demographics of overconfidence. Journal of Behavioral Finance 7, 5–11. Davidson, R., MacKinnon, J.G., 1993. Estimation and Inference in Econometrics. Oxford Univ. Press, Oxford. Dhar, R., Zhu, N., 2006. Up close and personal: Investor sophistication and the disposition effect. Management Science 52, 726–740. Dunning, D., Heath, C., Suls, J.M., 2004. Flawed self-assessment: Implications for health, education, and the workplace. Psychological Science in the Public Interest 5, 69–106. Feng, L., Seasholes, M.S., 2005. Do investor sophistication and trading experience eliminate behavioral biases in financial markets? Review of Finance 9, 305–351. Gervais, S., Odean, T., 2001. Learning to be overconfident. Review of Financial Studies 14, 1–27. Glaser, M., Weber, M., 2005. September 11 and stock return expectations of individual investors. Review of Finance 9, 243–279.
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Glaser, M., Weber, M., 2007. Overconfidence and trading volume. Geneva Risk and Insurance Review 32, 1–36. Glaser, M., Weber, M., 2008. Which past returns affect trading volume? Journal of Financial Markets, in press. Glaser, M., Nöth, M., Weber, M., 2004. Behavioral finance. In: Koehler, D.J., Harvey, N. (Eds.), Blackwell Handbook of Judgment and Decision Making. Blackwell, Malden, MA, pp. 527–546. Glaser, M., Langer, T., Reynders, J., Weber, M., 2007. Framing effects in stock market forecasts: The difference between asking for prices and asking for returns. Review of Finance 11, 325–357. Greenwood, R., Nagel, S., 2007. Inexperienced investors and bubbles. Working paper. Hong, H., Stein, J.C., 2007. Disagreement and the stock market. Journal of Economic Perspectives 21, 109–128. Karlsson, N., Loewenstein, G., Seppi, D., 2005. The “Ostrich Effect”: Selective attention to information about investments. Working paper. Kaustia, M., Knüpfer, S., 2007. Do investors learn from personal experience? Evidence from IPO subscriptions. Working paper, Helsinki School of Economics. Larrick, R.P., Burson, K.A., Soll, J.B., 2007. Social comparison and confidence: When thinking you’re better than average predicts overconfidence (and when it does not). Organizational Behavior and Human Decision Processes 102, 76–94. Moore, D.A., 2007. Not so above average after all: When people believe they are worse than average and its implications for theories of bias in social comparison. Organizational Behavior and Human Decision Processes 102, 42–58. Moore, D.A., Cain, D.M., 2007. Overconfidence and underconfidence: When and why people underestimate (and overestimate) the competition. Organizational Behavior and Human Decision Processes 103, 197–213. Moore, D.A., Healy, P.J., 2007. The trouble with overconfidence. Working paper, Carnegie Mellon University, David A. Tepper School of Business and Ohio State University, Department of Economics. Moore, D.A., Small, D.A., 2007. Error and bias in comparative judgment: On being both better and worse than we think we are. Journal of Personality and Social Psychology 92, 972–989. Nicolosi, G., Peng, L., Zhu, N., 2007. Do individual investors learn from their trading experience? Working paper. Odean, T., 1998. Volume, volatility, price, and profit when all traders are above average. Journal of Finance 53, 1887– 1934. Owhoso, V., Weickgenannt, A., 2007. Auditors’ self-perceived abilities in conducting domain audits. Critical Perspectives on Accounting, in press. Seru, A., Shumway, T., Stoffman, N., 2007. Learning by trading. Working paper, University of Michigan. Spanos, A., 1986. Statistical foundations of econometric modelling. Cambridge Univ. Press, Cambridge. Statman, M., Thorley, S., Vorkink, K., 2006. Investor overconfidence and trading volume. Review of Financial Studies 19, 1531–1565. Svenson, O., 1981. Are we all less risky and more skillful than our fellow drivers? Acta Psychologica 47, 143–148. Taylor, S.S., Brown, J.D., 1988. Illusion and well being: A social psychology perspective on mental health. Psychological Bulletin 103, 193–210. Weber, M., Welfens, F., 2007. An individual level analysis of the disposition effect: Empirical and experimental evidence. Working paper, University of Mannheim.
Why inexperienced investors do not learn: They do not know their past portfolio performance Markus Glaser a,∗ , Martin Weber a,b a Lehrstuhl für Bankbetriebslehre at the Business School, Universität Mannheim, L 5, 2, 68131 Mannheim, Germany b CEPR, London, UK
Received 21 July 2007; accepted 18 October 2007 Available online 26 October 2007
Abstract Recently, researchers have gone a step further from just documenting biases of individual investors. More and more studies analyze how experience affects decisions and whether biases are eliminated by trading experience and learning. A necessary condition to learn is that investors actually know what happened in the past and that the views of the past are not biased. We contribute to the above mentioned literature by showing why learning and experience go hand in hand. Inexperienced investors are not able to give a reasonable self-assessment of their own past realized stock portfolio performance which impedes investors’ learning ability. Based on the answers of 215 online broker investors to an Internet questionnaire, we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. We show that investors are hardly able to give a correct estimate of their own past realized stock portfolio performance and that experienced investors are better able to do so. In general, we can conclude that we find evidence that investor experience lessens the simple mathematical error of estimating portfolio returns, but seems not to influence their “behavioral” mistakes pertaining to how good (in absolute sense or relative to other investors) they are. © 2007 Elsevier Inc. All rights reserved. JEL classification: C93; D8; D10; D14; G1; G10; G11 Keywords: Return estimation; Portfolio return; Perceived returns; Self-assessment; Better than average effect; Overconfidence; Financial education; Financial literacy; Learning; Experience
* Corresponding author.
E-mail addresses: [email protected] (M. Glaser), [email protected] (M. Weber). 1544-6123/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2007.10.001
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1. Introduction Recently, researchers have gone a step further from just documenting biases of individual investors. More and more studies analyze how experience affects decisions and whether biases are eliminated by trading experience and learning. Consider, for example, one of the most extensively studied biases of individual investors, the disposition effect. Feng and Seasholes (2005) analyze the disposition effect, the investor’s reluctance to realize losses and his propensity to realize gains, and find that experience eliminates the reluctance to realize losses. Seru et al. (2007) analyze 22 million trades from more than one million individuals in Finland from 1995 to 2003 and also find that the disposition effect falls, and performance improves, as investors become more experienced. Dhar and Zhu (2006) use demographic and socioeconomic variables as proxies for investor literacy, and find empirical evidence that wealthier individuals exhibit a lower disposition effect. Weber and Welfens (2007) present empirical and experimental evidence that learning attenuates the magnitude of the disposition effect. Consistent with the studies above, trading frequency also tends to reduce the disposition effect. Kaustia and Knüpfer (2007) document a strong link between personal experience with IPOs and future subscriptions. Greenwood and Nagel (2007) find that around the peak of the stock market bubble in the year 2000, mutual funds run by inexperienced managers were more heavily invested in technology stocks. Nicolosi et al. (2007) also present evidence that individual investors learn from past trading experience. A necessary condition to learn is that investors actually know what happened in the past and that the views of the past are not biased. We contribute to the above mentioned literature by showing why learning and experience go hand in hand. Inexperienced investors are not able to give a reasonable self-assessment of their own past realized stock portfolio performance which impedes investors’ learning ability. Based on the answers of 215 online broker investors to an Internet questionnaire we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. Portfolio returns are calculated with the help of the stock portfolio positions of this investor group over the years preceding the questionnaire. Furthermore, we compare their perceived performance percentile with the actual performance percentile. Moreover, we analyze determinants of the cross-sectional heterogeneity in a regression analysis. The first focus of our paper is on the absolute difference between estimated and realized performance. A potential difference is presumably mainly driven by lack of knowledge or mathematical skills. No behavioral factors (should) come into play in this mathematical exercise. Thus, it is intuitive that expertise might play a role in explaining potential heterogeneity across investors. Furthermore, we analyze whether investors overestimate their past realized performance and their performance relative to other investors. We thus also contribute to the literature on overconfidence. The facets of overconfidence usually studied in the literature are (see Glaser et al., 2004; Glaser and Weber, 2007; or Moore and Healy, 2007): (1) overestimation of one’s actual performance, (2) overplacement of one’s performance relative to others, also called the better than average effect, and (3) excessive precision in one’s belief, also called miscalibration. Empirical and experimental studies show that these facets of overconfidence are hardly correlated (see Glaser and Weber, 2007 and Moore and Healy, 2007 and the references cited therein).
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The first two facets of overconfidence can be regarded as a psychological foundation of differences of opinion models in finance (see Hong and Stein, 2007) while the last facet resembles the way overconfidence is modeled in finance with investors inferring a higher signal-to-noise ratio in market news than is statistically appropriate with the consequence of too tight prediction intervals (see, for example, the models by Odean, 1998 and Gervais and Odean, 2001, and the survey by Glaser et al., 2004). By analyzing the determinants of the first two out of the three above mentioned facets of overconfidence, we contribute to the still scarce literature on the demographics of overconfidence in the spirit of Bhandari and Deaves (2006). Our main results can be summarized as follows. Investors are hardly able to give a correct estimate of their own past realized stock portfolio performance over the past four years. The correlation coefficient between return estimates and realized returns is not distinguishable from zero. Furthermore, people overrate themselves. On average, investors think, that they are better than others. The correlation between self ratings and actual performance is also not distinguishable from zero. High past realized stock portfolio performance does not make investors overconfident in the sense that they rate themselves as better than other investors. In other words, investors who think that they had above average performance actually did not have above average performance in the past. Investors with higher stock market investment experience and higher past portfolio returns are better able to estimate their past realized stock portfolio performance. The rest of the paper is organized as follows. In Section 2, we present the data sets analyzed and the design of the study. In Section 3, we analyze the correlation between return estimates and actual past realized portfolio returns. Results on the correlation between perceived performance percentile and actual performance percentile are presented in Section 4. Section 5 contains regression results on the determinants of cross-sectional heterogeneity in the answers provided. The last section summarizes and discusses the results and concludes. 2. Data sets and the design of the study This study is based on the combination of several data sets. The main data set consists of 563,104 buy and sell transactions of 3079 individual investors from a German online broker in the period from January 1997 to mid-April 2001. We considered all investors who trade via the Internet, had opened their account prior to January 1997, had at least one transaction in 1997, and have an e-mail address. The second data set consists of several demographic and other self-reported information (age, gender, investment strategy, investment experience), that was collected by the online broker at the time each investor opened her or his account. The third data set consists of the answers to an online questionnaire (see Glaser and Weber, 2005 and the next section for details). Data on the securities traded are obtained from Datastream, our fourth data source. In August and September 2001, our investor sample received an email from the online broker with a link to an online questionnaire. 215 investors answered the questionnaire.1 Glaser and Weber (2007) show that there is no indication of a sample selection bias. The results of this paper are based on parts of this questionnaire and will be discussed in the following sections. We calculate the monthly gross portfolio performance of each investor making the following simplifying assumptions: We assume that all stocks are bought and sold at the end of the month and we ignore intra-month trading. Barber and Odean (2000) show that these simplifying as1 See Glaser and Weber (2005) for details about this questionnaire.
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Table 1 Cross-sectional distribution of percentage monthly gross portfolio returns All investors Mean Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum DAX (arithmetic monthly return) Number of households
Respondents to the questionnaire
0.54%
0.30%
−16.02% −5.83% −2.99% −1.90% −0.49% 0.57% 1.50% 2.75% 3.92% 7.80% 23.81%
−10.73% −8.15% −3.96% −2.11% −0.58% 0.53% 1.40% 2.52% 3.42% 6.06% 7.09%
2.02% 2793 (91% of 3079)
2.02% 195 (91% of 215)
sumptions do not bias the measurement of portfolio performance. The gross portfolio return Rht of investor h in month t is calculated as follows: Rht =
Sht i=1
wiht Rit
Pit niht with wiht = S , ht i=1 Pit niht
(1)
Rit is the return of stock i in month t , Sht is the number of type of stocks held by individual h in month t , Pit is the price of stock i at the beginning of month t , and niht is the number of stocks of company i held by investor h in month t . wiht is the beginning-of-month-t market value of the holding of stock i of investor h divided by the beginning-of-month-t market value of the whole stock portfolio of investor h. Table 1 shows the results for all investors and the subgroup of respondents to the questionnaire. The cross-sectional distribution of the monthly gross returns is similar to the results in Barber and Odean (2000, Table IV, p. 791). We observe a large cross-sectional variation in the performance across investors. When we exclude investors with stock positions in 12 or fewer months, we find gross returns between −16% and +24% per month. On average, investors underperform relevant benchmarks. For example, the arithmetic average monthly return of the German blue chip index DAX from January 1997 to March 2001 is 2.02% whereas the mean gross monthly return of investors in our data set is 0.54%. Furthermore, parametric and nonparametric tests show that the distribution of monthly returns is not significantly different in the two groups. Thus, there is no indication of a sample selection bias.2 3. Do investors know their past portfolio returns? In this section, we present survey evidence on investors’ ability to give an estimate of their own past realized stock portfolio performance. We asked the investors to give an estimate of their portfolio performance in the past (from January 1997 to December 2000): 2 Glaser and Weber (2007) show that this is also true for all other variables used later in the present paper.
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Table 2 Return estimates Number of observations Mean Standard deviation Skewness Kurtosis Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum
210 14.93% 13.11% 2.01 24.33 −50% −15% 0% 5% 10% 15% 20% 27% 35% 41% 120%
Please try to estimate your past performance of your stock portfolio at your online broker. Please estimate the return of your stock portfolio from January 1997 to December 2000: [Answer] percent per year on average. Table 2 presents the results. 210 of 215 investors who answered at least one question answered the question presented above. The investors think, on average, that their own realized stock portfolio performance from January 1997 to December 2000 was about 15% per year. There is a large variation in the answers to this questions. The answers range from −50% to +120%. Figure 1 plots the realized portfolio returns versus return estimates of the individual investors who answered the questionnaire (variables are winsorized at the 10% level). The correlation coefficient between return estimates and realized returns is −0.0471 (p = 0.5203). This complete lack of correlation might seem extremely surprising. But another study that uses a design similar to ours documents exactly the same findings. Owhoso and Weickgenannt (2007) investigate the extent to which auditors’ ratings of self-perceived abilities correspond with their actual performance, and whether these perceptions are influenced by audit experience and effectiveness when conducting audits within their domain of specialization. 144 industry-specialized audit seniors and managers reviewed two sets of audit working paper cases. At the end of the review, the auditors rated their ability to perform an audit in their domain. One result is that there is no significant positive correlation between auditors’ self-perceived abilities and actual performance. The difference between return estimates and realized returns is positive (mean and median are higher than 10% points per year, see also Table 3). The difference is highly significantly positive (p < 0.0001). This finding is consistent with Fig. 1 which shows that most dots lie below the 45◦ line. Thus, many investors believe that they made money although they did not. This finding is consistent with psychological evidence that people overstate past performance in a variety of tasks (see Dunning et al., 2004; Moore and Healy, 2007; and Owhoso and Weickgenannt, 2007). Why is there no correlation between realized portfolio returns and return estimates? One interpretation is that investors do not have a good understanding of the concept “return.” Another explanation is the way the online broker presents returns. Usually, the online broker presents gains and losses (with the buying price as the reference point) for every stock in the portfolio
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Fig. 1. Return estimates and realized returns. This figure plots return estimates versus realized portfolio returns of the individual investors who answered the questionnaire. Furthermore, the figure shows a 45◦ line. Variables are winsorized at the 10% level.
separately which makes it difficult to estimate the monthly or yearly stock portfolio performance. The broker also presents the total value of the portfolio, day-by-day. However, still, it is hard to calculate the performance of the portfolio when investors are continuously buying and selling stocks. When stocks are bought every month with additional money from, say, a cash account the stock portfolio value can increase although the average stock had negative returns. The information that should be relevant to judge own stock selection ability, the own past realized stock portfolio performance, is not calculated by the online broker. The results in this subsection are related to the experimental literature which shows that individuals in general are poor at recalling price changes when compared to recalling prices. Andreassen (1988) finds in an experiment that errors recalling price changes were significantly larger than those made in recalling prices. He argues that subjects pay greater attention to prices than to price changes. This result is in line with Glaser et al. (2007) who show that a group of students has bigger problems stating return forecasts for financial time series when compared to price forecasts. Table 3 also shows that experienced investors are better able to estimate their past realized stock portfolio performance. The difference between the perceived return and the actual return is significantly lower for investors with more than 5 years of investment experience.3 Furthermore, the percentage of investors who estimate at least the right sign of their past realized portfolio performance is higher for experienced investors. Moreover, more experienced investors are reasonably close with their estimates (see the lines in the table which show the number of investors 3 We use a cutoff of 5 years as this is the median level of experience so that we obtain two groups of approximately equal size.
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Table 3 Return estimates, self-assessments, and experience All investors Low investment High investment p-value (with experience experience experience (Mann–Whitney) variable available) (less than 5 years) (more than 5 years) (difference in experience groups) Absolute return difference
0.098*
Mean Median Observations Different from 0 (Wilcoxon)
20.96 17.84 142 p < 0.0001***
23.68 21.01 64 p < 0.0001***
18.73 16.71 78 p < 0.0001***
Correct sign Wrong sign
87 55
37 27
50 28
Percent correct
61.27%
57.81%
64.10%
Less than 5% points wrong
35
13
22
Less than 10% points wrong
48
18
30
Perceived return– actual return
Mean Median Observations Different from 0 (Wilcoxon)
11.61 13.85 142 p < 0.0001***
13.18 14.13 64 p < 0.0001***
10.32 12.41 78 p < 0.0001***
0.42
Absolute percentile difference
Mean Median Observations Different from 0 (Wilcoxon)
25.33 26.00 140 p < 0.0001***
25.31 23.00 62 p < 0.0001***
25.35 27.00 78 p < 0.0001***
0.99
Actual percentile– perceived percentile
Mean Median Observations Different from 0 (Wilcoxon)
4.44 4.00 140 0.0485**
5.61 3.50 62 0.103
3.50 4.00 78 0.2328
0.73
Notes. This table presents mean, median, the number of observations as well as the p-value of a Wilcoxon test (null hypothesis: value is equal to 0) of the absolute return difference, the difference between the perceived return and the perceived return, the absolute performance percentile difference and the difference between actual performance percentile and the actual performance percentile for all investors (with stock market investment experience variable available) and investors with low (less than 5 years) and high (more than 5 years) stock market investment experience. 5 years is the median experience level in our data set so that we obtain two groups of approximately equal size. See Sections 3 and 4 for details. Furthermore, the table shows the number of cases and the percentage of cases in which the sign of the past return assessment was correct. Moreover, the table shows the number of investors who are reasonably close with their estimates (see the lines which show the number of investors who are less than 5% points or 10% points wrong). Variables are winsorized at the 10% level. * Indicates significance at 10%. ** Indicates significance at 5%. *** Indicates significance at 1%.
who are less than 5% points or 10% points wrong). These findings might explain why the studies mentioned in the Introduction find that experienced investors make better decisions.
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These results are supported by Amromin and Sharpe (2006). They examine answers to the following question: “Thinking about a diversified portfolio of stocks, what would you guess was the average annual return earned over the past 10 years?” from the Michigan Survey of Consumer Attitudes, conducted by the Survey Research Center (SRC) at the University of Michigan. In particular, they calculate the absolute value of the recall error, i.e. the difference between recalled and actual 10-year market returns, and regress this difference on demographic and stock ownership characteristics. They find that the accuracy of a respondent’s recall of past returns improves with both wealth and education, as well as other indicators of financial market knowledge. To summarize, the main result of this section is that investors are hardly able to give a correct estimate of their own past realized stock portfolio performance and that experienced investors are better able to do so. 4. Self-rating and actual performance Furthermore, we asked the following question to analyze investors’ self-ratings and their relation with actual performance: What percentage of customers of your discount brokerage house had higher returns than you in the four-year period from January 1997 to December 2000? (Please give a number between 0% and 100%) [Answer] percent of other customers had higher returns than I did. Table 4 presents the results. The mean is 46.99 indicating a slight better than average effect. This number is significantly different from 50 (p = 0.0335, Wilcoxon signed-rank test).4 We are thus able to confirm prior literature on the better than average effect (Taylor and Brown, 1988; Svenson, 1981). One reason for the finding that this number is so close to 50 might be that about 30% of all investors classify themselves as average, i.e. state 50 as an answer.5 Figure 2 plots the self-ratings in percentiles versus actual return percentiles of the individual investors who answered the questionnaire. Such a graph is often used in the literature (see for example Ackerman et al., 2002). The figure shows that there is no relation between the selfratings in percentiles and actual return percentiles. The correlation between the self-ratings and actual percentiles is −0.0110 (p = 0.8810) which is not significantly distinguishable from zero. We are thus able to confirm prior research which shows that a correlation between self-ratings in percentiles and objective measures in percentiles is not existent (see Larrick et al., 2007 for further references and Dunning et al., 2004 for a recent survey). Furthermore, the difference between the actual return percentile of the respective investor and the self-assessed percentile is positive on average (this difference is positive if an investor thinks, for example, that only 25% of the other investors had higher portfolio returns in the past even though 30% of the investors in the sample actually had higher returns). Thus, investors overestimate their relative position in terms of return percentiles. 4 Note that in Table 3 the results are slightly different as we show results for the subgroup of respondents for which we have data on investment experience in that table. 5 Furthermore, recent studies show that the better than average effect is not as universal as was previously documented in the literature (see Moore, 2007; Moore and Cain, 2007; and Moore and Small, 2007). Thus, our small better than average effect is not a puzzle.
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Table 4 Self-ratings Number of observations
212
Mean Standard deviation Skewness Kurtosis
46.99 19.33 0.04 2.87
Minimum 1st percentile 5th percentile 10th percentile 25th percentile Median 75th percentile 90th percentile 95th percentile 99th percentile Maximum
2 5 15 20 30 50 60 70 80 90 95
Fig. 2. Self-ratings in percentiles and actual percentiles. This figure plots the self-ratings in percentiles versus actual percentiles of the individual investors who answered the questionnaire.
Moreover, high returns in the past do not lead to high overconfidence as measured by perceived percentile in our questionnaire at the end of the sample period. Thus, we do not find support for the learning-to-be-overconfident hypothesis (Gervais and Odean, 2001), i.e. a high degree of overconfidence as a result of past investment success. We argue, that one reason is, that investors do not know their past realized stock portfolio performance as was presented in the
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previous section.6 Note, however, that Gervais and Odean (2001) model the third of the manifestations of overconfidence mentioned in the Introduction while we are analyzing the first two facets in this paper. However, there is also a further interpretation of these findings. We find that the correlation between investors’ self-assessed absolute performance and their self-assessed relative performance is 0.2704 (with a p-value of 0.0002). Therefore, investors are somehow consistent in their answers. This raises the question “which” returns are actually relevant for overconfidence. It is possible that not the actual realized returns are relevant for the learning-to-be-overconfident hypothesis but the perceived realized returns. It is possible that investors “feel overconfident” even without knowing the true performance, by simply allowing their overblown beliefs of own realized portfolio returns to influence their view of returns relative to others. Thus, it is intriguing that actual returns are uncorrelated with the self-perceived ranking, but perceived returns are. To summarize, investors who believe they have done well in the absolute sense, also believe they have done better than others. Which returns are actually more relevant for overconfidence is a question for future research. 5. Which investors are able to correctly estimate their past realized portfolio performance? Table 5 presents cross-sectional regression results on the determinants of the absolute difference between return estimates and realized returns (Regressions (1) and (2)), the difference between return estimates and realized returns (Regressions (3) and (4)), the absolute difference between perceived and actual return percentile (Regressions (5) and (6)), and the difference between actual and perceived return percentile (Regressions (7) and (8)) as dependent variables and stock market investment experience, a gender dummy variable, age, a mutual fund investor dummy, a warrant trader dummy variable, a high risk dummy, the logarithm of mean monthly stock portfolio value, the time-series average of the monthly stock portfolio performance of an investor, the logarithm of the standard deviation of monthly stock portfolio performance as a measure of portfolio risk, and the logarithm of number of stocks in portfolio.7 Stock market investment experience, gender and the high risk dummy are based on a voluntary self-report made by investors at the time the respective account was opened. This information was not updated afterwards by the online broker. The dependent variables and the monthly stock portfolio performance are winsorized at the 10% level. The table reports standardized beta coefficients (except for the intercept). Robust p-values are in parentheses. Regression (1) shows that stock market investment experience has a significantly negative effect on the absolute difference between return estimates and realized returns at the 1% level. This finding can be interpreted in the way that investors learn how to better judge their own 6 These results do not contradict the studies of Statman et al. (2006) or Glaser and Weber (2008). These studies find that returns over the past 6 months positively influence trading activity which is consistent with the learning-tobe-overconfident hypothesis. Statman et al. (2006) find, however, that returns with lags larger than 6 do not influence trading volume anymore. In connection with the findings presented in this study, we can conclude that learning-to-beoverconfident stories are more appropriate for the effects of past returns over shorter horizons than the four year horizon which we analyze in the present study. 7 We use the natural logarithm of variables that are positively skewed. Tests show, that we thus avoid problems like nonnormality, nonlinearity, and heteroscedasticity in the cross-sectional regression analysis. See Spanos (1986, chapter 21, especially, pp. 455–456), Davidson and MacKinnon (1993, chapter 14), and Atkinson (1985, pp. 80–81).
Table 5 Determinants of the difference between return estimates and realized returns and between perceived and actual return percentile: cross-sectional regressions Absolute difference between return estimate and realized return
Mutual fund investor (Dummy) Warrant trader (Dummy) High risk investment strategy (based on self-report; dummy) ln(stock portfolio value) (in EUR; time-series average per investor) Stock portfolio performance (time-series average per investor) ln(portfolio risk) (standard deviation of monthly portfolio returns) ln(number of stocks in portfolio) (time-series average per investor) Constant Observations Adjusted R-squared
Absolute difference between perceived percentile and actual percentile
Difference between actual percentile and perceived percentile
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
−0.202 (0.010)*** −0.074 (0.523) −0.014 (0.854) −0.102 (0.197) −0.063 (0.434) 0.031 (0.717) 0.037 (0.771) −0.467 (0.000)*** 0.221 (0.063)* −0.151 (0.231) 55.606 (0.000)*** 121 0.325
−0.186 (0.029)** −0.056 (0.619) −0.060 (0.538) −0.034 (0.694) −0.029 (0.759) −0.054 (0.460) 0.062 (0.645)
−0.088 (0.051)* 0.011 (0.557) 0.038 (0.490) −0.0758 (0.076)* 0.031 (0.417) −0.036 (0.427) −0.025 (0.704) −0.919 (0.000)*** −0.048 (0.351) 0.012 (0.882) 14.800 (0.039)** 121 0.828
−0.057 (0.519) 0.047 (0.686) −0.051 (0.622) 0.058 (0.539) 0.099 (0.311) −0.201 (0.026)** 0.0241 (0.879)
−0.040 (0.646) −0.032 (0.722) −0.096 (0.403) −0.051 (0.579) 0.046 (0.647) 0.028 (0.780) −0.236 (0.136) −0.126 (0.232) −0.011 (0.918) 0.072 (0.628) 59.101 (0.000)*** 119 0.002
−0.036 (0.691) −0.028 (0.749) −0.107 (0.344) −0.033 (0.712) 0.057 (0.574) 0.005 (0.960) −0.226 (0.150)
−0.088 (0.179) 0.028 (0.225) 0.027 (0.737) −0.074 (0.196) −0.044 (0.447) 0.0158 (0.784) −0.018 (0.857) −0.813 (0.000)*** 0.057 (0.385) 0.146 (0.150) 14.235 (0.327) 119 0.629
−0.056 (0.543) 0.056 (0.596) −0.047 (0.637) 0.041 (0.676) 0.026 (0.785) −0.131 (0.189) 0.043 (0.800)
0.231 (0.044)** −0.175 (0.230) 52.042 (0.001)*** 121 0.110
−0.027 (0.839) −0.036 (0.825) 5.352 (0.820) 121 0.000
−0.008 (0.943) 0.065 (0.658) 57.772 (0.000)*** 119 0.000
0.079 (0.505) 0.100 (0.498) −0.679 (0.983) 119 0.000
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Notes. This table presents cross-sectional regression results on the determinants of the absolute difference between return estimates and realized returns (Regressions (1) and (2)), the difference between return estimates and realized returns (Regressions (3) and (4)), the absolute difference between perceived and actual return percentile (Regressions (5) and (6)), and the difference between actual and perceived return percentile (Regressions (7) and (8)) as dependent variables and stock market investment experience, a gender dummy variable (the variable is set equal to 1 if the investor is male), age, a mutual fund investor dummy (the variable is set equal to 1 if the investor trades funds at least once in the time period from January 1997 until April 2001), a warrant trader dummy variable (the variable is set equal to 1 if the investor trades warrants at least once in the time period from January 1997 until April 2001), a high risk dummy (the variable is set equal to 1 if the investor classifies her or his investment strategy as high risk), the logarithm of mean monthly stock portfolio value, the time-series average of the monthly stock portfolio performance of an investor, the logarithm of the standard deviation of monthly stock portfolio performance as a measure of portfolio risk, and the logarithm of number of stocks in portfolio. Investment experience is reported within five ranges, where the top range is more than 15 years. In the regressions we use the midpoint of each range and 17.5 years for the top range. The dependent variables and the monthly stock portfolio performance are winsorized at the 10% level. The table reports standardized beta coefficients (except for the intercept). Robust p-values are in parentheses. * Indicates significance at 10%. ** Indicates significance at 5%. *** Indicates significance at 1%.
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Stock market investment experience (in years) Gender (Dummy; men = 1) Age
Difference between return estimate and realized return
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past realized stock portfolio performance over time. Stock portfolio performance is also negatively related to the absolute difference between return estimates and realized returns. In other words, the lower the returns the worse investors are when judging their realized returns. There are several interpretations of this result. On the one hand, investors may look at their portfolio less often when returns are negative and, as a consequence, they do not know how bad they have actually performed. On the other hand, it is possible, that investors do not want to admit that they have performed pretty badly. This is consistent with psychological studies showing that people often neglect bad outcomes or unfavorable experience (see Dunning et al., 2004 for a survey). Karlsson et al. (2005), for example, present related evidence that investors check the value of their portfolios more frequently in rising markets but “put their heads in the sand” when markets are flat or falling. This finding is therefore sometimes called the “Ostrich Effect.” Furthermore, Table 2 shows that only less than 5% of our investors think they had negative returns in the past while more than 25% actually had negative returns in the past. Thus, somehow mechanically, investors with high past returns are closer to their self-assessment on average. This is why we re-run the regression without stock portfolio performance as explanatory variable (see Regression (2)). The results are similar. Stock market experience remains highly significantly negative at the 5% level.8 Furthermore, portfolio risk has a positive effect on the absolute difference between return estimates and realized returns. This result is intuitive. The higher the standard deviation of returns, the more difficult is it to calculate the past realized stock portfolio performance. All the other variables are not robustly related to the dependent variable. Regression (3) shows that experienced investors and mutual fund investors are less likely to overestimate their past realized portfolio performance. However, this effect is not significant in Regression (4) anymore. Regressions (5) to (8) present the determinants of the (absolute) difference between perceived and actual percentile. Compared to Regressions (1) to (4), the adjusted R-squared values are quite low. Furthermore, we do not find a robust influence of our explanatory variables on the (absolute) difference between perceived and actual percentile. To summarize, we find that experience helps in calculating the own past realized portfolio performance. This task should be mainly driven by skills that are enhanced by investment experience. In contrast, the other measures analyzed in Regressions (3) to (8) are closely related to the manifestations of overconfidence mentioned in the Introduction, especially overestimation of one’s actual performance and overplacement of one’s performance relative to others. The regression analysis in this part is exploratory in the spirit of Bhandari and Deaves (2006) who analyze the demographics of overconfidence. We had no ex ante hypothesis of the effect of expertise (and the other variables) on these overconfidence measures. Our analysis shows that our explanatory variables are not related to these overconfidence measures. In general, we can conclude that we find evidence that investor experience lessens the simple mathematical error of estimating portfolio returns, but seems not to influence their “behavioral” mistakes pertaining to how good (in absolute or relative sense) they are.
8 All results are similar when we use a winsorization at the 2% or 5% level. For example, when variables are winsorized at the 5% level, the beta coefficient for experience is −0.185 with a p-value of 0.018 in Regression (1) and −0.171 (p-value = 0.041) in Regression (2). When we use quantile regressions, the significance of the experience variable in Regression (1) is even stronger (p-value = 0.003). In Regression (2), the experience variable remains significant at the 10% level.
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6. Summary, discussion, and conclusion Based on the answers of 215 online broker investors to an Internet questionnaire we analyze whether investors are able to correctly estimate their own realized stock portfolio performance. Furthermore, we compare their perceived performance percentile with the actual performance percentile. Moreover, we analyze determinants of the cross-sectional heterogeneity in a regression analysis. The main findings can be summarized as follows. Investors are hardly able to give a correct estimate of their own past realized stock portfolio performance. Experienced investors are better able to do so. Furthermore, people overrate themselves. On average, investors think, that they are better than others. Moreover, the correlation between self ratings and actual performance is not distinguishable from zero. We find that investors do not have a good understanding of the concept “return.” This result is consistent with other studies. Parts of our results can be explained by psychological reasons (such as the negative influence of past portfolio performance on the absolute difference between return estimates and realized returns). However, this is only one part of the story. We also find that stock market investment experience has a positive influence on the quality of estimates of past realized stock portfolio returns. This is consistent with other studies that document a positive effect of financial education on behavior. As investors are increasingly encouraged or even forced to invest for their own retirement savings, a good understanding of returns is essential. Future research should further investigate why people have problems dealing with returns and how these problems can be mitigated. Acknowledgments We would like to thank an anonymous referee for helpful comments. This paper was in parts written while Markus Glaser was visiting the Swedish Institute for Financial Research (SIFR) in Stockholm whose support is gratefully acknowledged. Financial Support from the Deutsche Forschungsgemeinschaft (DFG) is also gratefully acknowledged. References Ackerman, P.L., Beier, M.E., Bowen, K.R., 2002. What we really know about our abilities and our knowledge. Personality and Individual Differences 33, 587–605. Amromin, G., Sharpe, S., 2006. From the horse’s mouth: Gauging conditional expected stock returns from investor surveys. Working paper, Federal Reserve Bank of Chicago. Andreassen, P.B., 1988. Explaining the price–volume relationship: The difference between price changes and changing prices. Organizational Behavior and Human Decision Processes 41, 371–389. Atkinson, A., 1985. Plots, Transformations, and Regression. Clarendon Press, Oxford. Barber, B.M., Odean, T., 2000. Trading is hazardous to your wealth: The common stock investment performance of individual investors. Journal of Finance 55, 773–806. Bhandari, G., Deaves, R., 2006. The demographics of overconfidence. Journal of Behavioral Finance 7, 5–11. Davidson, R., MacKinnon, J.G., 1993. Estimation and Inference in Econometrics. Oxford Univ. Press, Oxford. Dhar, R., Zhu, N., 2006. Up close and personal: Investor sophistication and the disposition effect. Management Science 52, 726–740. Dunning, D., Heath, C., Suls, J.M., 2004. Flawed self-assessment: Implications for health, education, and the workplace. Psychological Science in the Public Interest 5, 69–106. Feng, L., Seasholes, M.S., 2005. Do investor sophistication and trading experience eliminate behavioral biases in financial markets? Review of Finance 9, 305–351. Gervais, S., Odean, T., 2001. Learning to be overconfident. Review of Financial Studies 14, 1–27. Glaser, M., Weber, M., 2005. September 11 and stock return expectations of individual investors. Review of Finance 9, 243–279.
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