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Electronic copy available at: http://ssrn.com/abstract=1002092
Why Inexperienced Investors Do Not Learn:
They Do Not Know Their Past Portfolio Performance
Markus Glaser and Martin Weber∗
Final Version, Finance Research Letters 4(4), 203-216
Winner of the “Ross Best Paper Award” for
the best paper published in “Finance Research Letters” in 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 eliminatedby trading experience and learning. A necessary condition to learn is that investors actually knowwhat happened in the past and that the views of the past are not biased. We contribute to theabove mentioned literature by showing why learning and experience go hand in hand. Inexperiencedinvestors are not able to give a reasonable self-assessment of their own past realized stock portfolioperformance which impedes investors’ learning ability. Based on the answers of 215 online brokerinvestors to an internet questionnaire, we analyze whether investors are able to correctly estimatetheir own realized stock portfolio performance. We show that investors are hardly able to give a correctestimate of their own past realized stock portfolio performance and that experienced investors arebetter able to do so. In general, we can conclude that we find evidence that investor experiencelessens 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) theyare.
Keywords: Return Estimation, Portfolio Return, Perceived Returns, Self-Assessment, Better Than Aver-
age Effect, Overconfidence, Financial Education, Financial Literacy, Learning, Experience
JEL Classification Code: D8, G1
∗Markus Glaser is from the Lehrstuhl fur Bankbetriebslehre at the Business School, Universitat Mannheim, L 5, 2, 68131
Mannheim. E-Mail: [email protected]. Martin Weber is from the Lehrstuhl fur Bankbetriebslehre at the
Business School, Universitat Mannheim, L 5, 2, 68131 Mannheim and CEPR, London. E-Mail: [email protected]
mannheim.de. 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.
1
Electronic copy available at: http://ssrn.com/abstract=1002092
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, Shumway, and Stoffman (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 Knupfer (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, Peng, and Zhu (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 lit-
erature by showing why learning and experience go hand in hand. Inexperienced investors
2
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, Noth, and Weber (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
3
correlated (see Glaser and Weber (2007) and Moore and Healy (2007) and the references
cited therein). 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, Noth, and Weber (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 cor-
rect 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 dis-
tinguishable 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 per-
formance 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. In-
vestors 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
4
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 3,079 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 sev-
eral 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 ques-
tionnaire (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 follow-
ing simplifying assumptions: We assume that all stocks are bought and sold at the end of
1See Glaser and Weber (2005) for details about this questionnaire.
5
the month and we ignore intra-month trading. Barber and Odean (2000) show that these
simplifying assumptions 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
wihtRit with wiht =Pitniht
Sht∑i=1
Pitniht
(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 ques-
tionnaire. 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 po-
sitions 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 non-parametric 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
2Glaser and Weber (2007) show that this is also true for all other variables used later in the present paper.
6
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):
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 percent 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
7
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 percentage points per year, see also Table 3). The difference is highly
significantly positive (p < 0.0001). This finding is consistent with Figure 1 which shows
that most dots lie below the 45-degree 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, Heath, and Suls
(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 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.
8
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, Langer,
Reynders, and Weber (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 who are less than 5 percentage points or 10 percentage
points wrong). These findings might explain why the studies mentioned in the Introduction
find that experienced investors make better decisions.
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
3We use a cutoff of 5 years as this is the median level of experience so that we obtain two groups of approximately equal
size.
9
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 cor-
rect 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 about 30 % of all investors classify themselves as
4Note 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.
10
average, i.e. state 50 as an answer.5
Figure 2 plots the self-ratings in percentiles versus actual return percentiles of the individ-
ual investors who answered the questionnaire. Such a graph is often used in the literature
(see for example Ackerman, Beier, and Bowen (2002)). The figure shows that there is no
relation between the self-ratings in percentiles and actual return percentiles. The corre-
lation 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, Burson, and Soll (2007) for further references
and Dunning, Heath, and Suls (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.
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
5Furthermore, 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.
11
as was presented in the 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 correla-
tion 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 con-
sistent 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.
6These results do not contradict the studies of Statman, Thorley, and Vorkink (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-to-be-overconfident hypothesis. Statman, Thorley, and Vorkink (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-be-overconfident 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.
12
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 percent 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
percent level. This finding can be interpreted in the way that investors learn how to bet-
7We use the natural logarithm of variables that are positively skewed. Tests show, that we thus avoid problems like
non-normality, non-linearity, 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.
13
ter judge their own 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, Heath, and Suls (2004) for a survey).
Karlsson, Loewenstein, and Seppi (2005), for example, present related evidence that in-
vestors 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 percent
of our investors think they had negative returns in the past while more than 25 percent
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 Regres-
sion (2)). The results are similar. Stock market experience remains highly significantly
negative at the 5 percent level.8
Furthermore, portfolio risk has a positive effect on the absolute difference between return
8All results are similar when we use a winsorization at the 2 percent or 5 percent level. For example, when variables
are winsorized at the 5 percent 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
percent level.
14
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 overesti-
mate 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 per-
ceived 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 invest-
ment 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 perfor-
mance 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 over-
confidence 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.
15
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 psycholog-
ical 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 influ-
ence 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 in-
vestigate why people have problems dealing with returns and how these problems can be
mitigated.
16
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Owhoso, V., and A. Weickgenannt, 2007, “Auditors’ self-perceived abilities in conducting
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Statman, M., S. Thorley, and K. Vorkink, 2006, “Investor Overconfidence and Trading
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20
Table 1: Cross-Sectional Distribution of Percentage Monthly Gross Portfolio Returns
This table shows the cross-sectional distribution of the monthly gross returns of our investor sample (allinvestors and the subgroup of respondents to the questionnaire). Gross monthly portfolio performance ofeach investor was calculated making the following simplifying assumptions: We assume that all stocks arebought and sold at the end of the month and we ignore intra-month trading. The gross portfolio returnRht of investor h in month t is calculated as follows:
Rht =Sht∑
i=1
wihtRit with wiht =Pitniht
Sht∑i=1
Pitniht
Rit is the return of stock i in month t, Sht is the number of type of stocks held by individual h in montht, Pit is the price of stock i at the beginning of month t, and niht is the number of stocks of company iheld by investor h in month t. wiht is the beginning-of-month-t market value of the holding of stock i ofinvestor h divided by the beginning-of-month-t market value of the whole stock portfolio of investor h.Time period is January 1997 to March 2001. Investors with 12 or less portfolio return observations areexcluded from the sample. The table also shows the arithmetic monthly return of the German blue chipindex DAX from January 1997 to March 2001 and the number of investors with more than 12 portfolioreturn observations in our 51 month sample period. Parametric and non-parametric tests show that thedistribution of monthly returns is not significantly different in the two groups.
All Respondents toinvestors the questionnaire
Mean 0.54% 0.30%
Minimum −16.02% −10.73%1st percentile −5.83% −8.15%5th percentile −2.99% −3.96%10th percentile −1.90% −2.11%25th percentile −0.49% −0.58%Median 0.57% 0.53%75th percentile 1.50% 1.40%90th percentile 2.75% 2.52%95th percentile 3.92% 3.42%99th percentile 7.80% 6.06%Maximum 23.81% 7.09%
DAX (arithmetic monthly return) 2.02% 2.02%
Number of households 2,793 195(91% of 3,079) (91% of 215)
21
Table 2: Return Estimates
We asked the investors to give an estimate of their portfolio performance in the past (from January 1997to December 2000):
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.
This table presents the answers to this question (mean, median, standard deviation, skewness, kurtosis,minimum, maximum, and various percentiles).
Number of observations 210
Mean 14.93 %Standard deviation 13.11 %Skewness 2.01Kurtosis 24.33
Minimum −50 %1st percentile −15 %5th percentile 0 %10th percentile 5 %25th percentile 10 %Median 15 %75th percentile 20 %90th percentile 27 %95th percentile 35 %99th percentile 41 %Maximum 120 %
22
Table 3: Return Estimates, Self-Assessments, and Experience
This table presents mean, median, the number of observations as well as the p-value of a Wilcoxontest (null hypothesis: value is equal to 0) of the absolute return difference, the difference between theperceived return and the actual return, the absolute performance percentile difference and the differencebetween actual performance percentile and the perceived performance percentile for all investors (withstock market investment experience variable available) and investors with low (less than 5 years) andhigh (more than 5 years) stock market investment experience. 5 years is the median experience levelin our data set so that we obtain two groups of approximately equal size. See Sections 3 and 4 fordetails. Furthermore, the table shows the number of cases and the percentage of cases in which the signof the past return assessment was correct. Moreover, the table shows the number of investors who arereasonably close with their estimates (see the lines which show the number of investors who are less than5 percentage points or 10 percentage points wrong). Variables are winsorized at the 10 percent level. *indicates significance at 10%; ** indicates significance at 5%; *** indicates significance at 1%.
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 inexperience groups)
Absolute return Mean 20.96 23.68 18.73 0.098*difference Median 17.84 21.01 16.71
Observations 142 64 78Different from 0 p < 0.0001*** p < 0.0001*** p < 0.0001***(Wilcoxon)
Correct sign 87 37 50Wrong sign 55 27 28
Percent correct 61.27% 57.81% 64.10%
Less than 5 percentage 35 13 22points wrong
Less than 10 percentage 48 18 30points wrong
Perceived return Mean 11.61 13.18 10.32 0.42-actual return Median 13.85 14.13 12.41
Observations 142 64 78Different from 0 p < 0.0001*** p < 0.0001*** p < 0.0001***(Wilcoxon)
Absolute percentile Mean 25.33 25.31 25.35 0.99difference Median 26.00 23.00 27.00
Observations 140 62 78Different from 0 p < 0.0001*** p < 0.0001*** p < 0.0001***(Wilcoxon)
Actual percentile Mean 4.44 5.61 3.50 0.73-perceived percentile Median 4.00 3.50 4.00
Observations 140 62 78Different from 0 0.0485** 0.103 0.2328(Wilcoxon)
23
Table 4: Self-Ratings
We asked the investors to answer the following question:
What percentage of customers of your discount brokerage house had higher returns thanyou in the four-year period from January 1997 to December 2000? (Please give a numberbetween 0 % and 100 %)
[Answer] percent of other customers had higher returns than I did.
This table presents the answers to this question (mean, median, standard deviation, skewness, kurtosis,minimum, maximum, and various percentiles).
Number of observations 212
Mean 46.99Standard deviation 19.33Skewness 0.04Kurtosis 2.87
Minimum 21st percentile 55th percentile 1510th percentile 2025th percentile 30Median 5075th percentile 6090th percentile 7095th percentile 8099th percentile 90Maximum 95
24
Tab
le5:
Det
erm
inan
tsof
the
Diff
eren
ceB
etw
een
Ret
urn
Est
imat
esan
dR
ealize
dR
eturn
san
dB
etw
een
Per
ceiv
edan
dA
ctual
Ret
urn
Per
centi
le:C
ross
-Sec
tion
alR
egre
ssio
ns
This
table
pre
sents
cross
-sec
tionalre
gre
ssio
nre
sult
son
the
det
erm
inants
ofth
eabso
lute
diff
eren
cebet
wee
nre
turn
esti
mate
sand
realize
dre
turn
s(R
egre
ssio
ns
(1)and
(2))
,
the
diff
eren
cebet
wee
nre
turn
esti
mate
sand
realize
dre
turn
s(R
egre
ssio
ns
(3)
and
(4))
,th
eabso
lute
diff
eren
cebet
wee
nper
ceiv
edand
act
ualre
turn
per
centi
le(R
egre
ssio
ns
(5)
and
(6))
,and
the
diff
eren
cebet
wee
nact
ualand
per
ceiv
edre
turn
per
centi
le(R
egre
ssio
ns
(7)
and
(8))
as
dep
enden
tvari
able
sand
stock
mark
etin
ves
tmen
tex
per
ience
,a
gen
der
dum
my
vari
able
(the
vari
able
isse
teq
ualto
1if
the
inves
tor
ism
ale
),age,
am
utu
alfu
nd
inves
tor
dum
my
(the
vari
able
isse
teq
ualto
1if
the
inves
tor
trades
funds
at
least
once
inth
eti
me
per
iod
from
January
1997
unti
lA
pri
l2001),
aw
arr
ant
trader
dum
my
vari
able
(the
vari
able
isse
teq
ualto
1if
the
inves
tor
trades
warr
ants
at
least
once
inth
eti
me
per
iod
from
January
1997
unti
lA
pri
l2001),
ahig
hri
skdum
my
(the
vari
able
isse
teq
ualto
1if
the
inves
tor
class
ifies
her
or
his
inves
tmen
tst
rate
gy
as
hig
hri
sk),
the
logari
thm
of
mea
nm
onth
lyst
ock
port
folio
valu
e,th
eti
me-
seri
esaver
age
of
the
month
lyst
ock
port
folio
per
form
ance
of
an
inves
tor,
the
logari
thm
of
the
standard
dev
iati
on
ofm
onth
lyst
ock
port
folio
per
form
ance
as
am
easu
reofport
folio
risk
,and
the
logari
thm
ofnum
ber
ofst
ock
sin
port
folio.In
ves
tmen
tex
per
ience
isre
port
edw
ithin
five
ranges
,w
her
eth
eto
pra
nge
ism
ore
than
15
yea
rs.In
the
regre
ssio
ns
we
use
the
mid
poin
tof
each
range
and
17.5
yea
rsfo
rth
eto
pra
nge.
The
dep
enden
tvari
able
sand
the
month
lyst
ock
port
folio
per
form
ance
are
win
sori
zed
at
the
10
per
cent
level
.T
he
table
report
sst
andard
ized
bet
aco
effici
ents
(exce
pt
for
the
inte
rcep
t).R
obust
p-v
alu
esare
inpare
nth
eses
.*
indic
ate
ssi
gnifi
cance
at
10%
;**
indic
ate
ssi
gnifi
cance
at
5%
;***
indic
ate
ssi
gnifi
cance
at
1%
.
Abso
lute
diff
eren
ceD
iffer
ence
Abso
lute
diff
eren
ceD
iffer
ence
bet
wee
nbet
wee
nbet
wee
nbet
wee
nre
turn
esti
mate
and
retu
rnes
tim
ate
and
act
ualper
centi
leact
ualper
centi
lere
alize
dre
turn
realize
dre
turn
and
per
ceiv
edper
centi
leand
per
ceiv
edper
centi
le(1
)(2
)(3
)(4
)(5
)(6
)(7
)(8
)
Sto
ck
market
invest
ment
experie
nce
-0.2
02
-0.1
86
-0.0
88
-0.0
57
-0.0
40
-0.0
36
-0.0
88
-0.0
56
(in
yea
rs)
(0.0
10)*
**
(0.0
29)*
*(0
.051)*
(0.5
19)
(0.6
46)
(0.6
91)
(0.1
79)
(0.5
43)
Gender
-0.0
74
-0.0
56
0.0
11
0.0
47
-0.0
32
-0.0
28
0.0
28
0.0
56
(Dum
my;m
en=
1)
(0.5
23)
(0.6
19)
(0.5
57)
(0.6
86)
(0.7
22)
(0.7
49)
(0.2
25)
(0.5
96)
Age
-0.0
14
-0.0
60
0.0
38
-0.0
51
-0.0
96
-0.1
07
0.0
27
-0.0
47
(0.8
54)
(0.5
38)
(0.4
90)
(0.6
22)
(0.4
03)
(0.3
44)
(0.7
37)
(0.6
37)
Mutu
alfu
nd
invest
or
-0.1
02
-0.0
34
-0.0
758
0.0
58
-0.0
51
-0.0
33
-0.0
74
0.0
41
(Dum
my)
(0.1
97)
(0.6
94)
(0.0
76)*
(0.5
39)
(0.5
79)
(0.7
12)
(0.1
96)
(0.6
76)
Warrant
trader
-0.0
63
-0.0
29
0.0
31
0.0
99
0.0
46
0.0
57
-0.0
44
0.0
26
(Dum
my)
(0.4
34)
(0.7
59)
(0.4
17)
(0.3
11)
(0.6
47)
(0.5
74)
(0.4
47)
(0.7
85)
Hig
hris
kin
vest
ment
strate
gy
0.0
31
-0.0
54
-0.0
36
-0.2
01
0.0
28
0.0
05
0.0
158
-0.1
31
(base
don
self-r
eport
;dum
my)
(0.7
17)
(0.4
60)
(0.4
27)
(0.0
26)*
*(0
.780)
(0.9
60)
(0.7
84)
(0.1
89)
ln(s
tock
portf
olio
valu
e)
0.0
37
0.0
62
-0.0
25
0.0
241
-0.2
36
-0.2
26
-0.0
18
0.0
43
(in
EU
R;ti
me-
seri
esaver
age
per
inves
tor)
(0.7
71)
(0.6
45)
(0.7
04)
(0.8
79)
(0.1
36)
(0.1
50)
(0.8
57)
(0.8
00)
Sto
ck
portf
olio
perfo
rm
ance
-0.4
67
-0.9
19
-0.1
26
-0.8
13
(tim
e-se
ries
aver
age
per
inves
tor)
(0.0
00)*
**
(0.0
00)*
**
(0.2
32)
(0.0
00)*
**
ln(p
ortf
olio
ris
k)
0.2
21
0.2
31
-0.0
48
-0.0
27
-0.0
11
-0.0
08
0.0
57
0.0
79
(sta
ndard
dev
iati
on
ofm
onth
lyport
folio
retu
rns)
(0.0
63)*
(0.0
44)*
*(0
.351)
(0.8
39)
(0.9
18)
(0.9
43)
(0.3
85)
(0.5
05)
ln(n
um
ber
ofst
ocks
inportf
olio)
-0.1
51
-0.1
75
0.0
12
-0.0
36
0.0
72
0.0
65
0.1
46
0.1
00
(tim
e-se
ries
aver
age
per
inves
tor)
(0.2
31)
(0.2
30)
(0.8
82)
(0.8
25)
(0.6
28)
(0.6
58)
(0.1
50)
(0.4
98)
Const
ant
55.6
06
52.0
42
14.8
00
5.3
52
59.1
01
57.7
72
14.2
35
-0.6
79
(0.0
00)*
**
(0.0
01)*
**
(0.0
39)*
*(0
.820)
(0.0
00)*
**
(0.0
00)*
**
(0.3
27)
(0.9
83)
Obse
rvati
ons
121
121
121
121
119
119
119
119
Adju
sted
R-s
quared
0.3
25
0.1
10
0.8
28
0.0
00
0.0
02
0.0
00
0.6
29
0.0
00
25
Figure 1: Return Estimates and Realized Returns
This figure plots return estimates versus realized portfolio returns of the individual investors who answeredthe questionnaire. Furthermore, the figure shows a 45-degree line. Variables are winsorized at the 10percent level.
-30
-20
-10
0
10
20
30
40
0 5 10 15 20 25 30 35 40
Return estimates (% p.a.)
Realized
retu
rns (
% p
.a.)
26
Figure 2: Self-Ratings in Percentiles and Actual Percentiles
This figure plots the self-ratings in percentiles versus actual percentiles of the individual investors whoanswered the questionnaire.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Self-rating (past returns in percentiles)
Actu
al p
erc
en
tile
27
