Do individual investors learn from their mistakes?

Transcription

1 Do individual investors learn from their mistakes? Maximilian Koestner 1, Steffen Meyer 2, and Andreas Hackethal 3 This version: August 2, 2012 Abstract: Based on recent empirical evidence which suggests that as investors gain experience, their investment performance improves, we hypothesize that the specific mechanism through which experience translates to better investment returns is closely related to learning from investment mistakes. To test our hypotheses, we use an administrative dataset which covers the trading history of 19,487 individual investors. Our results show that underdiversification and the disposition effect do not decline as investors gain experience. However, we find that experience correlates with less portfolio turnover, suggesting that investors learn from overconfidence. We conclude that compared to other investment mistakes, it is relatively easy for individuals to identify and avoid costs related to excessive trading activity. When correlating experience with portfolio returns, we find that as investors gain experience, their portfolio returns improve. A comparison of returns before and after accounting for transaction costs reveals that this effect is indeed related to learning from overconfidence. JEL classification: D03, D14, G11 Keywords: Investor Learning, Investment Mistakes, Household Finance 1 Maximilian Koestner (koestner@fas.harvard.edu), Retail Banking Competence Center - Goethe University Frankfurt, House of Finance, Grüneburgplatz 1, Frankfurt am Main, Germany. Phone: Steffen Meyer (meyer@finance.uni-frankfurt.de), Retail Banking Competence Center - Goethe University Frankfurt, House of Finance, Grüneburgplatz 1, Frankfurt am Main, Germany. Phone: Andreas Hackethal (hackethal@gbs.uni-frankfurt.de), Chair of Finance, Goethe University Frankfurt, House of Finance, Grüneburgplatz 1, Frankfurt am Main, Germany. Phone: Electronic copy available at:

2 Do individual investors learn from their mistakes? This version: March 5, 2012 Abstract: Based on recent empirical evidence which suggests that as investors gain experience, their investment performance improves, we hypothesize that the specific mechanism through which experience translates to better investment returns is closely related to learning from investment mistakes. To test our hypotheses, we use an administrative dataset which covers the trading history of 19,487 individual investors. Our results show that underdiversification and the disposition effect do not decline as investors gain experience. However, we find that experience correlates with less portfolio turnover, suggesting that investors learn from overconfidence. We conclude that compared to other investment mistakes, it is relatively easy for individuals to identify and avoid costs related to excessive trading activity. When correlating experience with portfolio returns, we find that as investors gain experience, their portfolio returns improve. A comparison of returns before and after accounting for transaction costs reveals that this effect is indeed related to learning from overconfidence. JEL classification: D03, D14, G11 Keywords: Investor Learning, Investment Mistakes, Household Finance Electronic copy available at:

3 Introduction Since the formal beginnings of behavioral finance in the 1980s, numerous empirical studies have documented behavioral biases that lead to costly investment mistakes. In aggregate, investment mistakes result in significant underperformance of individual investors not just compared to institutional investors, but also compared to the overall market. Empirical studies suggest that the magnitude of negative abnormal returns ranges from 0.7% (French (2008)) to 3.7% per year (Barber and Odean (2000)). Barber et al. (2009) estimate that annual losses of Taiwanese individual investors aggregate to an amount equivalent to 2.2% of Taiwan s gross domestic product. While it is well documented that the average investor underperforms the market, there is also evidence that some individual investors persistently outperform their peers. Coval, Hirshleifer, and Shumway (2005) find that a few highly-skilled investors persistently generate abnormal returns. Barber and Odean (2000) present evidence that the excessive trading of overconfident investors leads to poor investment performance, while individual investors with a low portfolio turnover achieve returns close to the market. Dhar and Zhu (2006) document that the disposition effect, the tendency to sell winning stocks too quickly and hold on to stocks that have lost value, is weaker among individuals considered financially literate. If some individual investors persistently achieve better returns than their peers, then the question arises where this skill originates from. Recent studies by Nicolosi, Peng, and Zhu (2009) and Seru, Schumway, and Stoffman (2010) suggest that learning plays a significant role in explaining the heterogeneity in investment performance. They provide evidence that as investors gain experience, their investment performance improves. We hypothesize that the specific mechanism through which experience translates into better investment performance is closely related to learning from investment mistakes. Studies in consumer markets have documented a range of occasions when individuals learn from their mistakes, such as in the context of credit card add-on fees (Agarwal et al. (2008)) and penalty fees for late returns of rental videos (Fishman and Pope (2006)). If poor investment performance is caused by various investment mistakes and if investors achieve higher investment returns as they gain more experience, then we should find that individual investors are less prone to investment mistakes as they gain investment experience. To test our hypotheses, we use an administrative dataset which covers the complete trading history of 19,487 German retail investors over a period of eight years. Considering that we only look at investors who started trading during the observed period, the sample appears to be a reasonable representation of the average private investor in Germany. We exploit the dataset s panel structure to explore the relationship of three well documented investment mistakes underdiversification, overconfidence, and the disposition effect with investment experience. We opt for these investment mistakes not just because they rank among the most cited investment mistakes in finance literature, but also because a 1

4 significant negative effect on investment performance has been documented for each of the three investment mistakes (e.g., Goetzmann and Kumar (2008), Barber and Odean (2000), Odean (1998a)). The results show that underdiversification and the disposition effect do not decline as investors gain experience. Nevertheless, we find evidence that gains in experience are associated with less portfolio turnover, suggesting that investors learn from excessive trading which is associated with overconfidence. We find that a gain in experience equivalent to 100 additional trades is associated with a decline in monthly portfolio turnover of 0.8 percentage points, which is a considerable reduction considering that the average investor in the sample has an active portfolio turnover of 16.2% per month. Our findings are robust to the inclusion of various control variables in the regression specification, including investor and year fixed effects, measures for changes in the market environment and investment style, as well as various robustness checks using different subsamples. We conclude that compared to underdiversification and the disposition effect, it is relatively easy for individual investors to identify excessive trading activity, understand the nature and resulting costs of the mistake, and avoid it in the future. We are furthermore able to show that the findings of previous studies, which document that experience is related to higher short-term returns on purchased stocks as well as better trade quality, do translate into higher portfolio returns. When correlating investment experience with portfolio returns, we find strong evidence that experience leads to higher raw portfolio returns on an annual basis. The relationship of experience and risk-adjusted portfolio returns is also positive, but less clear cut. A comparison of portfolio returns before and after accounting for transaction costs reveals that the increase in portfolio returns we observe is indeed related to learning from overconfidence: When using returns including transaction costs, we document a strong correlation with investment experience. When using returns that ignore transaction costs, the relationship is considerably weaker. The remainder of the chapter is organized as follows. Section 2 discusses related literature and derives three testable hypotheses regarding investor learning. Section 3 summarizes the data used with a particular focus on the representativeness of the sample. Section 4 outlines the way we measure investment mistakes, portfolio returns, and investment experience. Additionally, the empirical model is discussed. Structured along three specific investment mistakes, Section 5 presents and elaborates the results. Section 6 presents several robustness checks and Section 7 summarizes our findings and concludes the chapter. 1. Related Literature and Hypotheses A growing body of literature documents behavioral biases that lead to costly investment mistakes among individual investors. Individual investors have been shown to systematically overreact to unexpected and dramatic news events (e.g., De Bondt and Thaler (1985)), to suffer from a status quo bias in financial decision making (e.g., Samuelson and Zeckhauser (1988)), to hold investment portfolios that are underdiversified (e.g., French and Poterba (1991), Grinblatt and Keloharju (2001a)), to 2

5 suffer from overconfidence ( e.g., Camerer and Lovallo (1999)) leading to excessive trading volume in financial markets (e.g., Odean (1999)), to neglect background risks (e.g., Heaton and Lucas (2000)) such as holding their employer s stock (e.g., Gerhardt (2008)), to engage in attention-based trading leading to herding behavior and investment decisions that are suboptimal (e.g., Kumar and Lee (2006)), and to suffer from disposition effects (e.g., Shefrin and Statman (1985)) that makes them hold losing investments too long and sell winning investments too early (e.g., Odean (1998a). 4 In light of the variety of circumstances when the actual investment decisions of individual investors diverge from what orthodox finance theory describes as choices that maximize welfare (Campbell (2006)), it is not surprising that empirical studies have shown that the average household investor underperforms the market. Using a large dataset provided by a US discount brokerage firm, Barber and Odean (2000) find that the average household underperforms the market by 1.1% annually. When using the Fama-French three factor model to estimate returns, this underperformance increases to 3.7% annually. Similarly, French (2008) concludes that a typical investor in the US could increase portfolio returns by 0.7% annually by holding the market portfolio. Barber et al. (2009) come to a similar conclusion using the trading history of all investors in Taiwan. They estimate that losses of individual investors aggregate to an amount equivalent to 2.2% of Taiwan s gross domestic product. While it is well documented that the average investor underperforms the market, there is also evidence that some individual investors persistently outperform their peers. Coval, Hirshleifer, and Shumway (2005) find strong persistence in the investment performance of individual investors. They conclude that few highly-skilled investors are able to systematically exploit market inefficiencies and thereby generate abnormal returns. Along the same line of research, Ivkovic, Sialm, and Weisbenner (2008), as well as Goetzmann and Kumar (2008) find that a small subset of individual investors deliberately underdiversifies and achieves abnormal returns because of superior stock-picking abilities. However, most investors persistently underdiversify, which results in significant economic costs. Barber and Odean (2000) present evidence that the excessive trading of overconfident investors leads to poor investment performance, while individual investors with a low portfolio turnover achieve returns close to the market. Dhar and Zhu (2006) document that the disposition effect is weaker for individuals considered financially literate. If some individual investors persistently make fewer investment mistakes than their peers, then the question arises where this skill originates from. Feng and Seasholes (2005) show in their empirical study that investor sophistication (defined as static differences across investors) alone cannot explain why some investors are suffering from disposition effects while others are not. However, investor sophistication combined with experience (defined as an individual investor s evolving behavior) together eliminates the reluctance to realize losses. List (2003) arrives at similar conclusions when studying the endowment effect in an experimental setting: Experience plays a significant role in elimi- 4 For a more comprehensive and detailed review and discussion of behavioral biases among investors, see, for example, Barberis and Thaler (2003) or Subrahmanyam (2007). 3

6 nating market anomalies. Similarly, Greenwood and Nagel (2009) find that inexperienced mutual fund managers are more likely to make investment mistakes. They document that compared to experienced managers, young managers show trendchasing behavior that lead to high losses during the dot-com bubble. Based on these findings, we hypothesize that at least some of the skill that differentiates individual investors who make investment mistakes from those that tend not to, is related to experience. That is, investors learn from their investment mistakes. The type of learning we have in mind is consistent with learning by doing. In his paper on the economic implications of learning by doing, Arrow (1962) points out that learning is the product of experience (p. 155). Building on the work of psychologists and economists, he argues that learning only happens through attempts to solve problems and therefore requires activity. Based on previous experience, individuals gain insights from the solution of problems that help them improve their future problem solving skills. The type of learning Arrow describes is in line with learning through Bayesian updating of posterior subjective beliefs (e.g., Kalai and Lehrer (1993)). Translated into the learning from mistakes that we expect to see among individual investors, our first hypothesis is: Hypothesis 1: As individual investors gain investment experience, they make fewer investment mistakes. Agarwal, Driscoll, Gabaix, and Laibson (2008) study the credit card market and find that individual households learn to avoid add-on fees related to late payment, over limit, and cash advance fees. They document that monthly fee payments are quite large immediately after the opening of the account, but then drop by 75% over the subsequent four years. Agarwal et al. conclude that learning from mistakes is driven by negative feedback: Paying fees teaches credit card holders to avoid triggering add-on fees in the future. Since the feedback mechanism is crucial for this kind of learning, it is questionable whether individuals will learn if they are not able to observe the outcomes of their decisions (e.g., Grossman, Kihlstrom, and Mirman (1977)). With reference to many investment mistakes, it may be difficult for the average investor to detect and avoid the given mistake because he or she is either not aware of its existence (e.g., background risks), is not able to measure and identify it (e.g., the disposition effect), or is not able to distinguish meaningful information from market noise (e.g., portfolio performance). We assume that the magnitude of learning relates to how easy it is for individual investors to detect and avoid an investment mistake. Our second hypothesis summarizes this argument: Hypothesis 2: Learning from investment mistakes is stronger for those investment mistakes that are easy to detect and avoid. If Hypothesis 1 holds, then the investment behavior of individual investors should converge with the predictions of orthodox finance theory as they gain experience. Thus, the gap between the portfolio and market returns should decrease as investors gain investment experience. And indeed, Seru, Schumway, and Stoffman (2010) provide evidence for a positive relationship between investment 4

7 experience and the returns earned by securities in the 30 trading days following a purchase. Similarly, Nicolosi, Peng, and Zhu (2009) find that trade quality (measured as average raw and excess buyminus-sell returns) increase as investors gain experience. As various studies have identified investment mistakes as a reason for reduced portfolio returns, we predict that an increase in investment experience leads to a reduction in investment mistakes, which in turn results in improved portfolio returns. This leads to our third hypothesis: Hypothesis 3: An increase in investment experience is associated with an increase in portfolio returns. 2. Data Description We base this study on an administrative dataset provided by a large German branchless direct bank. The data includes the complete trading history (roughly 7 million transactions) across all asset classes of 19,487 individual investors between January 2000 and December The dataset consists of a file containing investor socio-demographics (such as gender, age, profession, self-reported risk appetite, etc.), a position file containing security-level monthly portfolio positions, and a table listing all transactions in the sample period. Dorn and Hubermann (2005), who use a similar dataset, note that in 2000 the five largest direct banks in Germany had nearly 1.5 million retail customers, which is a sizeable market share considering that at that point in time only 6.2 million Germans owned stocks (Deutsches Aktieninstitut (2009)). The success of direct banks in Germany is not surprising, considering that they combine low fees with a wide product offering, ranging from discount brokerage to financial planning and insurance products, which attracts a wide spectrum of clients. Contrary to clients of German universal banks which tend to sell the products of their asset management divisions (Dorn and Hubermann (2005)), direct bank customers are able to choose from the entire universe of securities and are accordingly institutionally unbounded. The investors in the sample are individual (private) investors, which means the data does not include accounts held by corporations, professional investment managers, or investment clubs. The investors are self-directed, which implies that they did not opt for the investment advice or financial planning services offered by the bank. To place orders, they can either log onto the bank s website, send a fax or letter, or contact a call center agent. All investors opened their investment account during the observed time period, which means that we are able to observe their entire transaction history with the bank. Figure 1.1 summarizes how many investors per year entered and left the sample, as well as the number of investors trading per year. About 40% of the investors in the sample opened their account in the year 2000, while in each of the subsequent years roughly 10% started trading. The front loaded nature is not surprising when considering that overall stock market participation in Germany peaked in the year 2001 shortly after the height of the dot-com bubble. According to figures by the Deutsches 5 In this chapter we focus on 19,487 individual investors that opened their account during the observed time period, which is a subset of the overall dataset that includes 69,734 investors. 5

8 0-2, ,000 2,000 4,000 6,000 8,000 10,000 15,000 20,000 Aktieninstitut (2009), a German research association of listed companies and institutions, the number of Germans who own stocks or mutual funds increased from 5.6 million in 1997 to 12.9 million in 2001 and then dropped to 10.3 million in Table 1.1 presents summary statistics for the dataset. The socio-demographics in Panel A are self-reported by the investors at the point in time when they opened their account with the bank. The average age of the sample investors at account opening is 40.2 years, which is far Figure 1: Sample Characteristics The left part of Figure 1.1 presents the number of individual investors entering and exiting the sample per year. Entering is defined as the point in time when the investor opened the account with the bank and exiting is defined as the point in time when the investor closed his/her account. The right part of Figure 1.1 presents the number of investors who placed at least one trade in the given year. Transactions triggered by saving plans are excluded. Investors Entering and Exiting Investor Participation Investors entering sample Investors exiting sample below the average of the investor population (about 47 years) according to a representative survey conducted in the year 2000 on behalf of Deutsches Aktieninstitut (2009). The fact that the investors in the sample are considerably younger than the overall population leads us to the assumption that a large share of the sample investors had no or only limited investment experience before opening their investment account. This claim is further supported by a representative study conducted by the Federal Statistical Office of Germany (Statistisches Bundesamt (2004)), which in 2003 surveyed 74,600 households about their financial assets, real property, and debt. The results show that for households whose principal earner is between 25 and 45 years old (63.3% of the sample investors belong to this age bracket), financial assets account for about 25% of the average maximum lifetime financial assets. In other words, the investors in the sample tend to be at the beginning of their investment life cycle, and it is therefore more likely that we observe investment mistakes and subsequent learning from those mistakes. 6

9 With regard to other socio-demographic as well as investment portfolio characteristics, the sample investors are reasonably representative of the average German investor. 6 According to figures provided by Deutsches Aktieninstitut (2009), 18% of German shareholders had an annual income of more than EUR 80k in 2000, which is close to the 22% of sample investors who earned more than EUR 75k. Similarly, 24% of the German shareholder population earned less than EUR 35k in 2000, which is comparable to the 13% of the sample investors that had incomes of less than EUR 25k. When looking at gender, we find that the sample includes more males compared to the overall German shareholder population (83% vs. 63%). The difference could be related to the sample selection, as the sample excludes investors who receive financial advice, which tend to include a higher share of females (e.g., Kramer (2009), Bhattacharya et al. (2010)). According to figures provided by the Deutsche Bundesbank (2010) and Deutsches Aktieninstitut (2009), the average German investor owned equities and mutual funds worth EUR 53.7k in the year On average, the investors in the sample owned equities and mutual funds worth EUR 21.3k when they opened their investment account. However, the difference between the sample and the population is not surprising when considering the young age of the sample investors. It is important to note that despite the fact that the value of the investment portfolio is smaller than for the overall population, the portfolios nevertheless are equal to a significant fraction of annual income for most investors. 78% of investors state that they earn less than EUR 75k per year, which translates into a disposable income (after deducting taxes, social security contributions, and health insurance premiums) of less than EUR 48k. This is roughly equal to twice the size of the average investment portfolio of the sample investors. Accordingly, it is unlikely that the portfolios represent play money accounts. Overall, even though we observe differences between the sample and the overall investor population in Germany in terms of socio-demographics and portfolio characteristics, we are reasonably confident that the sample is fairly representative. The differences seem to be related to the particular group of investors we are looking at, namely self-directed investors who only recently started investing in financial products. 6 When comparing our sample with the German investor population, we focus on the year 2000, because this is when the largest fraction of investors appeared in the sample for the first time. 7

10 Table 1: Summary Statistics Table 1.1 presents summary statistics for socio-demographics (Panel A), portfolio and trading characteristics (Panel B), as well as asset allocation (Panel C) of the 19,487 investors in the sample. The socio-demographic data is taken from the account opening form submitted by the investor at account opening. The data on portfolio, trading, and asset allocation is measured over the first 12 months after the investor appeared in the sample. 25th 75th Mean Percentile Median Percentile Panel A: Socio-Demographics Age (at account opening) Gender (1 = male) Married (1 = yes) Risk appetite (1 = low to 6 = high) Income below 25k EUR p.a. (1 = yes) Income above 75k EUR p.a. (1 = yes) Panel B: Portfolio and Trading Characteristics Investment portfolio (in EUR) 24,264 5,756 13,650 28,977 Transaction volume per month (in EUR) 18, ,927 10,165 Average trade volume (in EUR) 3, ,009 3,758 Active trades per month Number of securities in portfolio Risky asset share (in % of portfolio) International securities (in % of portfolio) Stocks in portfolio (1 = yes) Mutual funds in portfolio (1 = yes) Savings plan customer (1 = yes) Portfolio returns (monthly average in %) Panel C: Asset Allocation Stock volume (in EUR) 15,494 1,027 6,319 17,966 Bond volume (in EUR) Mutual fund volume (in EUR) 5, ,118 Investment certificates (in EUR) 1, Other asset classes (in EUR) 1, Stock volume (in % of portfolio ) Bond volume (in % of portfolio ) Mutual fund volume (in % of portfolio ) Investment certificates (in % of portfolio ) Other asset classes (in % of portfolio ) Empirical Methodology 3.1. Measuring Investment Mistakes To test our hypotheses, we examine the relationship of investment experience and mistakes with regard to three investment mistakes: underdiversification, overconfidence, and the disposition effect. We focus on these investment mistakes for several reasons: First, they are well-documented by a number of empirical studies using different datasets and rank among the most cited investment mistakes in finance literature. Second, for each of the three investment mistakes a significant negative effect on investment performance has been documented (e.g., Goetzmann and Kumar (2008), Barber 8

11 and Odean (2000), Odean (1998a)). Third, they represent a wide spectrum of different investment mistakes, ranging from strategic and tactical asset allocation to suboptimal decisions related to investor psychology. To measure underdiversification, we adapt the approach outlined by Blume and Friend (1975) and approximate how closely an investor s portfolio resembles the market portfolio. To do so, we follow Goetzmann and Kumar (2008) and calculate the sum of squared investment portfolio weights. This approach originated from competition and antitrust laws as the Herfindahl-Hirschman Index (HHI) and is used to measure the size of an individual firm relative to a given industry. We calculate HHI based on the following formula: ( ) ( ) ( ) (1) For each point in time t, w it is the investment portfolio weight of security we and w mt is the weight of security we in the market portfolio, and N mt is the number of securities in the market portfolio. The idea behind the measure is that the number of securities in the market portfolio is very large and the corresponding weight of each individual security is very small. Hence, HHI t can be approximated by the sum of squared investment portfolio weights. HHI t will therefore be between one for an underdiversified portfolio with only one security and close to zero for well-diversified portfolios. Table 1.1 shows that 49% of the sample investors own at least one mutual fund, which typically consist of a large number of securities and are reasonably well-diversified. To account for this inherent diversification, we adapt the approach of Dorn and Hubermann (2005) and adjust HHI t by replacing mutual funds with a portfolio of 50 equal-weighted securities. We estimate HHI t for each investormonth observation using the position file containing security-level monthly portfolio positions. To generate investor-specific HHI t values per calendar year, we compute the (equal-weighted) average across all months the investor was active in a given calendar year. We consider an investor as active if he/she held at least one security in his/her portfolio. When we pool all investor-year observations, the mean HHI t value turns out to be and the median These values are close to the values reported by Dorn and Hubermann (2005) using a similar dataset. To measure overconfidence, we follow Barber and Odean (2000), who argue that overconfidence is closely related to excessive trading activity. Similar to Barber and Odean (2001), we approximate overconfidence by the monthly active portfolio turnover, which we calculate as one half the monthly active purchase turnover and one half the monthly active sales turnover. By active turnover we mean trades actively triggered by investors, which excludes transactions triggered by monthly saving plans. For each client and month, we compute the beginning-of-month value of the investment portfolio from the portfolio positions. The monthly active purchase turnover is then calculated by dividing the EUR volume of all purchases in the previous month by the portfolio value of the current month. The month- 9

12 ly active sales turnover is the EUR volume of all purchases in the current month divided by the current month s portfolio value. If in a given month more securities are sold than held at the beginning of that month, then we assume the entire position is sold. Similarly, if fewer securities are held at the beginning of a given month than purchased in the previous month, we assume that the entire position was purchased in the previous month. Accordingly, our measure for active portfolio turnover will not exceed 100% per month. This restriction, however, affects less than 0.5% of the investors in the sample. The following formula summarizes the approach of calculating the monthly active portfolio turnover (APT): ( ) ( ) (2) To calculate the active portfolio turnover per calendar year, we compute the (equal-weighted) average across all months per investor in a given calendar year. To avoid biases caused by investors who stopped trading but did not close their account, we only include the period between the first and last month the investor traded. However, since 83% of investors did not stop trading in the sample period, this convention is likely to affect only a small number of investors. When pooling all investors and years, the average active portfolio turnover is 13.7% per month and the median value is 4.6%. Those values are about twice the size that Barber and Odean (2001) report, who, however, used a dataset spanning from February 1991 to January Compared to our dataset, it did not include the dot-com bubble (which led to more trading activity 7 ) and the subsequent rapid decline in equity markets (and therefore average portfolio values), which are both related to higher portfolio turnover. To measure the disposition effect, we adopt the methodology proposed by Odean in 1998 and which has since then been used in various studies and is probably the most widely-used method for testing the disposition effect empirically. Instead of counting the number of gains and losses realized, which would be biased since stock prices tend to rise, Odean defines the disposition effect as the difference between the proportion of gains realized (PGR) and of losses realized (PLR). In this context, PGR represents an investor s willingness to sell winners (stocks that trade at above purchase price) and PLR represents the willingness to sell losers (stocks that trade at below purchase price). More specifically, Odean computes the following ratios: (3) (4) 7 Statman, Thorley, and Vorkink (2006) document that market-wide turnover is strongly positively related to lagged returns for many months. 10

13 For a given period t, a realized gain is counted when an investor sells a security at a price above the purchase price and a realized loss is counted when the investor sells a security at a price below the purchase price. For the securities that are not sold, a paper gain is recorded if the daily low is above the purchase price and a paper loss if the daily high is below the purchase price. No paper gain or loss is counted in case the purchase price lies between the daily high and low. On trading days where no securities are sold, no gains or losses are counted. To determine whether an investor suffers from the disposition effect (DE t ), we simply compare PGR t and PLR t : If PGR t >PLR t, then an investor is more likely to realize gains than losses, which is evidence for the disposition effect. Formally, we define (5) which indicates that if DE t is larger than 0, an investor suffers from the disposition effect. Higher DE t values are associated with stronger disposition effects. In the empirical analysis, we compute PGR t and PLR t per calendar year over the period 2000 to 2008, which means that per investor we have a maximum of eight separate DE t estimates. For 14,801 of the investors we are able to compute at least two DE t estimates; on average, we are able to calculate 4.4 DE t estimates. Like Odean (1998a), we find that PGR t is significantly larger than PLR t : Pooled across all calendar years and investors, the average PGR t is and the average PLR t is 0.185, resulting in an average DE t of Figure 1.2 illustrates the distribution of the three investment mistakes of interest in the form of histograms. 11

14 Figure 2: Distribution of Investment Mistakes Figure 1.2 illustrates the distribution of the Herfindahl-Hirschmann Index, Active Portfolio Turnover, and the Disposition Effect in the form of histograms. The vertical axis represents the fraction of the sample and the horizontal axis of the respective discrete intervals (bins). The data is pooled across all years and all sample investors. Herfindahl-Hirschmann-Index Active Portfolio Turnover Disposition Effect (PGR-PLR) Measuring Portfolio Returns To calculate portfolio returns, we opt for the Modified Dietz Method (MDM). Despite that the dataset only includes monthly portfolio positions as opposed to daily portfolio valuations, MDM allows us to calculate a reasonable close approximation to the time-weighted rate of return (e.g., Shestopaloff and Shestopaloff (2007)). We compute portfolio returns according to MDM per investor and month using the following formula: ( ) ( ) where (6) EMV t denotes the end-of-month value of the investment portfolio, BMV t is the beginning-of-month market value, and CF t are the net contributions in the given month t, which comprise contributions to portfolio, withdrawals, and transaction fees. CF it represent the individual contributions, withdrawals, or transaction fees and W it is a weight factor, which is calculated as the share of the total number of days in the month in which the contribution occurred. CD t is the total number of calendar days in the given month and D it denotes the day of the month on which the investor made the contribution. We compute monthly returns for each investor and then derive the average (equal weighted) monthly return per calendar year. 12

15 As portfolio returns calculated according to the Modified Dietz Method do not account for differences in investment risk, we furthermore use two alternative measures of portfolio performance: First, we adopt the approach outlined by Jensen (1968) to calculate abnormal returns, which is widely known as Jensen s Alpha. The measure captures the difference in returns realized by a given investment portfolio and a benchmark portfolio with the same systematic risk. We opt for a single factor over a multi factor model because recent studies (e.g., Carhart (1997) or Kosowski et al. (2006)) have shown that multi factor models offer no significant advantage over single factor models, i.e., the results remain the same. For each individual investor and calendar year, the model we use has the form: ( ) (7) where is the monthly MDM portfolio return, is the average monthly yield-to-maturity of German government bonds with one year to maturity 8 in month t, is the return in month t of the CDAX index, a stock market index consisting of all German companies listed in the General or Prime Standard of Frankfurt Stock Exchange, is the sensitivity of the investor s MDM portfolio returns to the market premium ( ), is the risk-adjusted return of the portfolio (Jensen s Alpha), and t is the error term. Figure 1.3 illustrates the distribution of MDM portfolio returns and Jensen s Alpha. Second, we use the Sharpe Ratio as defined by Sharpe (1994) to calculate risk-adjusted portfolio returns. The ratio measures the portfolio return achieved in excess of the risk free rate of return compared to the portfolio s riskiness as measured by the standard deviation of the differential return. We use the following formula to calculate the Share Ratio for each investor and calendar year: (8) Where is the MDM return of investment portfolio in month t, is the average monthly yield-tomaturity of German government bonds with one year to maturity in month t, and deviation of the differential return over the period of one year. is the standard 8 We use a remaining maturity of one year because this maturity is the closest to the average holding period of securities in the sample. 13

16 Figure 3: Distribution of Portfolio Returns The left part of Figure 1.3 presents the distribution of monthly MDM portfolio returns and the right part the distribution of Jensen s Alphas. The vertical axis represents the fraction of the sample and the horizontal axis the respective discrete intervals (bins). The curves displayed are normal density estimates with identical mean and standard deviation as the distributions of the return measure. The data is pooled across all years and sample investors. MDM Portfolio Returns Jensen's Alphas Measuring Investment Experience To measure investment experience, we build on existing literature and derive three separate measures that proxy investment experience. First, we follow Seru, Shumway, and Stoffman (2010) who argue along the lines of learning by doing. They bring forward the argument that when investors make investment decisions, they will gain experience by observing the results of their investment decisions. Accordingly, we define the first experience measure as the cumulative number of active trades since account opening. 9 Figure 1.4 reports the distribution of investment experience among the sample investors. Second, we follow the argumentation of Nicolosi, Peng, and Zhu (2009) and use the time since account opening as a proxy for experience. Nicolosi et al. argue that investors with longer account tenures have more opportunities to infer their forecasting ability. Accordingly, they proxy experience by the number of months since account opening. To avoid biases caused by investors who opened their account but then did not trade, as well as econometric issues related to the limited variability in the change of the explanatory variable (it will increase by one month for all investors every month), we opt for an adjusted measure. Instead of counting all months since account opening, we only count those months in which the investor placed at least one trade. Accordingly, the second experience measure is the cumulative number of months traded since account opening. Third, we adopt the approach taken by Feng and Seasholes (2005), who study the disposition effect and proxy experience by the number of positions an investor has taken since opening his/her account. 9 By active we mean trades that are actively triggered by the investor, which excludes saving scheme trades. 14

17 They define positions as round trip transactions, which may include several buy and/or sell transactions, therefore allowing positions to build up. We take a similar approach and count the cumulative number of securities traded since account opening. By number of securities we mean the number of different ISIN codes traded. Figure 4: Distribution of Experience Variables The figures on the left side represent the average cumulative number of trades, months traded, and securities traded per year after account opening. The figures on the right side illustrate the distribution of number of trades, months traded, and securities traded in the sample period across all investors. Cumulativ e No. of Trades Dis tribution of No. of Trades Years after Account Opening Trades in Sample Period Cumulativ e No. of Months Traded Dis tribution of No. of Ac tiv e Months Years after Account Opening Months Traded in Sample Period Cumulativ e No. of Sec urities Traded Dis tribution of No. of Sec urities Traded Years after Account Opening Securities Traded in Sample Period 3.4. Empirical Model To test the outlined hypotheses, we exploit the panel structure of the data and use a fixed effect regression model, which allows us to control for observed and unobserved time-invariant differences between individual investors. The model specification is motivated by previous studies of learning (e.g., Seru, Schumway, and Stoffman (2010)) and has the form: 15

18 (9) where the dependent variable y it+1 is either the investment mistake or portfolio return measure of interest for individual investor we in the year t+1. We use t+1 in order to estimate the influence of experience in a given year on the investment mistake or portfolio return in the following year. Experience it represents the investor and year specific measure of investment experience, Χ it is a vector of control variables to account for changes in the investor s investment style (e.g., risk appetite) or in the market environment, λ t is an unobserved year fixed effect to capture differences between years that affect all investors, α i is an unobserved individual investor effect, and ε it is a random error term potentially correlated within investor observations and possibly heteroskedastic (Petersen (2009)). The parameter of interest is β 1, which represents the influence of experience on investment mistakes or portfolio returns. Seasholes and Zhu (2010) note that cross-correlation might be a serious issue in studies on private investor behavior. We address this issue by including year and investor fixed effects into our models. Additionally, we use clustered standard error according to Rogers (1993) in the reported tables. 4. Results and Discussion Structured along the measures for investment mistakes and portfolio returns described in Section 1.4, this section presents our empirical results and discusses the findings Learning from Underdiversification Table 1.2 presents the estimation results with regard to learning from underdiversification for the sample of investor-year observations between 2000 and Specification (1) reveals that after removing both investor and year fixed effects, increases in experience as measured by the cumulative number of active trades are associated with decreases in diversification. Taking the estimates at face value shows that one hundred additional trades are related to an increase of the Herfindahl-Hirschman Index by 1.3 percentage points, which is a significant increase, considering the index scale from zero to one. Specification (2) incorporates additional explanatory variables that control for changes in the investor s portfolio (value of investment portfolio, equity share) and changes in the market environment (level of CDAX stock market index). However, this has no impact on the results. Specification (3) uses the cumulative number of months (actively) traded to measure experience, however, the results remain similar to specifications (1) and (2). One additional month of active trading experience is associated with a 0.3 percentage point increase of the Herfindahl-Hirschman Index, which is a statistically highly significant increase. Including additional control variables does not change the picture. In specifications (5) and (6), we use the cumulative number of (different) securities traded to proxy experience, but again we see a significant negative relationship with diversification. 16

19 Trading one additional security is related to an increase of the Herfindahl-Hirschman Index by 0.1 percentage points. Adding control variables to the regression does not change our findings. Table 2: Learning from Underdiversification Table 1.2 presents the results of fixed effects panel regressions where the dependent variable is the investor and year specific portfolio Herfindahl-Hirschman Index, on a scale from 0 to 1, with smaller numbers representing a more diversified portfolio. Investment experience is measured either by the Cumulative no. of active trades, the Cumulative no. of months traded, or the Cumulative no. of securities traded since account opening. All regressions include investor and year fixed effects. The sample consists of investor-year observations between 2000 and Robust t-statistics, clustered by investor, are reported in parentheses, and ***, **, and * denote significance at 1%, 5%, and 10%, respectively. Coefficient (1) (2) (3) (4) (5) (6) Cumulative no. of active trades ( 10 2 ) (3.97)*** (3.95)*** Herfindahl-Hirschman Index Cumulative no. of months traded (21.63)*** (21.71)*** Cumulative no. of securities traded (11.59)*** (11.59)*** Level of CDAX- index (in points) (19.36)*** (29.04)*** (24.22)*** Value of investment portfolio (in EUR) (-1.10) (-1.10) (-1.10) Equity share (in % of portfolio) (6.67)*** (6.66)*** (6.70)*** Intercept (109.62)*** (10.95)*** (116.40)*** (7.01)*** (115.80)*** (10.91)*** Investor fixed effects Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes Yes Yes Yes Yes Observations 112, , , , , ,724 Unique investors 19,477 19,477 19,477 19,477 19,477 19,477 Adjusted R² Despite the considerable benefits of diversification (e.g., Goetzmann and Kumar (2008)), individual investors apparently do not learn from underdiversification as they gain investment experience. Hirshleifer (2010) provides a possible explanation for this behavior. In his model, social interactions are the reason why investors choose to invest actively and thus frequently lose. To maintain their personal reputation, investors prefer to talk to peers about successful rather than poor investments. As picking few (preferably high idiosyncratic volatility) stocks is more likely to result in noteworthy investment victories than replicating the market portfolio, investors will opt for an active investment approach resulting in underdiversified portfolios. Hirshleifer concludes that active stock picking strategies will spread across the population unless sufficiently low mean returns offset the perceived benefits Learning from Overconfidence Table 1.3 presents the results of regressions with the active portfolio turnover as the dependent variable, which we use to proxy overconfidence. In specification (1) we use the cumulative number of trades to proxy experience. The estimation results show a significant negative relationship between 17

20 experience and overconfidence. One hundred additional trades are associated with a drop in (monthly) active portfolio turnover by 0.8 percentage points, which is a significant reduction considering that the average investor in the sample has an active portfolio turnover of 16.2% per month. Adding control variables for changes in the investor portfolio or market environment (specification (2)) does not lead to significant changes. Table 3: Learning from Overconfidence Table 1.3 presents the results of fixed effects panel regressions where the dependent variable is the investor and year specific portfolio Active Portfolio Turnover, on a scale from 0 to 1, with smaller numbers representing less trading activity. Investment experience is measured either by the Cumulative no. of active trades, the Cumulative no. of months traded, or the Cumulative no. of securities traded since account opening. All regressions include investor and year fixed effects. The sample consists of investor-year observations between 2000 and Robust t-statistics, clustered by investor, are reported in parentheses, and ***, **, and * denote significance at 1%, 5%, and 10%, respectively. Coefficient (1) (2) (3) (4) (5) (6) Cumulative no. of active trades ( 10 2 ) (-5.87)*** (-5.84)*** Active Portfolio Turnover Cumulative no. of months traded (-13.53)*** (-13.55)*** Cumulative no. of securities traded (-4.10)*** (-3.96)*** Level of CDAX- index (in points) (32.04)*** (26.85)*** (34.56)*** Value of investment portfolio (in EUR) (0.99) (1.02) (0.95) Equity share (in % of portfolio) (-2.71)*** (-2.69)*** (-2.80)*** Number of securities in portfolio (-4.52)*** (-4.18)*** (-3.76)*** Intercept (115.43)*** (12.41)*** (119.93)*** (15.40)*** (118.15)*** (11.81)*** Investor fixed effects Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes Yes Yes Yes Yes Observations 108, , , , , ,335 Unique investors 19,463 19,463 19,463 19,463 19,463 19,463 Adjusted R² In specifications (3) and (4) we use the cumulative number of months traded to measure investment experience. Again, we find a significant negative relationship between the measure of experience and active portfolio turnover, indicating that investors learn from this mistake as they gain experience. Specifications (5) and (6) present the results of regressions using the cumulative number of securities traded as an experience measure. Similar to the two previous measures for experience, we find a very 18