2012.08.do individual investors learn from their mistakespdf

7/27/2019 2012.08.Do Individual Investors Learn From Their Mistakespdf

1/35Electronic copy available at: http://ssrn.com/abstract=2122652

Do individual investors learn from their mistakes?

Maximilian Koestner1, Steffen Meyer2, and Andreas Hackethal3

This version: August 2, 2012

Abstract:Based on recent empirical evidence which suggests that as investors gain experience, their investment perfor-mance improves, we hypothesize that the specific mechanism through which experience translates to betterinvestment returns is closely related to learning from investment mistakes. To test our hypotheses, we use anadministrative dataset which covers the trading history of 19,487 individual investors. Our results show thatunderdiversification and the disposition effect do not decline as investors gain experience. However, we find thatexperience correlates with less portfolio turnover, suggesting that investors learn from overconfidence. Weconclude that compared to other investment mistakes, it is relatively easy for individuals to identify and avoidcosts related to excessive trading activity. When correlating experience with portfolio returns, we find that asinvestors gain experience, their portfolio returns improve. A comparison of returns before and after accountingfor 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

1Maximilian Koestner ([email protected]), Retail Banking Competence Center - Goethe UniversityFrankfurt, House of Finance, Grneburgplatz 1, 60323 Frankfurt am Main, Germany. Phone: + 49 69 79833675

2Steffen Meyer ([email protected]), Retail Banking Competence Center - Goethe University

Frankfurt, House of Finance, Grneburgplatz 1, 60323 Frankfurt am Main, Germany. Phone: + 49 69 79833675

3Andreas Hackethal ([email protected]), Chair of Finance, Goethe University Frankfurt, House ofFinance, Grneburgplatz 1, 60323 Frankfurt am Main, Germany. Phone: + 49 69 798 33700
mailto:[email protected]:[email protected]:[email protected]:[email protected]


2/35Electronic copy available at: http://ssrn.com/abstract=2122652

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 perfor-mance improves, we hypothesize that the specific mechanism through which experience translates to betterinvestment returns is closely related to learning from investment mistakes. To test our hypotheses, we use anadministrative dataset which covers the trading history of 19,487 individual investors. Our results show thatunderdiversification and the disposition effect do not decline as investors gain experience. However, we find thatexperience correlates with less portfolio turnover, suggesting that investors learn from overconfidence. Weconclude that compared to other investment mistakes, it is relatively easy for individuals to identify and avoidcosts related to excessive trading activity. When correlating experience with portfolio returns, we find that asinvestors gain experience, their portfolio returns improve. A comparison of returns before and after accountingfor 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


3/35

1

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 mis-

takes 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 Taiwans 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 andOdean (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, Schum-

way, 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 trans-

lates 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 datasets panel structure to explore the

relationship of three well documented investment mistakesunderdiversification, overconfidence, and

the disposition effect with investment experience. We opt for these investment mistakes not justbecause they rank among the most cited investment mistakes in finance literature, but also because a


4/35

2

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 overconfi-

dence. We find that a gain in experience equivalent to 100 additional trades is associated with a de-

cline in monthly portfolio turnover of 0.8 percentage points, which is a considerable reduction consid-

ering 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, includ-

ing 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 identifyexcessive 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 relation-

ship 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 portfo-

lio 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 in-

vestment 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 HypothesesA 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 portfo-

lios that are underdiversified (e.g., French and Poterba (1991), Grinblatt and Keloharju (2001a)), to


5/35

3

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 employers 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 con-

clusion 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 Taiwans 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 investors 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 inves-

tors, see, for example, Barberis and Thaler (2003) or Subrahmanyam (2007).


6/35

4

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 indi-

vidual 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 eco-

nomic 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 throughBayesianupdatingof 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 disposi-

tion 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 inves-

tors 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 portfolioand market returns should decrease as investors gain investment experience. And indeed, Seru,

Schumway, and Stoffman (2010) provide evidence for a positive relationship between investment


7/35

5

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 buy-

minus-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 DescriptionWe 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 classesof 19,487 individual investors between January 2000 and December 2007.5 The dataset consists of a

file containing investor socio-demographics (such as gender, age, profession, self-reported risk appe-

tite, 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, consider-

ing 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 banks website, send a fax

or letter, or contact a call center agent. All investors opened their investment account during the ob-

served 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 ob-served time period, which is a subset of the overall dataset that includes 69,734 investors.


8/35

6

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 2007. 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 isdefined as the point in time when the investor opened the account with the bank and exiting is defined as the point in timewhen the investor closed his/her account. The right part of Figure 1.1 presents the number of investors who placed at leastone trade in the given year. Transactions triggered by saving plans are excluded.

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 in-

vestment 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.

0

2000 2001 2002 2003 2004 2005 2006 2007

Investors Entering and Exiting

Investors entering sampleInvestors exiting sample

0

5,0

00

10,0

00

15,0

00

20

,000

2000 2001 2002 2003 2004 2005 2006 2007

Investor Participation


9/35

7

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 provid-

ed 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 year2000. 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 popu-

lation, the portfolios nevertheless are equal to a significant fraction of annual income for most inves-

tors. 78% of investors state that they earn less than EUR 75k per year, which translates into a disposa-

ble 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 sam-ple 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.


10/35

8

Table 1: Summary Statistics

Table 1.1 presents summary statistics for socio-demographics (Panel A), portfolio and trading characteristics (Panel B), aswell as asset allocation (Panel C) of the 19,487 investors in the sample. The socio-demographic data is taken from theaccount opening form submitted by the investor at account opening. The data on portfolio, trading, and asset allocation ismeasured over the first 12 months after the investor appeared in the sample.

3. Empirical Methodology3.1. Measuring Investment MistakesTo 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 mis-takes 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

25th 75thMean Percentile Median Percentile

Age (at account opening) 40.2 32.0 38.0 48.0

Gender (1 = male) 0.83 1.00 1.00 1.00

Married (1 = yes) 0.56 0.00 1.00 1.00

Risk appetite (1 = low to 6 = high) 4.51 4.00 5.00 6.00

Income below 25k EUR p.a. (1 = yes) 0.13 0.00 0.00 0.00

Income above 75k EUR p.a. (1 = yes) 0.22 0.00 0.00 0.00

Investment portfolio (in EUR) 24,264 5,756 13,650 28,977

Transaction volume per month (in EUR) 18,842 910 2,927 10,165

Average trade volume (in EUR) 3,332 976 2,009 3,758

Active trades per month 4.22 0.33 1.17 4.00

Number of securities in portfolio 6.71 2.75 5.00 8.75

Risky asset share (in % of portfolio) 0.92 0.96 1.00 1.00

International securities (in % of portfolio) 0.43 0.14 0.40 0.68

Stocks in portfolio (1 = yes) 0.82 1.00 1.00 1.00

Mutual funds in portfolio (1 = yes) 0.49 0.00 0.00 1.00

Savings plan customer (1 = yes) 0.14 0.00 0.00 0.00

Portfolio returns (monthly average in %) -0.029 -0.051 -0.014 0.006

Stock volume (in EUR) 15,494 1,027 6,319 17,966

Bond volume (in EUR) 667 0 0 0

Mutual fund volume (in EUR) 5,762 0 0 6,118

Investment certificates (in EUR) 1,163 0 0 0

Other asset classes (in EUR) 1,179 0 0 119

Stock volume (in % of portfolio ) 0.62 0.17 0.79 1.00

Bond volume (in % of portfolio ) 0.02 0.00 0.00 0.00

Mutual fund volume (in % of portfolio ) 0.27 0.00 0.00 0.51

Investment certificates (in % of portfolio ) 0.03 0.00 0.00 0.00

Other asset classes (in % of portfolio ) 0.07 0.00 0.00 0.01

Panel A: Socio-Demographics

Panel B: Portfolio and Trading Characteristics

Panel C: Asset Allocation


11/35

9

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 inves-

tor psychology.

To measure underdiversification, we adapt the approach outlined by Blume and Friend (1975) and

approximate how closely an investors 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, wit is the investment portfolio weight of security we and wmt is the weight of

security we in the market portfolio, and Nmtis 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, HHIt can be approximated by

the sum of squared investment portfolio weights.HHIt will therefore be between one for an underdi-

versified 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 con-sist 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 adjustHHIt by replacing

mutual funds with a portfolio of 50 equal-weighted securities. We estimateHHIt for each investor-

month observation using the position file containing security-level monthly portfolio positions. To

generate investor-specificHHIt values per calendar year, we compute the (equal-weighted) average

across all months the investor was active in a given calendar year. We consideran investor as active

if he/she held at least one security in his/her portfolio. When we pool all investor-year observations,

the meanHHItvalue turns out to be 0.267 and the median 0.159. 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 turnoverand one half the monthly active sales turnover. By active turnoverwe 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-


12/35

10

ly active sales turnover is the EUR volume of all purchases in the current month divided by the current

months 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 begin-

ning 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 sam-

ple. The following formula summarizes the approach of calculating the monthly active portfolio turn-

over (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 1997. Compared to our dataset, it did not include the dot-com

bubble (which led to more trading activity7) 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 investors 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 positivelyrelated to lagged returns for many months.


13/35

11

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 (DEt), we simply compare PGRt and PLRt: IfPGRt>PLRt, 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 ifDEt is larger than 0, an investor suffers from the disposition effect. HigherDEt

values are associated with stronger disposition effects.

In the empirical analysis, we computePGRt andPLRt per calendar year over the period 2000 to 2008,

which means that per investor we have a maximum of eight separateDEt estimates. For 14,801 of the

investors we are able to compute at least twoDEt estimates; on average, we are able to calculate 4.4

DEtestimates. Like Odean (1998a), we find thatPGRtis significantly larger thanPLRt: Pooled across

all calendar years and investors, the averagePGRtis 0.324 and the averagePLRtis 0.185, resulting in

an average DEt of 0.139. Figure 1.2 illustrates the distribution of the three investment mistakes of

interest in the form of histograms.


14/35

12

Figure 2: Distribution of Investment Mistakes

Figure 1.2 illustrates the distribution of the Herfindahl-Hirschmann Index, Active Portfolio Turnover, and the DispositionEffect in the form of histograms. The vertical axis represents the fraction of the sample and the horizontal axis of the respec-tive discrete intervals (bins). The data is pooled across all years and all sample investors.

3.2. Measuring Portfolio ReturnsTo 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)

EMVt denotes the end-of-month value of the investment portfolio,BMVt is the beginning-of-month

market value, and CFt are the net contributions in the given month t, which comprise contributions to

portfolio, withdrawals, and transaction fees. CFitrepresent the individual contributions, withdrawals,

or transaction fees and Wit is a weight factor, which is calculated as the share of the total number of

days in the month in which the contribution occurred. CDtis the total number of calendar days in the

given month and Dit 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.

0

.05

.1

.15

.2

0 .2 .4 .6 .8 1

Herfindahl-Hirschmann-Index

0

.1

.2

.3

.4

0 .2 .4 .6 .8 1

Active Portfolio Turnover

0

.02

.04

.06

.08

.1

-1 -.5 0 .5 1

Disposition Effect (PGR-PLR)


15/35

13

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

Jensens 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 Ger-man government bonds with one year to maturity8 in month t, is the return in month t of theCDAX 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 investors MDM portfolio returns to

the market premium ( ),is the risk-adjusted return of theportfolio (Jensens Alpha), and tisthe error term. Figure 1.3 illustrates the distribution of MDM portfolio returns and Jensens 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 com-

pared to the portfolios 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-to-maturity of German government bonds with one year to maturity in month t, and

is the standard

deviation of the differential return over the period of one year.

8 We use a remaining maturity of one year because this maturity is the closest to the average holdingperiod of securities in the sample.


16/35

14

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

Jensens Alphas. The vertical axis represents the fraction of the sample and the horizontal axis the respective discrete inte r-vals (bins). The curves displayed are normal density estimates with identical mean and standard deviation as the distributionsof the return measure. The data is pooled across all years and sample investors.

3.3. Measuring Investment ExperienceTo 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 makeinvestment 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 ac-

count opening as a proxy for experience. Nicolosi et al. argue that investors with longer account ten-

ures 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 schemetrades.

0

.05

.1

.15

.2

-.2 -.1 0 .1 .2

MDM Portfolio Returns

0

.1

.2

.3

-.2 -.1 0 .1 .2

Jensen's A lphas


17/35

15

They define positions as round trip transactions, which may include several buy and/or sell transac-

tions, 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 yearafter account opening. The figures on the right side illustrate the distribution of number of trades, months traded, and securi-ties traded in the sample period across all investors.

3.4. Empirical ModelTo test the outlined hypotheses, we exploit the panel structure of the data and use a fixed effect regres-

sion model, which allows us to control for observed and unobserved time-invariant differences be-

tween individual investors. The model specification is motivated by previous studies of learning (e.g.,

Seru, Schumway, and Stoffman (2010)) and has the form:

0

1

00

200

300

0 1 2 3 4 5 6 7 8

Years after Acc ount Opening

Cumulative No. of Trades

0

.05

.1

.15

.2

.25

0 200 400 600 800 1000

Trades in Sample Per iod

Distribution of No. of Trades

0

10

20

30

40

0 1 2 3 4 5 6 7 8


Cumulative N o. of Months Traded

0

.02

.04

.06

.08

0 20 40 60 80 100

Months Traded in Sample Period

Distribution of No. of Active Months

0

20

40

60

80

0 1 2 3 4 5 6 7 8


Cumulative No. of Securities Traded

0

.05

.1

.15

0 50 100 150 200 250

Securities Traded in Sample Per iod

Distribution of No. of Secur ities Traded


18/35

16

(9)

where the dependent variable yit+1 is either the investment mistake or portfolio return measure of

interest for individual investorwe in the yeart+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.Experi-

enceit represents the investor and year specific measure of investment experience,it is a vector of

control variables to account for changes in the investors investment style (e.g., risk appetite) or in the

market environment, tis an unobserved year fixed effect to capture differences between years that

affect all investors, iis an unobserved individual investor effect, and it is a random error term poten-

tially correlated within investor observations and possibly heteroskedastic (Petersen (2009)). The

parameter of interest is 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 DiscussionStructured along the measures for investment mistakes and portfolio returns described in Section 1.4,

this section presents our empirical results and discusses the findings.

4.1. Learning from UnderdiversificationTable 1.2 presents the estimation results with regard to learning from underdiversification for the

sample of investor-year observations between 2000 and 2007. 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

investors portfolio (value of investment portfolio, equity share) and changes in the market environ-

ment (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 trad-

ing 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.


19/35

17

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

portfolioHerfindahl-Hirschman Index, on a scale from 0 to 1, with smaller numbers representing a more diversified portfo-lio. Investment experience is measured either by the Cumulative no. of active trades, the Cumulative no. of months traded, orthe Cumulative no. of securities traded since account opening. All regressions include investor and year fixed effects. Thesample consists of investor-year observations between 2000 and 2007. Robust t-statistics, clustered by investor, are reportedin parentheses, and ***, **, and * denote significance at 1%, 5%, and 10%, respectively.

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. Hirsh-

leifer (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 personalreputation, 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.

4.2. Learning from OverconfidenceTable 1.3 presents the results of regressions with the active portfolio turnover as the dependent varia-ble, 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

Coefficient (1) (2) (3) (4) (5) (6)

Cumulative no. of active trades (10 2) 0.013 0.013

(3.97)*** (3.95)***

Cumulative no. of months traded 0.003 0.003

(21.63)*** (21.71)***

Cumulative no. of securities traded 0.001 0.001(11.59)*** (11.59)***

Level of CDAX- index (in points) 0.000 0.000 0.000

(19.36)*** (29.04)*** (24.22)***

Value of investment portfolio (in EUR) 0.000 0.000 0.000

(-1.10) (-1.10) (-1.10)

Equity share (in % of portfolio) 0.065 0.065 0.066

(6.67)*** (6.66)*** (6.70)***

Intercept 0.346 0.121 0.361 0.075 0.347 0.116

(109.62)*** (10.95)*** (116.40)*** (7.01)*** (115.80)*** (10.91)***

Investor fixed effects Yes Yes Yes Yes Yes YesYear fixed effects Yes Yes Yes Yes Yes Yes

Observations 112,724 112,724 112,724 112,724 112,724 112,724

Unique investors 19,477 19,477 19,477 19,477 19,477 19,477

Adjusted R 0.654 0.656 0.654 0.657 0.652 0.655

Herfindahl-Hirschman Index


20/35

18

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 specificportfolio Active Portfolio Turnover, on a scale from 0 to 1, with smaller numbers representing less trading activity. Invest-ment experience is measured either by the Cumulative no. of active trades, the Cumulative no. of months traded, or theCumulative no. of securities traded since account opening. All regressions include investor and year fixed effects. Thesample consists of investor-year observations between 2000 and 2007. Robust t-statistics, clustered by investor, are reportedin parentheses, and ***, **, and * denote significance at 1%, 5%, and 10%, respectively.

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

Coefficient (1) (2) (3) (4) (5) (6)

Cumulative no. of active trades (10 2) -0.008 -0.008

(-5.87)*** (-5.84)***

Cumulative no. of months traded -0.002 -0.002

(-13.53)*** (-13.55)***

Cumulative no. of securities traded -0.000 -0.000

(-4.10)*** (-3.96)***


(32.04)*** (26.85)*** (34.56)***

Value of investment portfolio (in EUR) 0.000 0.000 0.000

(0.99) (1.02) (0.95)

Equity share (in % of portfolio) -0.020 -0.020 -0.021

(-2.71)*** (-2.69)*** (-2.80)***

Number of securities in portfolio -0.001 -0.001 0.000

(-4.52)*** (-4.18)*** (-3.76)***

Intercept 0.262 0.097 0.254 0.120 0.263 0.091

(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 108,335 108,335 108,335 108,335 108,335 108,335


Adjusted R 0.646 0.646 0.646 0.646 0.644 0.644

Active Portfolio Turnover


21/35

19

significant negative relationship between experience and active portfolio turnover. Adding control

variables does not change our findings.10

The learning from overconfidence we observe is broadly consistent with the predictions of a learning

model developed by Gervais and Odean (2001). In their multiperiod model, investors constantly

observe the success of their investment decisions and thereby gradually infer about their own ability.

When assessing their investment returns, investors take too much credit for successful investments and

revise their beliefs about their own ability upward by too much. This leads to overconfidence among

inexperienced investors, resulting in high levels of trading activity at the beginning of their careers. As

investors gain investment experience, they learn to better recognize their own abilities and realize

when their behavior is not beneficial. Overconfidence will diminish and their trading behavior will

converge to rational behavior, leading to a gradual decrease in trading activity.

4.3. Learning from the Disposition EffectTable 1.4 presents the estimation results of regressions with the disposition effect as the dependent

variable. As described in section 3.1, we estimate the disposition effect based on the methodology

proposed by Odean (1998a) as the difference between the proportion of gains realized (PGR) and of

losses realized (PLR). Since not every investor sold securities in every year of the sample period, we

could not estimate the disposition effect for all investoryear combinations and consequently, the

number of observations is lower compared to the previously discussed investment mistakes.

Specifications (1) and (2) reveal that there is a positive relationship between the cumulative number of

active trades and the disposition effect, which suggests that experience does not eliminate the invest-

ment mistake. When using the other two measures to approximate investment experience (specifica-

tions (3) to (6)), the results are similar. Increases in experience are related to significant increases in

the disposition effect. Adding control variables that account for changes in the investor portfolio or

market environment does not change our findings.

10 Note that in Table 3 the number of observations and that of unique investors included in the regres-

sion is slightly lower than in Table 2. For an investor-year observation to be included in the regres-sion, we require the given investor to have been a customer of the bank for at least three months. If,for example, an investor started trading in November, then this investor-year observation is not in-cluded in the regression as there are only two months of portfolio turnover data available.


22/35

20

Table 4: Learning from the Disposition Effect

Table 1.4 presents the results of fixed effects panel regressions where the dependent variable is the investor and year specificportfolioDisposition Effect (PGR-PLR) on a scale from -1 to +1, with positive numbers representing the disposition effect.Investment experience is measured either by the Cumulative no. of active trades, the Cumulative no. of months traded, or theCumulative no. of securities traded since account opening. All regressions include investor and year fixed effects. Thesample consists of investor-year observations between 2000 and 2007. Robust t-statistics, clustered by investor, are reported

in parentheses, and ***, **, and * denote significance at 1%, 5%, and 10%, respectively.

Our finding that experience and disposition effect are positively correlated contradicts the studies by

Seru, Shumway, and Stoffman (2010), who find some evidence for a negative correlation, and Feng

and Seasholes (2005), who find a strong negative relationship. We see two possible explanations for

the difference in findings. First, both studies use a dataset from a period that differs from the period of

our dataset. Seru, Shumway, and Stoffman use data from Finland that covers the years 1995 to 2003

and Feng and Seasholes use a Chinese dataset covering 1999 and 2000. In the sample from 2000 to

2007, we find a considerable variation among the average disposition effect estimates per calendar

year, ranging from 0.08 to 0.15. Accordingly, it is difficult to compare results that use different sample

periods, especially if they only include a few years of data as in the case of Feng and Seasholes. The

second reason is related to the approach of estimating the disposition effect. Both studies use a hazard

model to measure the disposition effect, which is different from the PGR-PLR approach used in the

majority of empirical papers.

In summary, we find that investment experience is associated with less overconfidence, but not less

underdiversification or less disposition effect. Based on these findings, we cannot rejectHypothesis 1.

Coefficient (1) (2) (3) (4) (5) (6)

Cumulative no. of active trades (10 2) 0.008 0.007

(3.89)*** (3.81)***

Cumulative no. of months traded 0.002 0.002

(8.18)*** (8.26)***

Cumulative no. of securities traded 0.001 0.001

(8.50)*** (8.66)***


(-11.35)*** (-6.95)*** (-10.85)***Value of investment portfolio (in EUR) 0.000 0.000 0.000

(-0.43) (-0.49) (-0.42)

Equity share (in % of portfolio) 0.021 0.022 0.021

(1.45) (1.50) (1.45)

Number of securities in portfolio -0.002 -0.003 -0.003

(-3.85)*** (-3.85)*** (-3.96)***

Intercept 0.124 0.295 0.138 0.257 0.126 0.287

(20.87)*** (15.48)*** (20.80)*** (12.93)*** (21.64)*** (15.24)***

Investor fixed effects Yes Yes Yes Yes Yes Yes

Year fixed effects Yes Yes Yes Yes Yes Yes

Observations 68,262 68,262 68,262 68,262 68,262 68,262


Adjusted R 0.317 0.320 0.317 0.320 0.318 0.321

Disposition Effect (PGR-PLR)


23/35

21

Interestingly, the reason why investors seem to learn from overconfidence but not the other two in-

vestment mistakes is potentially related toHypothesis 2, which we cannot reject either. For individual

investors it is very easy to identify and avoid the costs related to excessive trading caused by overcon-

fidence. After each trade, the bank that provided us with the dataset sends an order confirmation to the

customer, which lists all transaction related fees. If at the end of a year the customer realizes that his or

her investment return is small compared to the transaction fees, then he or she can easily reduce trad-

ing activity in the next year. With regard to underdiversification and the disposition effect, the feed-

back investors receive is more ambiguous. It requires a lot more financial knowledge (and time) for

the individual to detect the mistake and understand the costs associated with it. Accordingly, the

chances that he or she will avoid the mistake are small.

4.4. Learning and Portfolio ReturnsNext, we turn to the question whether investors achieve higher portfolio returns as they gain experi-

ence. Specifications (1), (3), and (5) of Table 1.5 present the base regression estimates with portfolio

returns estimated according to the Modified Dietz Method, inclusive of transaction fees11, as the

dependent variable. The coefficients of all three experience variables are positive and significant either

at the 1% or 5% level, indicating that investors indeed achieve higher portfolio returns as they gain

investment experience. Specification (1) reveals that 100 additional active trades are associated with

an increase in portfolio performance of 0.15% per month. With regard to experience measured by the

number of active months, specification (3) reveals that one additional month of active trading is asso-

ciated with an increase in monthly portfolio returns by 0.02%. Similarly, one additional traded security

correlates with a rise in portfolio performance of 0.01% per month. Specifications (2), (4), and (6)

incorporate control variables used in previous papers to address concerns regarding omitted variables.

Studies of investment returns among individual investors have shown that portfolio value and equity

share are positively related to investment performance (e.g., Kramer (2009)). To rule out that changes

to the investment portfolio unrelated to learning affect the return estimates, we add the value of the

investment portfolio and the equity share to the regression; however, this does not change our findings.

Barber and Odean (2000) provide evidence that the average households gross returns (before transac-tion costs) are close to those earned by an investment in the market portfolio. However, net returns

(after transaction costs) are significantly lower, leading to considerable underperformance relative to

the market. They conclude that overconfident investors trade excessively and thereby generate transac-

tion costs which substantially reduce portfolio returns. If the learning from overconfidence document-

ed in section 4.2 is the reason for the increase in portfolio returns as investors gain experience, then

this should be reflected in the difference between portfolio returns before and after accounting for

11 We define transaction fees as all costs related to executing a buy or sell order, such as fixed andvariable commissions, over-the-counter transaction fees, phone or broker-assisted markups, foreignexchange fees, etc. In contrast to Barber and Odean (2000), our measure f or transaction fees doesnot, however, include costs related to the bid-asks spread and market impact of a transaction.


24/35

22

transaction costs. The right part of Table 1.5 presents the regression results with portfolio returns that

exclude transaction fees as the dependent variable. As expected, we find that the correlation between

investment experience and returns before transaction fees is much weaker than for returns including

fees. For two of the three experience variables, the coefficients are not different from zero at conven-

tional levels of significance (specifications (8) and (10)), and for the third, the coefficient halved

(specification (12)). Our estimates are conservative, because we only considered observable transac-

tion costs. Apart from explicit commissions and other fees paid to the bank, there are also implicit

transaction costs, such as the bid-ask spread and possibly market impact, which we cannot observe.

Excluding these hidden costs from the portfolio returns before transaction fees would probably further

weaken the relationship to investment experience.

Since portfolio returns calculated according to the Modified Dietz Method do not control for differ-

ences in investment risk, we repeat the analysis using Jensens Alpha as well as the Sharpe Ratio asmeasures for risk-adjusted portfolio returns. The left part of Table 1.6 presents the regression estimates

with Jensens Alpha as the dependent variable and the right part the results with the Sharpe Ratio as

the dependent variable. Both measures are calculated including transaction fees. We find no significant

correlation between investment experience and Jensens Alphas. The coefficients of two of the three

experience measures are positive; however, they do not significantly differ from zero. Adding control

variables for changes to the investment portfolio and to the regressions (specifications (2), (4), and (6))

does not change our findings. When using Sharpe Ratios instead, the results indicate a positive rela-

tionship between experience and risk-adjusted returns. For two of the three measures for investmentexperience they are significant at the 10% and 5% level, respectively.


25/35

23

Table6:ExperienceandR

isk-AdjustedPortfolioRetur

ns

Table1.6p

resentstheresultsoffixedeffectspanelr

egressionswherethedependentvariable

istheinvestorandyearspecificJensens

AlphaorSharpeRatio,bothcalculatedincludingtransaction

fees.Investmentexperienceismeasuredeitherbyth

eCumulativeno.ofactivetrades,theCu

mulativeno.ofmonthstraded,ortheCu

mulativeno.ofsecuritiestradedsincea

ccountopening.All

regressions

includeinvestorandyearfixedeffects.T

hesampleconsistsofinvestor-yearobservationsbetween2000and2007.Robust

t-statistics,clusteredbyinvestor,arerepo

rtedinparentheses,

and***,**

,and*denotesignificanceat1%,5%,an

d10%,respectively.

Coefficien

t

(1)

(2)

(3)

(

4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Cumulati

veno.o

factivetrades(102)

-0.0

03

-0.0

03

7.76

0

7.6

82

(-0.7

6)

(-0.7

6)

(1.2

8)

(1.2

7)

Cumulati

veno.o

fmonthstraded(102)

0.0

09

0.0

09

108.1

97

104.8

94

(0.8

6)

(0.8

3)

(1.9

0)*

(1.8

4)*

Cumulati

veno.o

fsecuritiestraded(102)

0.0

06

0.0

06

66.7

72

66.4

52

(1.2

9)

(1.2

9)

(2.0

3)**

(2.0

2)**

Valueofi

nvestmentportfolio(inEUR)

0.0

00

0.0

00

0.0

00

0.0

00

0.0

00

0.0

00

(0.0

3)

(0.2

5)

(0.2

7)

(0.4

7)

(0.1

7)

(0.2

1)

Equitysh

are(in%ofportfolio)

0.0

16

0.0

16

0.0

16

169.2

44

169.0

95

169.1

85

(1.5

9)

(1.5

6)

(1.5

6)

(2.3

7)**

(2.3

7)**

(2.3

7)**

Intercept

-0.0

28

-0.0

43

-0.0

26

-0.0

41

-0.0

26

-0.0

41

-454.23

6

-612.9

69

-450.4

31

-609.1

34-450.8

13

-609.4

22

(-15.9

6)***

(-4.3

5)***(-14.9

3)***

(-4.1

6)***(-15.3

2)***

(-4.1

3)***

(-54.4

2)*

**

(-8.9

4)***(-55.7

5)***

(-8.8

8)***(-54.1

2)***

(-8.9

0)***

Investorfixedeffects

Yes

Yes

Yes

Y

es

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yearfixed

effects

Yes

Yes

Yes

Y

es

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations

108,7

43

108,7

43

108,7

43

108

,743

108,7

43

108,7

43

108,722

108,7

22

108,7

22

108,7

22

10

8,7

22

108,7

22

Uniquein

vestors

19,4

41

19,4

41

19,4

41

19,4

41

19,4

41

19,4

41

19,4

40

19,4

40

19,4

40

19,4

40

19,4

40

19,4

40

Adjusted

R

0.0

48

0.0

48

0.0

48

0.048

0.0

48

0.0

48

0.1

39

0.1

40

0.1

39

0.1

39

0

.139

0.1

40

Jensen'sAlp

ha

SharpeRatio


26/35

24

Ta

ble7:RobustnessChecksfor

LearningfromInvestmentM

istakes

Table7pre

sentstheresultsoffixedeffectspanelregressionswherethedependentvariableisameasureforunderdiversification(specifications(1)-(3)),overconfidence(speci

fications(4)-(6)),or

thedisposit

ioneffect(specifications(7)-(9))aslistedontopofthecolumn.Onlythecoeffici

entsfortherespectivemeasureofexperiencearereported:Cumulativeno.ofactiv

etrades(specifica-

tions(1),(4),and(7)),

Cumulativeno.ofmonthstr

aded(specifications(2),(5),and(8)),C

umulativeno.ofsecuritiestraded(spec

ifications(3),(6),and(9)).

Thefirstrow

(EntireSample)

reportsesti

matesfortheentiresampleasinspecific

ations(2),(4),and(6)ofTables1.2,1.3,and1.4.Thefollowingrowspresentestimatesforsixsubsamplesoftheentiresa

mpleasindicatedin

brackets.A

llregressionsincludeinvestorandyearfixedeffects.Thesampleconsistsofinves

tor-yearobservationsbetween2000and2007.Robustt-statistics,clusteredbyinvestor,arereportedin

parentheses,and***,**,and*denotesignificanceat1%,5%,and10%,respectively.

Trades

M

onths

Securities

Trades

M

onths

Securities

Trades

Mo

nths

Securities

Sample

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

EntireSample

0.013

0.003

0.001

-0.008

-0.002

-0.000

0.007

0.002

0.001

(3.95)***

(21.71)***

(11.59)***

(-5.84)***

(-13.55)***

(-3.96)***

(3.81)***

(8.26)***

(8.66)***

1stSub

sample

(investorsfromthehighestmistakequintile)

0.017

0.006

0.001

-0.005

-0.002

-0.000

0.019

0.007

0.001

[n=3,892investors]

(5.81)***

(14.15)***

(4.86)***

(-4.18)***

(-6.54)***

(-2.47)**

(2.87)***

(12.48)***

(2.44)**

2ndSu

bsample

(investorsthatdroppedou

tofthesample)

0.022

0.006

0.001

-0.018

-0.004

-0.001

0.007

0.002

0.001

[n=3,470investors]

(6.86)***

(13.03)***

(9.81)***

(-4.72)***

(-8.92)***

(-4.54)***

(2.27)**

(2.42)**

(4.56)***

3rdSubsample

(investorsthatremainedin

thethesample)

0.012

0.003

0.001

-0.007

-0.001

-0.000

0.007

0.002

0.001

[n=16,017investors]

(3.52)***

(20.54)***

(10.04)***

(-5.74)***

(-11.64)***

(-2.41)**

(3.44)***

(8.21)***

(7.80)***

4thSubsample

(investorsfromthefirstagequintile)

0.024

0.004

0.001

-0.017

-0.002

-0.000

0.018

0.003

0.001

[n=3,495investors]

(6.89)***

(9.34)***

(9.84)***

(-5.84)***

(-6.20)***

(-3.23)***

(4.04)***

(3.93)***

(6.24)***

5thSubsample

(excludinghighestandlow

esttradingquintile)

0.008

0.004

0.001

-0.006

-0.002

-0.000

0.000

0.000

0.000

[n=11,175investors]

(2.62)***

(13.75)***

(5.96)***

(-4.32)***

(-8.95)***

(-3.40)***

(0.41)

(0.09)

(2.15)**

6thSubsample

(excludinghighestandlow

estwealthquintile)

0.009

0.003

0.001

-0.008

-0.002

-0.000

0.005

0.002

0.000

[n=11,689investors]

(2.57)**

(16.91)***

(7.60)***

(-4.13)***

(-11.28)***

(-3.65)***

(2.46)**

(6.81)***

(4.91)***

Contro

ls

LevelofCDAX-index(inp

oints)

X

X

X

X

X

X

X

X

X

Valueofinvestmentportfo

lio(inEUR)

X

X

X

X

X

X

X

X

X

Equityshare(in%ofportfolio)

X

X

X

X

X

X

X

X

X

Numberofsecuritiesinpo

rtfolio

X

X

X

X

X

X

FixedE

ffects

Investorfixedeffects

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Y

es

Yes

Yearfixedeffects

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Y

es

Yes

Herfindahl-HirschmanIndex

ActivePortfolioTurnover

DispositionEffect(PGR-PLR)


27/35

25

In summary, we find strong evidence for a positive relationship between investment experience and

MDM portfolio returns (including fees), and some evidence for a positive association between experi-

ence and risk-adjusted portfolio returns. Accordingly, the previous findings by Seru, Schumway, and

Stoffman (2010) that experience leads to higher returns over a 30-day period following purchases and

by Nicolosi, Peng, and Zhu (2009) that trade quality increases, do translate into higher returns for the

overall portfolio. We therefore cannot rejectHypothesis 3. The analysis of portfolio returns before and

after accounting for transaction costs reveals that the increase in portfolio returns is indeed related to

the learning from overconfidence we document in section 4.2. We assume that the reason why the

evidence for risk-adjusted returns turns out to be weaker is related to our empirical methodology.

Since we estimate risk-adjusted returns per calendar year, we only use 12 monthly MDM portfolio

return observations to calculate Jensens Alpha and the Sharpe Ratio. We presume that this introduces

considerable noise and leads to less significant results.

4.5. Robustness ChecksTo verify the robustness of our results with regard to learning from investment mistakes, we rerun the

regressions using subsets of the original sample. We start by looking at those investors who are the

most likely to suffer from the three investment mistakes we use in the study. The idea is that not all

investors in the sample are underdiversified, suffer from overconfidence, or are subject to the disposi-

tion effect. By only looking at those most likely to suffer from these investment mistakes, we isolate

those who are the most likely to learn from their mistakes. To do so, we divide the sample of investors

into quintiles according to the magnitude of each investment mistakes in the first year investors ap-

peared in the sample. We then rerun the regressions using only investors from the highest mistake

quintile, those that are the most likely to suffer from the specific investment mistake. Table 1.7 pre-

sents the regression estimates. If we compare the estimates for this 1st subsample with the results of the

entire sample, we find no differences. Hence, we conclude that our findings are not biased by investors

who do not suffer from specific investment mistakes.

Next, we turn to investors who stopped trading during the observed sample period. Seru, Schumway,

and Stoffman (2010) argue that attrition plays an important role in the context of learning in financialmarkets. They find that a substantial amount of aggregate learning occurs when low-skilled investors

learn about their poor abilities and consequently stop trading. Applied to our study this could mean

that the learning we observe with regard to overconfidence could result from frequent (but unprofita-

ble) traders leaving the sample and


28/35

26

not from learning on the individual level. To verify this, we split the sample into two parts: 3,470

investors that dropped out of the sample (2nd Subsample) and 16,017 investors that remained active

until the end of the observed sample period (3rd Subsample). When comparing the two subsamples, we

find that the regression results do not differneither compared to each other, nor compared to the

entire sample. Accordingly, we conclude that our findings are not biased by investor attrition related to

learning about their poor abilities.

Even though the sample only includes investors who began trading in the observed sample period, one

might argue that investors previously held investment portfolios with other banks and therefore were

not new to investing at the time they opened the account we observe. To address this concern, the 4th

Subsample only includes investors from the lowest age quintile. All investors in this subsample were

younger than 30 years when they opened their account; the average age at account opening was ap-

proximately 25 years. It is therefore unlikely that they held accounts with other banks before then.Table 1.7 illustrates that there is no difference in estimation results between the subsample of young

investors and the overall sample. We therefore conclude that the results are not biased by investors that

previously held accounts with other banks and entered the sample with prior investment experience.

Finally, we turn to outliers among the investors in the sample. Among the 19,487 individual investors,

we observe a wide spectrum of investment portfolio size, ranging from less than EUR 50 to more than

EUR 10 million. Also, the trading frequency differs considerably: While some investors do not trade

actively at all, there are some who trade more than 300 times month after month. To ensure that outli-

ers are not driving our findings, we rerun the regression excluding investors in the highest and lowest

investment portfolio quintile (5th Subsample) and the investors in the highest and lowest active portfo-

lio turnover quintile (6th Subsample). The results presented in Table 1.7 show that there are no signifi-

cant differences between the two subsamples and the overall sample. We therefore conclude that our

results are not driven by outliers in terms of financial wealth or trading activity.

5. Summary and ConclusionMotivated by empirical evidence which suggests that individual investors tend to make various in-

vestment mistakes that, in aggregate, lead to significant social costs, this paper examines whether

investors actually learn from their mistakes. To address this question, we use a large administrative

dataset which covers the complete trading history of 19,487 German retail investors over a period of

eight years. We exploit the datasets panel structure to explore the relationship of three well doc u-

mented investment mistakesunderdiversification, overconfidence, and the disposition effectwith

three different measures for investment experience.

We find that underdiversification and the disposition effect do not decline as investors gain investment

experience. However, our results also show that gains in experience are associated with less portfolio

turnover, suggesting that investors learn from overconfidence. We find that a gain in experience


29/35

27

equivalent to 100 additional trades is associated with a decline in monthly portfolio turnover of 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. Our findings are robust to the inclusion of vari-

ous control variables in the regression specification, including investor and year fixed effects, as well

as measures for changes in the market environment and investment style. Furthermore, a number of

additional robustness checks highlight that our results are not driven by investor attrition, investors

with prior experience, or outliers in the sample. We conclude that compared to underdiversification

and the disposition effect, it is relatively easy for investors to identify excessive trading activity,

understand the nature and resulting costs of the mistake, and avoid it in the future.

By correlating investment experience with portfolio returns, we are able to confirm the finding of

previous studies that as investors gain experience, their investment performance improves. A compari-

son of portfolio returns before and after accounting for transaction costs reveals that the increase inportfolio returns is indeed related to learning from overconfidence. In light of the significant underper-

formance of individual investors, our findings suggest that learning from investment mistakes helps

individual investors to close to some extent the performance gap to the overall market.


30/35


31/35

29

Camerer, Colin, and Dan Lovallo, 1999, Overconfidence and Excess Entry: An Experimental Ap-proach, American Economic Review 89, 306318.

Campbell, John Y., 2006, Household Finance,Journal of Finance 61, 15531604.

Carhart, Mark M., 1997, On Persistence in Mutual Fund Performance, Journal of Finance 52, 5782.

Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2002, Defined ContributionPensions: Plan Rules, Participant Choices, and the Path of Least Resistance,Tax Policy and theEconomy 16, 67113.

Choi, James J., David Laibson, and Brigitte C. Madrian, 2005, $100 Bills on the Sidewalk: SuboptimalInvestment in 401(k) Plans, Working Paper, National Bureau of Economic Research (NBER).

Coval, Joshua D., David A. Hirshleifer, and Tyler Shumway, 2005, Can Individual Investors Beat theMarket? Working Paper, Harvard University.

DAB Bank, 2004,Faszination Wertpapier: Fakten und Hintergrnde zum Anlegerverhalten inDeutschland(DAB-Bank, Munich).

De Bondt, Werner F. M., and Richard Thaler, 1985, Does the Stock Market Overreact?,Journal of

Finance 40, 793805.

Deutsche Bank Research, 2007,Retail Certificates: A German Success Story (Deutsche Bank AG,Frankfurt).

Deutsche Bundesbank, 1985, Wertpapierdepotstatistik(Deutsche Bundesbank, Frankfurt).

Deutsche Bundesbank, 2010, Wertpapierdepots Mrz 2010, Wertpapier-Kundendepots bei den einzel-nen Bankengruppen (Deutsche Bundesbank, Frankfurt).

Deutsches Aktieninstitut, 2009, DAI-Factbook 2009: Statistiken, Analysen und Graphiken zu Aktion-ren, Akti

2012.08.do individual investors learn from their mistakespdf

Documents