1

The trading behaviour of men and women in equity portfolio

diversification

Zheng Wu1

December 1, 2018

Abstract

This study shows that Finnish individual investors hold under-diversified portfolios, in

particular, female investors are less diversified than male investors. Over time, the average

diversification level improves, but the improved diversification does not necessarily imply

that investors’ portfolio composition skills have improved. The level of under-diversification

is greater among younger, low-income, less-educated, and less sophisticated investors. The

level of under-diversification is also correlated with investment choices that are consistent

with over-confidence. We find that as the level of diversification increases, both male and

female investors’ performance measure increase. Male investors earn a relative higher gross

monthly return than female investors including financial crisis period. Under-diversification

is costly to most investors, but a small subset of investors under-diversify because of superior

information.

JEL Classification: G3

Keywords: portfolio diversification; genders; portfolio performance

1 Corresponding author: University of Sydney, Finance Discipline, Business School, Building H69, Sydney,

NSW 2006, Australia, phone: 61-2-86276465, fax: 61-2-93516461, e-mail: vycke.wu@sydney.edu.au

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1. Introduction

Portfolio diversification is a cornerstone in the portfolio theory developed by Markowitz

(1952). In a stock portfolio, idiosyncratic risk can be minimized due to that returns for

different stocks are rarely perfectly correlated. Optimally, a well-diversified portfolio is only

subject to market risk once idiosyncratic risk is diversified away. In a study by Karhunen and

Keloharju (2001), it is observed that Finnish individual investors held under-diversified

portfolio. Barber and Odean (2001) report similar results in their study using data from a US

securities firm and report that a typical individual investor holds a portfolio with only four

stocks. Using the same brokerage sample, Goetzmann and Kumar (2008) find that investors

with fewer stocks in their accounts on average. Another study by Benartzi (2001) shows that

US pension contributions are also very poorly diversified and tend to be allocated to the

employer’s stock. Using data from the Survey of Consumer Finances (SCF), Polkovnichenko

(2005) provides evidence of under-diversification among U.S. households. These results

indicate that, on average, individual investors hold under-diversified portfolios.

Behavioral models can provide guidance to explaining the under-diversification among

individual investors. According to the Prospect Theory developed by Kahnemann and

Tversky (1979), a person has a varying attitude toward risk. Idiosyncratic returns, similar to

lotteries, offer the investor a small possibility to win and in this situation the investor is ready

to accept more risk than he or she would accept making other investment decisions. If we

assume that sophisticated investors make efficient investment decisions in the mean-variance

frame, both acknowledging the return and variance of their portfolios, then it is justified to

propose that portfolio diversification is a measure of investor sophistication.

Financial economists have long puzzled over investors' enthusiasm for active trading in

highly competitive securities markets. Overconfidence has lately been subject to a large

quantity of research in behavioral finance e.g. Odean (1998;1999;2001). Overconfidence has

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been explained as a characteristic of human information processing. A common human

feature is that we constantly learn about our abilities by observing our actions. It is, in short, a

“trial-and-error” process. But when processing information, a heuristic bias causes us to take

too much credit for our successes and blame failures on unmanageable external forces.

Overconfidence is e.g. a Darwinian mechanism that helps us to survive in a competitive

environment. Another interesting finding is that overconfidence is greater in areas that are

demanding and that lack direct and clear feedback. Investing in the stock market can be seen

as such an area that lacks clear and direct feedback. Barber and Odean (2000 and 2001)

conclude that excessive trading is a direct symptom of overconfidence. They find that

overconfident investors overestimate the precision of their knowledge about the value of a

security. This is why overconfident investors engage in frequent trading because they believe

that they achieve a superior return. Barber and Odean (2001) investigate the hypothesis of

overconfidence by dividing investors by gender. Their study show that male investors trade

more frequently and by doing so they lower their returns due to transaction costs and the

choice of securities. Our paper extends Barber and Odean (2001) work by examining the

portfolio diversification and performance by gender in recent decades. Gervais and Odean

(2001) further develop the theory that overconfidence is enhanced in investors that

experience high returns, even when those returns are simultaneously enjoyed by the entire

market.

An extensive academic literature documents that gender matters in a number of different

domains, including consumption, labor market, investment and corporate governance. In

particular, recent finance literature has claimed that male and female investors differ in terms

of risk aversion, overconfidence and mutual trust, with these dimensions impacting financial

decision making and performance. There is a growing body of empirical literature

investigated the benefits of board diversity in the form of improved decision making

(Milliken and Martins 1996), enhanced legitimacy of corporate practices (Hillman et al.

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2007), more stringent monitoring (Adams and Ferreira 2009, Adams and Funk 2012,

Adams and Kirchmaier 2016, Schwartz-Ziv 2017, Bernile, Bhagwat, and Yonkers 2017),

effective board oversight of strategic decisions (Nielsen and Huse 2010), and improved

financial performance (Gul et al. 2011).

In this study, we analyse the diversification choices of 1,115,200 individual investors in

Finland during a twenty-year period in recent (1995 – 2014) capital market history. We aim

to investigate whether female investors are more diversified than male investors, what

characters of male and female investors explains the under-diversification, and how under-

diversification relates to male and female investors’ portfolio performance. Our study focuses

on three key issues. First, we estimate the extent of under-diversification in Finnish investors’

portfolios and examine whether the level of diversification improves over time. Second, we

document how investors’ diversification choices correlate with their individual characteristics

and their trading and investment patterns. From these correlations, we try to gauge whether

the evidence is consistent with explanations of under-diversification based on trading costs,

information, stock preferences, or behavioural biases. Third, to quantify the potential welfare

effects of portfolio under-diversification, we investigate the relation between portfolio

diversification and performance.

Our results indicate that a large proportion of individual investors are under-diversified, in

addition, female investors are less diversified than male investors. We find that during the

1995 – 2014 sample period, the average number of stocks in female investor portfolios

increase from 2 to 3, while the average number of stocks in male investor portfolios increase

from 2 to 4. This increase in the number of stocks held is associated with a decrease in the

average normalized portfolio variance, but the improved diversification does not necessarily

imply that investors’ portfolio composition skills have improved.

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In the cross-section, we find that the degree of diversification varies considerably across

households. Diversification level of female and male investors increases with age, income,

wealth, education and experience. In contrast, Finnish-speaking investors whose trading

decisions are consistent with stronger behavioural biases exhibit greater under-diversification.

Examining the relation between diversification and performance, we find that male investors

trade more, who are more overconfident than female investors. However, male investors

earned a relative higher gross monthly return than female investors including financial crisis

period. We find that as the level of diversification increases, both male and female investors’

performance measure increase. Some investors under-diversify because they might be skilled

and might have superior private information.

The remainder of the paper is organized as follows. Section 2 describes the relevant literature

in the field. Section 3 presents the data and the sample country. In section 4, we provide

evidence of under-diversification over time. In section 5, we document the investor

characteristics and behavioural patterns associated with under-diversification. In section 6,

we estimate the performance of under-diversified portfolios. Section 7 concludes and

discusses the implications of our work.

2. Related Literature and Hypothesis Development

Despite the longstanding and widespread financial advice to hold well-diversified portfolios,

several studies find that many individual investors instead tend to concentrate their portfolios

in a small number of stocks. Blume and Friend (1975), Kelly (1995), and Polkovnichenko

(2005) document that many households are poorly diversified. Campbell (2006) and Calvet,

Campbell, and Sodini (2007) investigate the efficiency of Swedish households investment

decisions and find that a few households are very poorly diversified, but they argue that the

costs of diversification mistakes are quite modest. Kumar (2007) finds a substantial return

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spread between stocks held by less diversified and stocks held by more diversified investors

and argues that this spread is driven by sentiment-induced mispricing, asymmetric

information, and narrow risk framing among which the sentiment effect is the strongest.

Goetzmann and Kumar (2008) show that individual investors not only hold a small number of

stocks directly, but that the stocks that they do hold tend to be fairly highly correlated. They

conclude that most investors pay considerable costs for their suboptimal diversification

choices. Using the same US data, Ivkovic, Sialm, and Weisbenner (2008) also find that

households with large stock portfolios, but with few stocks do better than less concentrated

households. Anderson (2013) find that wealthier investors trade more persistently and

perform better than the average investor. These results suggest that individual investors are

under-diversified, however, some of them possess information and are able to trade profitably.

There are a few key reasons why households might hold poorly diversified portfolios. First,

fixed costs of trading securities make it uneconomical for households with limited wealth to

hold a large number of stocks directly. Second, a lack of diversification could be prompted by

behavioral biases such as familiarity or overconfidence. Third, individual investors might

hold concentrated portfolios because they are able to identify stocks with high expected

returns. Under such circumstances, rational investors would need to assess the trade-off

between the benefits of higher stock returns with the costs of higher risk and the implications

of combining such prospective investments with their existing portfolios.

Prior literature has focus on the evidence that investors tend to invest disproportionately in

familiar assets. French and Poterba (1991) find that investors favor domestic over

international stocks. Tesar and Werner (1995) show that U.S. investors exhibit a bias towards

Canadian stocks in their foreign investment. Kang and Stulz (1997) show that Japanese firms

with a greater "international presence," as evidenced by having ADRs, or a great deal of

export business, have greater foreign ownership. Coval and Moskowitz (1999b) document

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that mutual fund managers prefer to hold locally headquartered firms and hint that this may

be due to easier access to information about the firm. Huberman (2001) shows that the

shareholders of a regional Bell operating company tend to live in the area that it serves.

Ivkovic, Poterba and Weisbenner (2005) show that individuals exhibit a strong preference for

local investments and individual’s investments in local stocks outperform non-local stocks.

Massa and Simonov (2006) find that Swedish investors exhibit a strong tendency to hold

stocks to which they are geographically or professionally close. In the context of 401(k) plan

investing, participants on average have considerable holdings in own-company stock

(Benartzi 2001). Familiarity has many facets. The firm's language, culture, and distance from

the investor are three important familiarity attributes that might explain an investor's

preference for certain firms. Due to data availability, we test local bias based on postcode.

Overconfidence is the overestimation of one's actual ability or level of control (Moore and

Healy 2008). Overconfidence in general is supported by bias in self-attribution, as modeled in

Daniel, Hirshleifer, and Subrahmanyam (1998) and Gervais and Odean (2001); that is,

investors who have experienced high returns attribute this to their high skill and become more

overconfident, while investors who experience low returns attribute it to bad luck rather than

experiencing an offsetting fall in their overconfidence level. Overconfidence is likely to be

especially important when security markets are less liquid and when short-selling is difficult

or costly (Daniel and Hirshleifer 2015). The existing literature investigates the relation

between overconfidence and investment behavior of private households. It has been linked to

the portfolio turnover (Odean 1998, 1999, Nofsinger and Sias 1999, Barber and Odean 2000,

2001, 2002, Choi, Laibson, and Metrick 2002, Glaser and Weber 2007, Chen et al. 2007,

Barber et al. 2009, Grinblatt and Keloharju 2009, Kelley and Tetlock 2013), diversification

(Goetzmann and Kumar 2008, Merkle 2017), and risk taking (Benartzi, 2001, Dorn and

Huberman 2005, Seasholes and Zhu 2010, Nosic and Weber 2010, Merkle 2017) of investors.

The implications of overconfidence in this context are mostly viewed negatively, leading to

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excessive trading, under-diversification, and increased risk taking. Although overconfidence

causes problems in markets, it may bring some benefits. Overconfidence can induce investors

to investigate more, and/or to trade more aggressively based on their signals. This sometimes

results in greater incorporation of information into price (Hirshleifer, Subrahmanyam, and

Titman 1994, Kyle and Wang 1997, Odean 1998, Hirshleifer and Luo 2001). Overconfident

people are considered to be more knowledgeable (Price and Stone 2004). Thus, higher

overconfidence results in a higher social status (Anderson et al. 2012). Furthermore,

overconfidence encourages investors to participate in asset classes, such as the stock market

or international investing, that they might otherwise neglect such as fear of the unfamiliar.

Empirically, a greater feeling of competence about investing is associated with more active

trading and with greater willingness to invest in foreign stock markets (Graham, Harvey, and

Huang 2009). Overall, these results are consistent with the hypothesis that individual

investors are overconfident and trade excessively.

Another extensive academic literature documents that gender matters in a number of different

domains, including consumption, labor market, investment and corporate governance. In

particular, recent finance literature has claimed that male and female investors differ in terms

of risk aversion, overconfidence and mutual trust, with these dimensions impacting financial

decision making and performance. First, males seem to have more financial knowledge and

wealth and they are more confident in their investing decisions with more risk tolerance.

Women have a higher risk aversion, hold less volatile portfolios, and expect lower returns

(Levin et al. 1988, Jianakoplos and Bernasek 1998, Sunden and Surette 1998, Agnew et al.

2003, Croson and Gneezy 2009). Second, women are less overconfident and optimistic than

men when it comes to driving ability, exam answer confidence, stock trading, and the choice

of compensation scheme (Svenson 1981, Feingold 1994, Lundeberg et al. 1994, Barber and

Odean 2001, Niederle and Vesterlund 2007, 2011). Male investors invest more often and

more aggressively than female investors when facing financial opportunities (Deaux and

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Farris (1977). Male investors are more overconfident than female investors (Barber and

Odean 2001, and Niederle and Vesterlund 2007, 2011). However, Dorn and Huberman (2005)

find in a survey of investors matched up with their actual trading accounts that two proxies

for overconfidence fail to explain cross-sectional variation in trade intensity. From the

perspective of the theory of value and growth investing, Betermier, Calvet and Sodini (2016)

conclude that male investors are more likely to invest in growth stocks whereas female

investors prefer value investing. These baseline patterns are robust to control for the length of

risky asset market participation and other measures of financial sophistication. Third, women

have a better compliance with taxation rules, business ethics, financial reporting guidelines,

financial market regulations, and professional financial advice than men (Baldry 1987,

Barnett et al. 1994, Bernardi and Arnold 1997, Fallan 1999, Ittonen et al. 2013). Last, there is

a growing body of empirical literature investigated the benefits of board diversity. Female

firm managers who reach the top echelon of the corporate hierarchy may be more competent

and work harder than their male peers (Green et al. 2009). Kumar (2010) finds that female

stock analysts issue bolder and more accurate forecasts and thus to self-selection with only

the most talented females entering the field. Adams and Ferreira (2009) show that female

directors have a significant impact on board inputs and firm outcomes. Adams and Funk

(2012) find that women directors are less tradition and security oriented than male directors.

Gayle, Golan and Miller (2012) find female are paid more and their pay is tied more closely

to the firm’s performance. There is also evidence for close cooperation between female

directors and executives if both are in a minority position (Matsa and Miller 2011). Graham

et al. (2013) find that corporate financial policies are influenced by top executives’ behavioral

traits. Huang and Kisgen (2013) find that firms with male top executives engage in more

acquisitions and have more debt issuances than those with female executives. Barua et al.

(2010) and Francis et al. (2015) report that the appointments of female CFOs improve

accruals quality and increase the degree of accounting conservatism. Levi, Li and Zhang

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(2010) show that in the case of female CEOs, the bid premium over the pre-announcement

target share price is much smaller when compared to M&A deals with male counterparts.

Huang and Kisgen (2013) find that female CFOs issue debt less frequently, and debt and

equity issuances are associated with higher announcement returns. Faccio et al. (2016) show

that firms managed by female CEOs have lower leverage, less volatile earnings, and a higher

survival rate than those managed by male CEOs.

Beyond the finance literature, previous studies from cognitive psychology indicate that

females experience emotions more strongly than do males (Harshman and Paivio 1987). The

stronger emotional experience can affect the utility of a risk choice. In particular, female

show more intense nervousness and fear than male in anticipation of negative outcomes

(Brody and Hall 2000). If negative outcomes are experienced more severely by females than

males, they will naturally be more risk averse when facing a risky situation. In identical

situations, Bolla et al. (2004) has shown that male and females who solve the same decision-

making task involving a gambling task are different, with the males out-performing, because

their brain mechanisms differ. Grossman, Michele and Wood (1993) point out that female

tend to feel fear while male tend to feel anger. They are more likely to be afraid of losing,

relative to male and hence evaluate a given gamble as being more risky, and will act in a

more risk-averse way. Several explanations have been proposed in indicating different risk

attitudes across genders. The most basic explanation comes with biological roots. Cesarini

and et al. (2010), Cronqvist and Siegel (2014), and Cronqvist et al. (2015) explore the effect

of seasonal affective disorder (SAD) on risk attitudes and empirical regularities in financial

markets also speak to these differences, because females are affected by SAD more than

males.

According to portfolio theory and behavioral finance both diversification and trading activity

are relevant for the performance of investment portfolios. In earlier studies of Finnish

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investors Karhunen and Keloharju (2001) report low diversification and Grinblatt and

Keloharju (2000) conclude that private investors follow less sophisticated investment

strategies. Grinblatt and Keloharju (2001) investigate why investors trade as much as they do.

Whether Finnish individual investors trade excessively and how well they diversify their

investment portfolios has not been directly investigated. In addition, no prior studies have

investigated the direct impact of gender on portfolio diversification. This is why we in this

study include both these factors in a model of investor sophistication. We study investor

sophistication by measuring three features of investment strategy: trading activity, portfolio

diversification and portfolio value for a large sample of individual investors. Since portfolio

value may be related to investment strategy or to the initial wealth of an investor, we focus on

trading activity and diversification. The purpose of this paper is to extend the line of portfolio

diversification and performance, in particular, we examine whether gender difference has an

impact on portfolio diversification and performance for a large sample of individual investors

from a whole market. Further, we investigate what individual (male and female)

characteristics are associated with under-diversification and what are the performance of

under-diversified portfolio.

Therefore, the research hypothesis in this paper is:

𝐇𝟎: Finnish female investors are more diversified over time.

𝐇𝟏: Finnish male investors are less diversified over time.

In addition to providing new insights into the household portfolio diversification and

performance, our paper also yields two distinct empirical implications. Firstly, this paper

offers an in-depth critical analysis and evaluation of how gender difference affects portfolio

diversification and performance. Most empirical studies investigate portfolio diversification

and gender separately; we investigate the empirical link between household’s gender and

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portfolio diversification directly and examine what characteristic attribute to it. Secondly, our

study is original in analysing a comprehensive and complete sample data over a tweenty-year

period (1995-2014). The sample period includes the most prominent bubble cycles of recent

decade: the Global Financial Crisis of 2007-2008. Previous studies investigate a relative short

time period and in earlier 20th

century (Karhunen and Keloharju 2001, Grinblatt and

Keloharju 2000, 2001).

3. Data description

3.1 Sample summary statistics

The data set used for the study is a sample consisting of 1,115,200 individual private

investors that have been randomly selected from the Finnish Central Securities Depository

(FCSD) using a random number generator. The FCSD records the trades of all market

participants on a daily basis and includes a set of demographic variables of the investor. The

time period for the data set covers January 1, 1995 through December 30, 2014. Compared to

survey data and data from a single securities firm the prime advantage is that the data does

not suffer from potential problems with how representative it is. Also, since the shareholdings

are recorded at a daily basis, it is much more exact and extensive than brokerage accounts,

which at best provide data at a quarterly level. The data set provides records of the investors’

demographic characteristics. For instance, the age, gender, mother-tongue, and the area of

residence of each investor is included in the data set, thereby providing an excellent research

base for investment behavior related studies. The FCSD data is also used e.g. in Grinblatt and

Keloharju (2000 and 2001) and in Karhunen and Keloharju (2001).

The sample’s distribution of male and female investors as well as age categories is illustrated

in Figures 1 and 2. The division is rather even between the genders, there are 471,599 women

and 643,601 men in the sample. The ratio of female to male investors in the sample is thus

0.42 per investor. This is close to the gender distribution of 45.9% female investors and 54.1%

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male investors in the whole population of individual investors in the FCSD. The age

distribution of the sample corresponds well to the age distribution in the whole population as

well. We conclude that the investigated sample is representative of the investor population in

Finland.

< Figure 1 and 2>

The sample selection method in the current study limits a bias in the results by also including

investors who have opened a book-entry account during the study period as opposed to

selecting only investors who had opened a book-entry account before the study period. By

including later registered investors who may have different investor behavior one limits the

risk of a representative bias in the sample.

In addition to the individual investor data, we use other standard data sets. For each stock in

the sample, we obtain monthly prices, returns, and market capitalization data from

COMPUSTAT.

3.2 Choice of sample country

We chose Finland for several reasons. First, Finnish data set covers information needed to

calculate portfolio concentrations for small shareholders (e.g., as compared to data from 13F

filings provided by Thomson Financial, which cover institutional investors who manage more

than $100 million). Since the portfolio concentration measure is particularly relevant for

small investors who have constraints preventing them from scaling up information

acquisition, the unique Finnish data set is used in this study. The Finnish Central Securities

Depositary (FCSD) maintains daily comprehensive official records of share ownership and

trades in electronic form. The Finnish Central Securities Depository (FCSD) shareholder

register contains entries of virtually all transactions in the shares of publicly traded Finnish

firms from January 2, 1995 onward, as well as the balance of the register as of January 1,

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1995. Grinblatt and Keloharju (2000) report that the register covers approximately 97% of the

total market capitalization of all publicly traded Finnish firms as of the beginning of this time

period. Second, language differences also make Finland interesting to analyze. There are two

official languages in Finland: Finnish and Swedish. Finnish speakers account for 93 percent

of the population, whereas Swedish speakers account for 6 percent of the population.

However, the influence of the Swedish speaking investors in the Finnish financial markets

exceeds what their fraction of the population would suggest. At the beginning of 1997, for

example, Swedish speakers held 23 percent of household shareowner wealth. Finnish

companies also exhibit language differences. Some Finnish firms communicate exclusively in

Finnish, others communicate exclusively in Swedish, and still others communicate in

multiple languages, typically Swedish and Finnish, Swedish, Finnish, and English, or Finnish

and English. Last, the language of the company may differ from the cultural background of

senior management, and the cultural background of senior management differs across

multilingual firms, allowing us to distinguish language from cultural preference.

4. Evidence of portfolio diversification

In this section, we investigate if individuals are under-diversification and how it changes over

time.

4.1 Diversification measures

We use three related diversification measures to capture the extend of under-diversification in

individual investors’ portfolios.

The first measure is the normalized portfolio variance (NV), which is obtained by dividing

the portfolio variance by the average variance of stocks in the portfolio (Goetzmann and

Kumar 2008):

𝑁𝑉 =𝜎𝑝

2

𝜎2

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The covariancematrix is estimated using the past fourteen years of monthly returns data.

The NV measure indicates that portfolio variance can be reduced by increasing the

number of stocks in the portfolio or by a proper selection of stocks such that the

average covariance (or correlation) among stocks in the portfolio is lower. Variance

reduction through active and proper stock selection reflects “skill” in portfolio

composition, while addition of stocks in the portfolio without lowering the average

portfolio correlation is likely to reflect “portfolio breadth” (Goetzmann et al. 2005).

Second, the diversification level of a portfolio is measured as its deviation

from the market portfolio (Blume and Friend 1975). The weight of each security

in the market portfolio is very small. Thus, the diversification measure can be

approximated as the sum of squared portfolio weights (SSPW):

𝑆𝑆𝑃𝑊 = ∑(𝑤𝑖 − 𝑤𝑚)2

𝑁

𝑖=1

= ∑(𝑤𝑖 −1

𝑁𝑚)2 ≈ ∑ 𝑤𝑖

2

𝑁

𝑖=1

𝑁

𝑖=1

where N is the number of securities held by the investor, 𝑁𝑚 is the number of

stocks in the market portfolio, 𝑤𝑖 is the portfolio weight assigned to stock i in the

investor portfolio, and 𝑤𝑚 is the weight assigned to a stock in the market portfolio

(𝑤𝑚 = 1

𝑁𝑚). A lower value of SSPW reflects a higher level of diversification.

Last, we use the total number of stocks in the portfolio as a “crude” measure of

diversification:

𝑁𝑆𝑇𝐾𝑆 = 𝑁

This diversification measure is commonly used, but it often overstates the level of

diversification (Blume et al. 1974).

4.2 Summary statistics of portfolio diversification

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Table 1 reports annual statistics for the three diversification measures. In any given month,

only 0.67%- 6.23% of the portfolios contain more than ten stocks for female investors and

1.2%- 14.56% of the portfolios contain more than ten stocks for female investors. In fact, for

female investors, more than 49% of investor portfolios contain only one stock, more than 74%

contain one to three stocks, and more than 84% of households hold five or fewer stocks. For

male investors, more than 34% of investor portfolios contain only one stock, more than 57%

contain one to three stocks, and more than 69% of households hold five or fewer stocks.

These stock-holding estimates are broadly consistent with the evidence in related studies that

examine diversification levels of U.S. household portfolios using data from other sources (e.g.

Blume and Friend 1975, Kelly 1995, Polkovnichenko 2005). These summary statistics also

show that male investors are more diversified than female investors.

Table 1 Panel B reports the normalized variance (NV) statistics. As expected, the normalized

variance decreases as the number of stocks in the portfolio increases. The NV of concentrated

portfolios is roughly three to four times the NV of better diversified portfolios. For example,

in 1995, for female investor, the NV of better-diversified portfolios with 11 to 15 stocks is

0.383, while concentrated portfolios with only two stocks, on average, have an NV of 0.917.

These summary statistics indicate that the level of portfolio diversification varies in the cross-

section, but investors’ portfolio composition skills remain invariant.

<Table 1>

4.3 Diversification changes through time

We have a relatively long twenty-year sample period, and the time-series of the average level

of diversification reveals interesting patterns. We find that during the 1995 to 2014 period,

the average number of stocks in female investor portfolios increases almost monotonically

from 1.858 in 1995 to 2.792 in 2014 – an increase of almost 50.3%. Furthermore, the

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normalized portfolio variance steadily decreased from 0.885 in 1991 to 0.739 in 1996 – a

decrease of more than 16.5% (see Table 2, Panel A). Meanwhile, the average number of

stocks in male investor portfolios increases almost monotonically from 2.044 in 1995 to

4.002 in 2014 – an increase of almost 95.8%. Furthermore, the normalized portfolio variance

steadily decreased from 0.865 in 1991 to 0.614 in 2014– a decrease of more than 29.02% (see

Table 2, Panel B). These two observations seem to imply that the portfolio composition skills

of investors have improved over time.

<Table 2>

5. Correlates of portfolio diversification

Traditional portfolio theory posits that high transaction costs (e.g. Brennan, 1975), high

search costs (e.g., Merton 1987), small portfolio size, and investors’ inability to buy in round

lots could prevent investors from diversifying appropriately. Under-diversification can also

stem from a belief that any multiple-stock portfolio, irrespective of its covariance structure,

will be well-diversified. Similarly, investors could adopt an “erroneous” diversification

strategy where they hold stocks with lower volatility and ignore correlations among them.

Investors’ attraction to certain types of stocks could be correlated with the level of portfolio

diversification. For instance, under-diversified investors may over-weight stocks from certain

categories or styles (e.g., small-cap stocks, growth stocks, etc.) or certain industries (e.g.,

technology stocks), or they might prefer stocks with higher variance and positive skewness

(e.g. Simkowitz and Beedles 1978, Golec and Tamarkin 1998, Polkovnichenko 2005,

Barberis and Huang 2007). Furthermore, lack of diversification could be related to various

psychological factors and behavioral biases. In the section, we identify the factors that are

strongly correlated with the level of portfolio diversification.

5.1 Models

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Regression models are estimated to examine which individual characteristics and behavioural

bias proxies are strongly correlated with investors’ diversification choices.

We follow Goezmann and Kummar (2008) methodology and framework to measure the

determinants of portfolio under-diversification, and estimate the following main panel

regression for investor i and time t (male and female separately):

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝐹𝑒𝑚𝑎𝑙𝑒,𝑖,𝑡 = µ0 + µ1𝑆𝑖𝑧𝑒𝑖,𝑡 + µ2𝐼𝑛𝑐𝑜𝑚𝑒𝑖,𝑡 + µ3𝑃ℎ𝐷𝑖,𝑡 + µ4𝐿𝑎𝑛𝑔𝑢𝑎𝑔𝑒𝑖,𝑡 +

µ5𝐴𝑔𝑒𝑖,𝑡 + µ6𝐸𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑖,𝑡 + +µ7𝑂𝑣𝑒𝑟𝑐𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒𝑖,𝑡 + µ8𝐿𝑜𝑐𝑎𝑙 𝑏𝑖𝑎𝑠𝑖,𝑡 + Ʋ𝑖,𝑡

(1)

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑀𝑎𝑙𝑒,𝑖,𝑡 = ƞ0 + ƞ1𝑆𝑖𝑧𝑒𝑖,𝑡 + ƞ2𝐼𝑛𝑐𝑜𝑚𝑒𝑖,𝑡 + ƞ3𝑃ℎ𝐷𝑖,𝑡 + ƞ4𝐿𝑎𝑛𝑔𝑢𝑎𝑔𝑒𝑖,𝑡 +

ƞ5𝐴𝑔𝑒𝑖,𝑡 + ƞ6𝐸𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑖,𝑡 + ƞ7𝑂𝑣𝑒𝑟𝑐𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒𝑖,𝑡 + ƞ8𝐿𝑜𝑐𝑎𝑙 𝑏𝑖𝑎𝑠𝑖,𝑡 + ȹ𝑖,𝑡

(2)

A detailed definition and justifications of these variables can be found in Appendix A.

5.2 Investor-level regression estimates

We estimate several investor-level cross-sectional regressions for both female and male

investors. In these regressions, the negative value of normalized variance of an investor

portfolio is used as the dependent variable, and several household- and portfolio-level

variables are used as explanatory variables. Since the negative value of normalized variance

is within the range of -1 to 0 and the dependent variable is truncated, the Tobit model is used

(Long 1997).

Table 3 provides descriptive statistics for our main variables. On average, the normalized

variance of female investors is much higher than male investors, representing the fact that

male investors are more diversified. Compare to female investors, male investors hold a

19

larger portfolio size, richer, less educated, younger, less experienced, less overconfidence,

less local bias. Both investors speak similar language.

<Insert Table 3>

In the first regression specification, we use the following demographic characteristics as

explanatory variables: investor’s age, annual income, education, and language. To examine

whether investors make better diversification choices in different age group, we create a set

of age dummies in order to capture the influence of age on portfolio diversification. The

estimation results are presented in Table 4, Panel A reports the regression estimates for all

female investors, we find that diversification is positively related to age, in particular, the age

group of 50-59 (estimate = 0.108), Income (estimate = 1.193E-05), and Education (estimate =

1.690E-04). Panel B reports the regression estimates for all male investors, we find that

diversification is positively related to age, in particular, the age group of 30-39 (estimate =

0.215), Income (estimate = 1.895E-05), and Education (estimate = 1.600E-04). These

coefficient estimates indicate that older, high-income (wealthy), and better educated male

investors are relatively better diversified. The negative coefficient estimate of the language

indicates that both female and male Finnish-speaking investors hold less diversified

portfolios.

In the second regression specification, we consider a set of variables that are likely to reflect

consistency in investors’ diversification choices and capture their levels of financial

sophistication. Specifically, we use Investment Experience as an explanatory variable, which

is defined as the number of years between the account openings date and December 31, 2014.

The estimation results are presented in Table 4, we find that the coefficient estimates of

Investment Experience are positive and statistically significant; in particular, both female and

male investors with more than 20 years trading experience are most diversified.

20

In the third regression specification, we examine whether our proxies for behavioural biases

are correlated with the diversification decisions of investors. We consider an overconfidence

proxy and a local bias measure. The Overconfidence Proxy is set to one for an investor if he

or she belongs to the highest portfolio turnover quintile and the lowest risk-adjusted

performance quintile. Local Bias measure is defined as the proportion of investor portfolio

that is invested in stocks of firms located within a 250 mile radius from her location

(postcode). The estimation results for the third specification are presented in Table 4. For

both female and male investors, the negative signs on overconfidence proxy indicate that

stronger overconfidence is associated with lower levels of diversification. However, the local

bias variable has a positive coefficient estimate, which indicates that a certain degree of

diversification might be associated with investors’ regional advantage due to superior

information flows within the local region.

In the last regression specification, we consider the full set of explanatory variables. In

addition, portfolio size is used as a control variable, which is the average market

capitalization of the household portfolio during the sample period. The full specification

estimation results are presented in Table 4. For female investors, most estimates maintain

their signs and significance levels in the full specification. Furthermore, the control variable

has the expected sign. For instance, we find that larger portfolios are better diversified. While

this effect could be mechanically induced, it is also likely that investors with larger portfolios

apply more effort to properly diversify their portfolios (Goezmann and Kummar 2008). For

male investors, investment experience and behavioural bias proxies become insignificant;

other estimates remain the same signs and significance.

6. Portfolio diversification and performance

If under-diversified investors are taking large idiosyncratic risks for which they are not

compensated appropriately, their portfolios would exhibit lower risk-adjusted performance.

21

We use gross monthly return (Barber and Odean 2001) as the performance measure.

Consider the common stock portfolio for a particular household, the gross monthly return on

the household’s portfolio is calculated as:

𝑅ℎ𝑡𝑔𝑟

= ∑ 𝑝𝑖𝑡𝑅𝑖𝑡𝑔𝑟

𝑠ℎ𝑡

𝑖=1

where 𝑝𝑖𝑡 is the beginning-of-month market value for the holding of stock i by household h in

month t divided by the beginning-of month market value of all stocks held by household h,

𝑅𝑖𝑡𝑔𝑟

is the gross monthly return for that stock, and 𝑠ℎ𝑡 is the number of stocks held by

household h in month t.

To examine the relation between overconfidence and portfolio performance, we employ

Barber and Odean (2001) method to calculate the monthly portfolio turnover for each

household as one-half the monthly sales turnover plus one-half the monthly purchase

turnover.9 In each month during our sample period, we identify the common stocks held by

each household at the beginning of month t from their position statement. To calculate

monthly sales turnover, we match these positions to sales during month t. The monthly sales

turnover is calculated as the shares sold times the beginning-of-month price per share divided

by the total beginning-of-month market value of the household’s portfolio. To calculate

monthly purchase turnover, we match these positions to purchases during month t-1. The

monthly purchase turnover is calculated as the shares purchased times the beginning-of-

month price per share divided by the total beginning- of-month market value of the portfolio.

Table 5 reports the performance statistics of monthly gross return and turnover rate for male

and female investors over the entire twenty years. During our sample period, female investors

earned average monthly gross returns of 3.1%, while male investors earned average monthly

gross of return 4.9%. On average, male investors turned over their stocks more frequently

22

than female investors. Fig. 3 uses the results of Table 5 to graph the trends of the gross

monthly return of each investor category. On average, male investors earned a relative higher

gross monthly return than female investors including financial crisis period. The gross

monthly return of male investors rise rapidly in recent years, in particular, the gross monthly

return of male investors almost doubled as female investors in 2014. Barber and Odean (2001)

show that men are more overconfident than women, men will trade more and perform worse

than women. Our results indicate that male investors trade more, who are more overconfident

than female investors, however, male investors perform better than female investors. This

outperformance may due to proper diversification by male investors rather than trade for

entertainment.

<Insert Table 5>

<Insert Fig. 3>

To examine the relation between portfolio diversification and portfolio performance, using

the sample-period normalized variance (NV), we rank investors and divide them into five

categories (Goetzmann and Kummar 2008). Table 6 reports the performance statistics for the

ten diversification sorted investor categories. We find that as the level of diversification

increases, both male and female investors’ performance measure increase. For instance, the

mean monthly gross return of female investors for decile 5 (decile 2) is 4.9% (1.7%), the

mean monthly gross return of male investors for decile 5 (decile 2) is 5.2% (2.7%). It is

interesting to note that the least diversified investor earn the second highest return compare to

other groups, this group of investor may intend to under-diversify because they might have

superior private information (Goetzmann and Kummar 2008).

<Insert Table 6>

23

7. Conclusion

This study examines the diversification choices of individual investors (both female and male

investors) during a twenty-year period in recent Finland capital market. Using data from

Finnish Central Securities Depository (FCSD) for the period from 1995 to 2014, we find that

female investors in our sample are less diversified than male investors. Over time, the

average diversification level improves, but the improved diversification does not necessarily

imply that investors’ portfolio composition skills have improved.

There is considerable heterogeneity in the diversification choices of individual investors. In

the cross-section, older, wealthier, more experienced, and better educated female and male

investors hold relatively better diversified stock portfolios. In contrast, Finnish-speaking

investors whose trading decisions are consistent with stronger behavioral biases exhibit

greater under-diversification. The local bias indicates that a certain degree of diversification

might be associated with investors’ regional advantage due to superior information flows

within the local region.

Examining the relation between diversification and performance, we find that male investors

trade more, who are more overconfident than female investors. However, male investors

earned a relative higher gross monthly return than female investors including financial crisis

period. We find that as the level of diversification increases, both male and female investors’

performance measure increase. Some investors under-diversify because they might have

superior private information, e.g. the least diversified female and male investors earn the

second highest return compare to other groups.

24

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29

Figure 1 Women’s age distribution

Figure 1 illustrates the sample’s distribution of female investors as well as age categories.

Figure 2 Men’s age distribution

Figure 2 illustrates the sample’s distribution of male investors as well as age categories.

0

0.05

0.1

0.15

0.2

0.25

0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90+

Women's age distribution

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90+

Men's age distribution

30

Figure 3 Gross Monthly Return

Figure 3 illustrates the trends of the gross monthly return of each investor category (female

and male investors).

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Gross Monthly Return

Male_Return_Wins Female_Return_Wins

31

Table 1. Aggregate Level Diversification Measures: Summary Statistics (Male and

Female)

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of the twenty years in the sample period. Percentage portfolios report the percentage of

investor portfolios holding a certain number of stocks for male and female investors.

Normalized portfolio variance reports the mean normalized variance for portfolios with

different number of stocks for male and female investors. The normalized variance (NV) of a

portfolio is the ratio of portfolio variance and the average variance of stocks in the portfolio.

The covariance matrix is estimated using past twenty years of monthly returns data. The

individual investor data are from Finnish Central Securities Depository (FCSD) for the period

from 1995 to 2014.

Year Num of Stocks Percentage of Portfolios (Female)

Percentage of Portfolios (Male)

NV (Female) NV (Male)

1995 1 0.636 0.603 1.000 1.000

2 0.184 0.185 0.917 0.900

3 0.075 0.082 0.752 0.739

4 0.039 0.044 0.638 0.636

5 0.023 0.027 0.575 0.566

6 - 10 0.037 0.047 0.491 0.472

11 - 15 0.005 0.009 0.383 0.363

Over 15 0.001 0.003 0.280 0.288

1996 1 0.614 0.582 1.000 1.000

2 0.198 0.196 0.810 0.785

3 0.077 0.083 0.592 0.578

4 0.041 0.046 0.491 0.470

5 0.024 0.028 0.436 0.415

6 - 10 0.038 0.050 0.365 0.327

11 - 15 0.006 0.010 0.250 0.195

Over 15 0.002 0.005 0.119 0.105

1997 1 0.621 0.563 0.999 0.999

2 0.197 0.197 0.817 0.785

3 0.074 0.088 0.647 0.633

4 0.039 0.049 0.590 0.553

5 0.022 0.029 0.546 0.515

6 - 10 0.037 0.055 0.500 0.433

11 - 15 0.006 0.012 0.398 0.298

Over 15 0.002 0.007 0.250 0.165

1998 1 0.574 0.515 0.999 0.999

2 0.223 0.210 0.815 0.824

3 0.081 0.094 0.670 0.671

4 0.044 0.056 0.579 0.576

5 0.026 0.034 0.506 0.503

6 - 10 0.042 0.066 0.411 0.381

11 - 15 0.007 0.016 0.273 0.236

Over 15 0.003 0.009 0.147 0.114

32

1999 1 0.643 0.533 0.999 0.998

2 0.155 0.173 0.888 0.896

3 0.076 0.092 0.824 0.826

4 0.042 0.056 0.775 0.763

5 0.025 0.037 0.732 0.712

6 - 10 0.046 0.077 0.643 0.611

11 - 15 0.009 0.021 0.508 0.455

Over 15 0.004 0.013 0.342 0.290

2000 1 0.617 0.490 0.971 0.978

2 0.166 0.173 0.755 0.732

3 0.081 0.097 0.575 0.560

4 0.045 0.061 0.469 0.449

5 0.028 0.042 0.403 0.371

6 - 10 0.048 0.091 0.300 0.262

11 - 15 0.010 0.026 0.175 0.137

Over 15 0.005 0.020 0.094 0.070

2001 1 0.567 0.453 1.000 1.000

2 0.210 0.199 0.755 0.720

3 0.082 0.100 0.577 0.557

4 0.045 0.061 0.497 0.463

5 0.028 0.042 0.453 0.398

6 - 10 0.051 0.094 0.393 0.321

11 - 15 0.012 0.029 0.286 0.219

Over 15 0.006 0.023 0.197 0.137

2002 1 0.528 0.406 1.000 1.000

2 0.198 0.186 0.848 0.835

3 0.100 0.113 0.639 0.639

4 0.056 0.073 0.542 0.532

5 0.033 0.050 0.476 0.452

6 - 10 0.062 0.111 0.385 0.346

11 - 15 0.014 0.034 0.262 0.221

Over 15 0.008 0.027 0.156 0.120

2003 1 0.611 0.484 1.000 1.000

2 0.164 0.167 0.763 0.745

3 0.078 0.092 0.611 0.590

4 0.045 0.058 0.527 0.493

5 0.028 0.041 0.472 0.432

6 - 10 0.052 0.096 0.375 0.318

11 - 15 0.014 0.033 0.231 0.187

Over 15 0.008 0.029 0.128 0.093

2004 1 0.588 0.458 0.989 0.988

2 0.189 0.182 0.775 0.742

3 0.075 0.091 0.578 0.568

4 0.044 0.058 0.485 0.476

5 0.027 0.041 0.427 0.405

6 - 10 0.053 0.100 0.327 0.301

11 - 15 0.015 0.036 0.202 0.177

33

Over 15 0.010 0.034 0.100 0.083

2005 1 0.595 0.445 1.000 0.999

2 0.164 0.162 0.738 0.708

3 0.076 0.091 0.584 0.557

4 0.044 0.059 0.478 0.449

5 0.029 0.043 0.415 0.371

6 - 10 0.059 0.110 0.292 0.262

11 - 15 0.018 0.043 0.169 0.140

Over 15 0.015 0.046 0.066 0.058

2006 1 0.577 0.435 1.000 1.000

2 0.165 0.158 0.784 0.760

3 0.077 0.089 0.638 0.607

4 0.046 0.060 0.534 0.504

5 0.031 0.044 0.460 0.427

6 - 10 0.065 0.114 0.337 0.305

11 - 15 0.021 0.048 0.202 0.168

Over 15 0.018 0.054 0.094 0.073

2007 1 0.567 0.427 1.000 1.000

2 0.164 0.155 0.765 0.740

3 0.078 0.090 0.618 0.590

4 0.048 0.060 0.522 0.489

5 0.032 0.045 0.448 0.420

6 - 10 0.069 0.117 0.338 0.306

11 - 15 0.022 0.049 0.203 0.176

Over 15 0.020 0.056 0.093 0.082

2008 1 0.545 0.400 1.000 1.000

2 0.170 0.156 0.773 0.754

3 0.082 0.093 0.636 0.609

4 0.051 0.065 0.540 0.517

5 0.034 0.050 0.479 0.448

6 - 10 0.074 0.129 0.373 0.329

11 - 15 0.024 0.053 0.248 0.213

Over 15 0.019 0.055 0.146 0.118

2009 1 0.491 0.351 1.000 1.000

2 0.186 0.153 0.833 0.788

3 0.087 0.091 0.659 0.622

4 0.054 0.066 0.570 0.522

5 0.038 0.052 0.503 0.453

6 - 10 0.089 0.149 0.389 0.330

11 - 15 0.030 0.067 0.249 0.202

Over 15 0.024 0.070 0.143 0.111

2010 1 0.500 0.345 1.000 1.000

2 0.159 0.140 0.736 0.729

3 0.085 0.091 0.589 0.578

4 0.057 0.068 0.500 0.472

5 0.041 0.054 0.427 0.393

6 - 10 0.095 0.156 0.312 0.270

34

11 - 15 0.034 0.070 0.176 0.156

Over 15 0.028 0.075 0.091 0.073

2011 1 0.507 0.349 1.000 1.000

2 0.162 0.147 0.699 0.689

3 0.087 0.096 0.543 0.524

4 0.058 0.071 0.448 0.423

5 0.041 0.056 0.385 0.347

6 - 10 0.091 0.154 0.277 0.242

11 - 15 0.031 0.063 0.174 0.141

Over 15 0.024 0.063 0.094 0.072

2012 1 0.510 0.357 1.000 1.000

2 0.162 0.155 0.647 0.644

3 0.089 0.102 0.491 0.476

4 0.059 0.074 0.392 0.373

5 0.040 0.056 0.337 0.302

6 - 10 0.090 0.149 0.243 0.208

11 - 15 0.029 0.057 0.159 0.119

Over 15 0.020 0.050 0.079 0.064

2013 1 0.559 0.401 1.000 1.000

2 0.148 0.150 0.677 0.666

3 0.081 0.096 0.506 0.475

4 0.053 0.069 0.395 0.361

5 0.036 0.052 0.311 0.285

6 - 10 0.081 0.136 0.208 0.176

11 - 15 0.025 0.051 0.114 0.082

Over 15 0.018 0.043 0.060 0.039

2014 1 0.526 0.380 1.000 1.000

2 0.168 0.166 0.742 0.714

3 0.090 0.106 0.589 0.559

4 0.057 0.074 0.479 0.442

5 0.038 0.055 0.396 0.365

6 - 10 0.083 0.137 0.270 0.232

11 - 15 0.024 0.047 0.139 0.107

Over 15 0.016 0.035 0.059 0.045

35

Table 2 Time Variation in Portfolio Diversification

This table reports the actual and the expected aggregate level diversification measures for

each of the twenty years in the sample period. Three diversification measures are reported: (i)

number of stocks in the portfolio (NST KS), (ii) sum of squared portfolio weights (SSPW),

and (iii) normalized portfolio variance (NV). The normalized variance of a portfolio is the

ratio of portfolio variance and the average variance of stocks in the portfolio. The covariance

matrix is estimated using past twenty years of monthly returns data. Panel A reports the

means for all female investors, Panel B reports the means for all male investors. The

individual investor data are from Finnish Central Securities Depository (FCSD) for the period

from 1995 to 2014.

Panel A: Diversification Measures of All Female Investors

Year Number of Stocks

Sum of Squared Portfolio Weights

Normalized Variance

Gross monthly return

1995 1.858 0.688 0.885 0.002

1996 1.913 0.703 0.859 0.036

1997 1.905 0.694 0.879 0.050

1998 2.035 0.679 0.855 0.025

1999 2.012 0.709 0.905 0.006

2000 2.103 0.683 0.772 -0.013

2001 2.207 0.666 0.812 0.015

2002 2.418 0.658 0.825 -0.005

2003 2.231 0.666 0.827 0.036

2004 2.305 0.673 0.804 0.034

2005 2.480 0.655 0.791 0.046

2006 2.650 0.632 0.796 0.029

2007 2.740 0.619 0.785 0.020

2008 2.796 0.615 0.791 -0.032

2009 3.124 0.595 0.782 0.061

2010 3.288 0.573 0.728 0.042

2011 3.121 0.586 0.707 0.015

2012 3.022 0.580 0.690 0.045

2013 2.793 0.612 0.682 0.062

2014 2.792 0.658 0.739 0.137

Mean 2.490 0.647 0.796 0.031

Median 2.449 0.658 0.794 0.031

Min 1.858 0.573 0.682 -0.032

Max 3.288 0.709 0.905 0.137

25th 2.086 0.614 0.764 0.013

75th 2.794 0.680 0.834 0.045

36

Panel B: Diversification Measures of All Male Investors

Year Number of Stocks

Sum of Squared Portfolio Weights

Normalized Variance

Gross monthly return

1995 2.044 0.668 0.865 0.003

1996 2.144 0.684 0.823 0.041

1997 2.271 0.654 0.832 0.051

1998 2.504 0.625 0.811 0.036

1999 2.683 0.629 0.863 0.029

2000 3.033 0.577 0.684 0.002

2001 3.193 0.553 0.715 0.026

2002 3.546 0.537 0.732 0.004

2003 3.345 0.547 0.729 0.043

2004 3.568 0.543 0.695 0.043

2005 4.012 0.515 0.662 0.055

2006 4.271 0.494 0.675 0.036

2007 4.377 0.483 0.663 0.031

2008 4.468 0.471 0.667 -0.014

2009 5.117 0.439 0.636 0.080

2010 5.314 0.418 0.586 0.060

2011 4.932 0.434 0.569 0.036

2012 4.529 0.443 0.561 0.064

2013 4.182 0.476 0.543 0.090

2014 4.002 0.532 0.614 0.269

Mean 3.677 0.536 0.696 0.049

Median 3.785 0.534 0.679 0.039

Min 2.044 0.418 0.543 -0.014

Max 5.314 0.684 0.865 0.269

25th 2.945 0.474 0.630 0.028

75th 4.400 0.589 0.752 0.056

37

Table 3 Summary statistics of Investor-Level Cross-Sectional Regression variables

This table reports the summary statistics of regression variables. The normalized variance of

a portfolio is the ratio of portfolio variance and the average variance of stocks in the portfolio.

The covariance matrix is estimated using past twenty years of monthly returns data. Portfolio

size is the total value of portfolio held by household in Euro. Income is the total annual

household income. PhD represents the number of people in investor’s postcode that has

attained a PhD degree. The language dummy variable is set to 1 if the investor is Finnish

speaking, 0 otherwise. Age is the age of the head of the household. Investment Experience is

the number of years between account opening date and December 31, 2014. Among the

behavioural bias proxies, the Overconfidence Proxy is set to one for an investor if he or she

belongs to the highest portfolio turnover quintile and the lowest risk-adjusted performance

quintile. Local Bias measure is defined as the proportion of investor portfolio that is invested

in stocks of firms located within a 250 mile radius from her location (postcode). Panel A

reports the summary statistics for all female investors, Panel B reports the summary statistics

for all male investors. The individual investor data are from Finnish Central Securities

Depository (FCSD) for the period from 1995 to 2014.

Panel A: Regression summary statistics for female investors

Mean Median Std Dev Minimum Maximum 25th Pctl 75th Pctl

Normalized Variance 0.721 0.957 0.362 0.000 1.324 0.407 1.000

Portfolio Size 84550.350 5903.530 1283648.540 0.000 716124268.000 1489.150 26983.000

Income 31903.720 31668.000 4468.570 23849.000 41428.000 28422.000 34945.000

PhD 2884.040 605.000 3341.510 0.000 9263.000 35.000 6485.000

Language 0.782 1.000 0.413 0.000 1.000 1.000 1.000

Age of investors 50.526 53.000 20.093 -63.000 168.000 36.000 65.000

Investment Experience 60.063 63.000 20.397 -49.000 178.000 46.000 74.000

Overconfidence Proxy 0.031 0.000 0.174 0.000 1.000 0.000 0.000

Local Bias 0.931 1.000 0.254 0.000 1.000 1.000 1.000

Panel B: Regression summary statistics for male investors

Mean Median Std Dev Minimum Maximum 25th Pctl 75th Pctl

Normalized Variance 0.578 0.584 0.402 0.000 1.332 0.179 1.000

Portfolio Size 100462.880 8949.160 1721847.850 0.000 635244946.000 2101.400 39392.390

Income 32306.120 32023.000 4350.470 23849.000 41428.000 28713.000 34945.000

PhD 2451.270 232.000 3253.600 0.000 9263.000 19.000 5624.000

Language 0.784 1.000 0.411 0.000 1.000 1.000 1.000

Age of investors 47.542 48.000 18.058 -54.000 130.000 34.000 61.000

Investment Experience 56.044 56.000 18.584 -40.000 135.000 42.000 69.000

Overconfidence Proxy 0.023 0.000 0.151 0.000 1.000 0.000 0.000

Local Bias 0.919 1.000 0.273 0.000 1.000 1.000 1.000

38

Table 4 Investor-Level Cross-Sectional Regression Estimates

This table reports the estimates of cross-sectional regressions, where the negative of the

normalized variance (NV) of a household is the dependent variable and a set of household

and portfolio characteristics are used as independent variables. The normalized variance of a

portfolio is the ratio of portfolio variance and the average variance of stocks in the portfolio.

The covariance matrix is estimated using past twenty years of monthly returns data. Portfolio

size is the total value of portfolio held by household in Euro. Income is the total annual

household income. PhD represents the number of people in investor’s zip code that has

attained a PhD degree. The language dummy variable is set to 1 if the investor is Finnish

speaking, 0 otherwise. Age is the age of the head of the household. Investment Experience is

the number of years between account opening date and December 31, 2014. Among the

behavioural bias proxies, the Overconfidence Proxy is set to one for an investor if he or she

belongs to the highest portfolio turnover quintile and the lowest risk-adjusted performance

quintile. Local Bias measure is defined as the proportion of investor portfolio that is invested

in stocks of firms located within a 250 mile radius from her location (postcode). Panel A

reports the regression estimates for all female investors, Panel B reports the regression

estimates for all male investors. The individual investor data are from Finnish Central

Securities Depository (FCSD) for the period from 1995 to 2014.

39

Panel A: Regression Specification (Female)

1 2 3 4

Intercept -1.203*** -0.807*** -0.752*** -1.091***

0.004 0.001 0.001 0.004

Investor Characteristics

Income 1.193E-05*

8.297E-06*

0.000

0.000

PhD 1.690E-04***

1.490E-04***

0.000

0.000

Language -0.028***

-0.026***

0.001

0.001

Age of investors (years)

0 - 9 0.039***

-0.287***

0.004

0.007

10 - 19 0.075***

-0.210***

0.003

0.006

20 -29 0.083***

-0.150***

0.003

0.005

30 - 39 0.077***

-0.100***

0.003

0.005

40 - 49 0.083***

-0.045***

0.003

0.004

50 - 59 0.108***

0.018***

0.003

0.004

60 - 69 0.105***

0.052***

0.003

0.004

70 - 79 0.064***

0.050***

0.003

0.004

80 - 89 0.018***

0.017***

0.003

0.003

Sophistication Proxy

Investment Experience

0 - 9

0.114***

0.381***

0.003

0.008

10 - 19

0.100***

0.332***

0.002

0.006

20 +

0.089***

0.145***

0.001

0.003

Behavioural Bias Proxies

Overconfidence Proxy

-0.110*** -0.078***

0.001 0.002

Local Bias

0.037*** 0.004**

0.001 0.001

Control variables

Portfolio Size

4.554E-08*

0.000

Number of Investors 1,034,935 3,248,475 3,248,475 1,034,935

40

Panel B: Regression Specification (Male)

1 2 3 4

Intercept -1.398*** 0.776*** -0.626*** 1.238***

0.004 0.001 0.001 0.004

Investor Characteristics

Income 1.895E-05*

1.381E-05*

0.000

0.000

PhD 1.600E-04***

1.260E-04***

0.000

0.000

Language -0.028***

-0.028***

0.001

0.001

Age of investors (years)

0 - 9 -0.008**

-0.409***

0.004

0.006

10 - 19 0.059***

-0.343***

0.003

0.005

20 -29 0.175***

-0.190***

0.003

0.005

30 - 39 0.215***

-0.097***

0.003

0.004

40 - 49 0.201***

-0.048***

0.003

0.004

50 - 59 0.196***

0.019***

0.003

0.004

60 - 69 0.182***

0.070***

0.003

0.004

70 - 79 0.116***

0.072***

0.003

0.004

80 - 89 0.053***

0.048**

0.003

0.003

Sophistication Proxy

Investment Experience

0 - 9

0.071***

0.407

0.003

0.008

10 - 19

0.062***

0.402

0.002

0.005

20 +

0.193***

0.245

0.001

0.003

Behavioural Bias Proxies

Overconfidence Proxy

-0.010*** 0.018

0.001 0.002

Local Bias

0.053*** -0.003

0.001 0.001

Control variables

Portfolio Size

1.939E-08*

0.000

Number of Investors 2,016,840 6,499,674 6,499,674 2,016,840

41

Table 5 Portfolios performance and Turnover

This table reports the monthly gross return of each investor groups of the twenty years in the

sample period. Turnover rate is the average of monthly buy and sell turnover rates based on

Barber and Odean (2001) method. The following statistics are reported: mean, median, 25th

percentile, 75th percentile and yearly average return and turnover rate for both male and

female investors. The individual investor data are from Finnish Central Securities Depository

(FCSD) for the period from 1995 to 2014.

Year Monthly Gross Return(Female)

Monthly Gross Return(Male)

Turnover (Female)

Turnover (Male)

1995 0.002 0.003 8.019E-01 2.153E+12

1996 0.036 0.041 9.588E+11 1.113E+00

1997 0.050 0.051 7.527E-01 3.098E+12

1998 0.025 0.036 3.884E+11 1.408E+13

1999 0.006 0.029 1.110E+12 4.745E+12

2000 -0.013 0.002 2.275E+13 1.789E+26

2001 0.015 0.026 7.729E+08 1.056E+13

2002 -0.005 0.004 5.239E+10 5.622E+14

2003 0.036 0.043 2.587E+11 1.666E+13

2004 0.034 0.043 9.046E+12 1.266E+14

2005 0.046 0.055 1.715E+12 5.013E+13

2006 0.029 0.036 3.490E+00 5.481E+12

2007 0.020 0.031 2.742E+12 6.452E+13

2008 -0.032 -0.014 7.545E+24 1.164E+14

2009 0.061 0.080 3.078E+12 1.956E+13

2010 0.042 0.060 6.705E+11 7.713E+13

2011 0.015 0.036 1.495E+12 2.744E+13

2012 0.045 0.064 3.095E+11 2.875E+13

2013 0.062 0.090 7.681E+12 4.797E+13

2014 0.137 0.269 2.133E+11 4.217E+13

Mean 0.031 0.049 3.772E+23 8.947E+24

Median 0.031 0.039 8.146E+11 2.809E+13

Min -0.032 -0.014 7.527E-01 1.113E+00

Max 0.137 0.269 7.545E+24 1.789E+26

25th 0.013 0.028 1.730E+11 9.292E+12

75th 0.045 0.056 2.826E+12 6.767E+13

42

Table 6 Diversification and portfolios performance

This table reports the performance statistics for investor groups (deciles) formed by sorting

on the portfolio diversification measure (normalized variance). The normalized variance (NV)

of a portfolio is the ratio of portfolio variance and the average variance of stocks in the

portfolio. The covariance matrix is estimated using past twenty years of monthly returns data.

Barber and Odean (2001) monthly gross returns are used to compute the performance

measures over sample period. The following statistics are reported: mean, median, cross-

sectional standard deviation, 25th percentile, 75th percentile. Panel A reports the results for

all female investors, Panel B reports the regression estimates for all male investors. The

individual investor data are from Finnish Central Securities Depository (FCSD) for the period

from 1995 to 2014.

Panel A: Monthly gross return for All Female investors

Mean Median Std Dev Minimum Maximum 25th Pctl 75th Pctl

Low Div 0.036 0.026 0.072 -0.096 0.587 0.004 0.049

D2 0.017 0.015 0.058 -0.096 0.587 -0.009 0.033

D3 0.017 0.014 0.069 -0.096 0.587 -0.015 0.036

D4 0.023 0.014 0.085 -0.096 0.587 -0.010 0.037

High Div 0.049 0.020 0.123 -0.096 0.587 -0.003 0.051

Panel B: Monthly gross return for All Male investors

Mean Median Std Dev Minimum Maximum 25th Pctl 75th Pctl

Low Div 0.060 0.039 0.125 -0.096 1.439 0.015 0.071

D2 0.027 0.019 0.098 -0.096 1.439 -0.005 0.039

D3 0.025 0.014 0.123 -0.096 1.439 -0.013 0.035

D4 0.037 0.014 0.166 -0.096 1.439 -0.015 0.041

High Div 0.052 0.015 0.205 -0.096 1.439 -0.010 0.044

43

Appendix A: The definition of variables

Independent Variables:

Definition Justification

The normalized variance (NV) of a

portfolio is the ratio of portfolio

variance and the average variance of

stocks in the portfolio.

𝑁𝑉 =𝜎𝑝

2

𝜎2

The NV measure indicates that portfolio variance can be reduced by

increasing the number of stocks in the portfolio or by a proper selection of

stocks such that the average covariance (or correlation) among stocks in the

portfolio is lower. Variance reduction through active and proper stock

selection reflects “skill” in portfolio composition, while addition of stocks in

the portfolio without lowering the average portfolio correlation is likely to

reflect “portfolio breadth” (Goetzmann et al. 2005).

Dependent Variables:

Definition Justification

Income is the total annual household

income.

Goezmann and Kummar 2008 show that high-income investors are better

diversified than low-income investors.

PhD represents the number of people

in investor’s postcode that has attained

a PhD degree.

Prior studies demonstrate that individuals with higher IQs exhibit superior

trading performance (mainly driven by purchases), while those with a higher

level of education are more likely to be financially sophisticated (Calvet et

al, 2007).

Language dummy variable is set to 1

if the investor is Finnish speaking, 0

otherwise.

Most of the population in Finland speaks Finnish, with a minority of around

5% of the sample speaking a foreign tongue (mainly Swedish). Native

Finnish speakers prefer to hold and trade stocks of Finnish companies that

that publish annual reports in Finnish (Grinblatt and Keloharju, 2001). Based

on Karhunen and Keloharju (2001), that show that Swedish speaking

investors hold larger portfolios, we might expect Finnish speaking investors

to trade more than Swedish speaking investors. This would be a sign of a

tendency of less experienced investors to trade more than what is required to

rebalance the portfolio. We include a dummy variable for language to

determine the relationship between language background of the investor and

portfolio diversification.

Age is the age of the head of the

household.

Portfolio diversification could increase with age because with experience,

investors acquire more information about the market (King and Leape 1987).

We include a set of age dummy variables and analyze the relationship

between portfolio value and these age variables.

Investment experience is the number

of years between account opening date

and December 31, 2014.

Portfolio diversification could increase with experience; investors acquire

more information about the market (King and Leape, 1987).

44

Overconfidence proxy is set to one for

an investor if he or she belongs to the

highest portfolio turnover quintile and

the lowest risk-adjusted performance

quintile (Goezmann and Kummar

2008)..

To examine the overconfidence-diversification relation, we define an

overconfidence proxy and examine whether it is correlated with portfolio

diversification. The proxy is set to one for investors who are in the highest

portfolio turnover quintile and lowest performance quintile, i.e., those

investors who trade the most but attain the worst performance (Barber and

Odean 2001).

Local bias is defined as the proportion

of investor portfolio that is invested in

stocks of firms located within a 250

mile radius from her location

(Goezmann and Kummar 2008).

A stronger propensity to hold local stocks could be correlated with the level

of portfolio diversification. Several studies (e.g., Huberman, 2001; Zhu,

2002; Ivkovic and Weisbenner, 2005) indicate that individual investors

exhibit a preference for local stocks. Familiarity with local stocks could

exacerbate the illusion of control, and investors might fail to realize that

more knowledge about the selected stocks does not necessarily imply control

over the outcome (i.e., returns earned by the portfolio). Because of

familiarity, investors might also perceive local stocks to be relatively less

risky (Health and Tversky 1991).

Portfolio size is the total value of

portfolio held by household in Euro.

The most common traditional explanation for portfolio under-diversification

posits that investors fail to diversify appropriately because they hold small

portfolios (e.g. Brennan 1975, Goldsmith 1976).