Does concentration increase performance of equity funds?

Does concentration increase performance of

equity funds?

----An empirical study in the Chinese fund market

Xiangyu Tong

Rijksuniversiteit Groningen

MSc in Business Administration Finance

University of Groningen, Groningen, the Netherlands

Supervised by Drs. M.M. Kramer

Abstract

This paper examines the impact of investment concentration on fund performance in China, using 146 equity funds from December 2003 to March 2009. Both an industry concentration effect and a stock concentration effect are tested. After applying portfolio approach, cross sectional regression approach and panel regression approach, fund performance is found positively related with its concentration level, with style, age, size, expense ratio and turnover characteristics controlled. This finding supports the view that concentration offers superior performance. In addition, we find no significant effect from industry concentration, suggesting stock picking ability is of more importance for Chinese fund managers.

Table of Contents

1. Introduction ... 1

1.1 Concentration... 3

1.2 Performance ... 4

1.3 Other Influences on Performance ... 5

2. Methodology ... 6 2.1 Concentration Measure... 7 2.2 Performance Measure... 8 3. Data... 10 3.1 Sample Description... 10 3.2 Summary Statistics ... 10 4. Empirical Evidence ... 12 4.1 Portfolio Approach ... 12 4.1.1 Concentration Portfolios ... 13 4.1.2 Size Portfolios ... 16 4.1.3 Style Portfolios ... 18

4.2 Cross Sectional Regression ... 21

4.3 Panel Regression ... 23

4.4 Robust Test ... 25

1. Introduction

From the end of 2006 to the end of 2007, the Chinese security market enjoyed a boom. Reports show that in 2007 the average return of funds has almost reached 24%, and the Shanghai index increased by more than 30% from November 2006 to the end of 2007. Along with this prosperity in the security market, it is observed that funds were gradually enlarging their investment on sectors such as iron and steel, petrochemicals and automobiles. The average number of stocks held in equity funds in 2006 was about 97.26, yet until the end of 2007, this average number dropped by approximately 36.39% to an amount of 61.87. Among the 10 most concentrated funds in 2007, even the largest number of stocks held was only about 43. Evidence shows that fund managers have been gradually increasing their investment concentration to only a few industries or securities as the result of their increasing self- confidence and information availability within the flourishing market (Zhu, Li (2007)). Thus the question arises: Why do fund managers increase their investment concentration? Does concentration really offer superior performance and to what extent does it contribute to the high return of funds if it does? To my knowledge, most research conducted in China is focusing on the evaluation of fund performance. Very few studies have shed light on the influence of concentration of assets on fund performance up until now. In addition, the unresolved worldwide debate on this issue also leaves it as an open question in the field of investment study. A better understanding on the relationship between fund concentration and its performance will be of great importance for both investors and researchers. On this basis, the key issue addressed in this paper is whether concentrative investing creates value in China’s fund market.

out that index funds are more favorable due to their low cost. Bogle (2000) states that index funds outperform by 350 basis points as a result of management expenses, brokerage costs, sales charges and tax advantages. Arnott et al. (2000) co nfirm the superior performance of index funds and find that this superior performance is enhanced when taxes are considered.

increasing his own rewards or maximizing the returns to investors, or due to his own vision.

However, does concentration necessarily suggest a high pay-off? Actually, the performance of active managed funds has always been a topic of longstanding debate. Starting from Jensen (1968), many researchers have shown that the performance of active managed funds on average has been inferior to that of index funds. This includes the important empirical research by Sharpe (1966) and Jensen (1987), which first states that in a long period of time, the returns of investment funds should be lower than the returns of market indices with its corresponding period. However, a completely opposite result is provided in several subsequent studies. Since Grossman and Stiglitz (1980) brought force questions to the theory of ‘efficient capital markets’, which argued that prices cannot perfectly reflect the information that is available because of the cost of information, a competitive equilibrium cannot exist. Quite a lot of subsequent relevant evidence supported market inefficiency, which provides a theoretical basis for active management. Based on this, several literatures on the performance of fund management have emerged, such as Grinblatt and Titman (1989), Dainel et al.(1997), Black et al.(1999), Brinson et al.(1986, 1991), Chen et al. (2000), Wermers (2000), Wermers (2003), Pinnuck (2003), Gallagher and Looi (2005). In particular, Wermers (2003) examined the relationship between active fund returns and tracking errors for a sample of US mutual funds. A positive relationship was found, indicating that cross-sectional variation in fund returns is explained by successful managers taking larger portfolio bets. However, as the comparison benchmark differs in these studies, consistent results have never arrived on whether active funds create significant excess returns, and the source of excess returns. Based on this, my paper will focus on the issue of concentrative investing of equity funds in the Chinese market, thereby trying to give some empirical evidence for the value of active investing.

1.1 Concentration

concentration has mainly two aspects which are derived from relevant research: industry concentration, which reflects the ability of industry selection by fund managers, and security concentration, which reflects the ability of stock selection by fund managers.

Kacperczyk, Sialm and Zheng (2005) discussed the interrelationship between the degree of industry concentration in active managed equity funds and the fund returns. Their results showed that in the USA there is a significant positive correlation. The funds with high investment concentration have an average annual abnormal return of 1.58% before deducting costs and 0.33% after deducting costs. For funds with a low degree of concentration, the average annual abnormal returns become 0.36% and -0.77%, respectively. Simone Brands et al (2006) also suggested a positive relationship between fund performance and portfolio concentration. The positive relationship is stronger for stocks in which active managers hold overweight positions, and for stocks outside the largest 50 stocks listed on the Australian Stock Exchange (ASX). In contrast, Yan (2008) finds no evidence that focused funds outperform, stating that focused funds even significantly underperform after deducting expenses.

Both Simone Brands et al (2006) and Kacperczyk, Sialm and Zheng (2005) applied the Industry Concentration Index (ICI) as a measure of Industry concentration. Ivkovic (2008) uses the Herfindahl index to evaluate the concentration of stock holdings by individual investors. However, among the research subjected to fund concentration, Kacperczyk et al. (2005) only take industry concentration as a measurement for the degree of investing concentration. As a result, it does not consider the influence of individual security concentration on the value of funds. Although, Yan (2008) uses the number of stock holdings as a concentration measure, which might have a potential large fund bias. Thus, this paper will apply both the industry concentration index from Kacperczyk et al. (2005) and stock concentration indices to further investigate the influence from industry concentration and individual stock concentration on the value of funds in the Chinese market.

1.2 Performance

studies on fund performance began to accumulate. Jensen (1968) suggests the Jensen alpha as a measure of fund performance. Thereafter, Fama and French (1993) proposed a three factor model, which was used to measure stock performance, considering the influence of firm size, book-to-market ratio and excess return to market average on the performance of funds. Carhart (1997) added a momentum factor to Fama’s three factor model, which is now the so called four factor model.

Most research in China adopts these above mentioned methods. Yang and Wang (2003) use the Jensen Alpha and Fama and French three- factor model in turn, to evaluate fund performance. The Fama and French model is found to be more applicable as an explanation of the fund performance in the Chinese market. Therefore, the Fama and French three factor model and raw return (explained in paragraph 2.2) is chosen to represent the fund performance measurement in this paper.

1.3 Other Influences on Performance

Recent research shows that the performance of a fund is affected to some extent by its size. Chen, Hong and Kubik (2004) believe that the funds’ performance decays with their size, as a result of diseconomies of scale. Yan (2008) supports this viewpoint by examining the effect of liquidity and investment style on the relation between fund size and fund performance. He suggests liquidity as an important reason why fund size erodes performance. Kacpertczyk et al (2005) also supported this. Besides that, fund age is also an important issue whenever coming to fund performance discussions. For instance, both Kacpertczyk et al (2005) and Yan （2008）have found negative relationship between fund age and its performance. There is also quite a lot empirical evidence supporting a negative effect from the expense ratio and positive influence from turnover on fund performance. (Grinblatt and Titman (1989) and Wermers (2000)) Therefore, this paper will control the size, age, expense ratio and turnover of funds, and further investigate whether these fund characteristics have influence on fund performance.

and panel regression approach and a robust test by dividing the sample into two sub-periods. Section 5 will conclude the findings.

2. Methodology

The main hypothesis of this paper is：

The relationship between fund performance and its concentration level is positive. More concentrated funds have higher returns than less concentrated funds.

To test the impact of investment concentration on fund performance, we apply the portfolio, cross sectional, and panel approaches separately. (a) For the portfolio approach, we compare the difference of performance between several sub-portfolios, sorted by the concentration level, size and investment style of funds separately. Concentration portfolios are used to test concentration effects whilst size and style portfolios are used for controlling effects from fund size and investment style on the concentration-performance relation..

(b) Then after the cross sectional approach will be used with the Fama-French 3 factor alpha as the performance measure. We build on a basic relationship between a concentration index and other variables for control. We use size, age, expense ratio and turnover of the funds as control variables, which have been identified as important in the literature on fund performance. The relationship can be written as:

i i i i i i

i CI Size Age EXP TU

(c) In the cross sectional approach, we take the equally weighted time series average of each variable as representative for the true values. This results in the loss of quite a few time series information. To further investigate the inherent performance- concentration relation, taking full advantage of our p anel data, we apply panel regression method, with the raw returns of funds as the performance measure. Moreover, panel regression can also provide us a robust check for the feasibility of the Fama-French alpha as a measure for fund performance. As the Fama-French alpha already includes information about the 3 risk factors, in the panel regression approach, using raw return as a performance measure, the influence of market, size and value factors should be considered. Therefore, the tested model can be written as follows:

t i t i t i t i t i t

i CI Size Age EXP TU

Per_, ₀₁ _, ₂ln( )_, ₃ln( )_, ₄( )_, ₅ln( )_,

₆(R_m,t R_f,t)₇SMB_t ₈HML_t _i,t (2)

Where,Per_i,t is the performance of fund i at time t, which is measured with fund raw return. Similar with equation (1), the independent variable CI_i,t stands for the equally weighted average degree of concentration for fund i at time t, measured with the industry concentration index and stock concentration indices, separately. As for the expense ratio, the Fama-French 3 risk factors, the natural logarithm of fund size, age, and turnover are applied to control the other effects on fund performance.

Finally, we apply a robust test on the concentration-performance relation. Since the Chinese security market suffered a dramatic change around the beginning of 2007, we separate the sample period into 2 sub-periods: the fourth quarter of 2003 to the last quarter of 2006, and the first quarter of 2007 to the first quarter of 2009, on a quarterly basis. By comparing regression results between the 2 sub-periods, we can see if the relationship between concentration and fund performance is affected by the change of external environments.

2.1 Concentration Measure

deviates from the market portfolio. Kacpertczyk et al (2005) defined it as1: 2 , 1 , ) ( it N i t i w w ICI 



The variable stands for the weight of the investment in industry i over the whole investment at time t2, and wi,t is the market average weight of industry i, measured

with the weight of industry i in the whole investment, by all of the sample funds in our study. N represents the number of industries spread in the corresponding fund.

Next to the ICI measure we use the stock concentration index, which is defined as:



Where, N stands for the number of most weighted stock holdings under measurement. For example, Top3 is the sum of weights from the top 3 most weighted stocks in a fund. Thus, the stock concentration indices Top3, Top5 and Top10 are expressed as:

3 , 1 i t i w 







2.2 Performance Measure

We apply both the Fama-French three factor alpha and raw return to measure the performance of funds, for the cross sectional and panel regression analyses, respectively. The raw return of funds is expressed as:

) / ln( _{, , 1} ,t  it it i P P RR (5)

In which, RRi,tis the raw return of fund i at time t, Pi,tand Pi,t1 represent the price

of fund i at time t, and time t -1, respectively. (For closed-end funds, Pi,t is defined

as the net asset value fund i at time t.)

1

The industry concentration index is kind of a market-adjusted Herfindahl Index, which is widely used in industry study, defined as



, . Replacing the Industry Concentration Index by Herfindahl Index does not

change the qualitative aspects of our results.

2

Due to the limited explanatory ability of a one factor model for Chinese funds, as Yang and Wang (2003) suggested, we apply the Fama-French three factor model:

t i t t t i t f t m t i t f t i R R R SMB HML R,  ,  1, ( ,  , )2,  3,  , (6)

Where,R_i,_t, Rf,t and Rm,t stands for the raw return of fund iat time t , and the

risk free and market return at time t, respectively. SMB is the excess return caused by the size factor, and HML is the excess return due to the value factor.

The ZhongXin Standard & Poor's style indices are applied to calculate SMB and HML factors in the Fama & French (1993) model. The difference between ZhongXin S&P small cap index and large cap index stands for SMB, and the difference between ZhongXin S&P value index and growth index stands for HML.

The risk free rate applied in this paper is the corresponding annual interest rate on a fixed deposit in each period, discounted on a quarterly basis. The annual interest rate on fixed deposit was published by the Industrial & Commercial Bank of China (ICBC) and was updated on the 29th Oct 2004, 19th Aug 2006, 18th Mar 2007, 19th May 2007, 21st Jul 2007, 22nd Aug 2007, 15th Sep 2007, 21st Dec 2007, 9th Oct 2008, 30th Oct 2008, 27th Nov 2008 and 23rd Dec 2008.

3. Data

3.1 Sample Description

On the 28th of June, 2009, there were 427 open-end funds and 31 closed-end funds in the Chinese security market, of which 272 were equity funds. This paper uses all of these equity funds as studying objects. After deleting the funds without data or with wrong data, and funds which have no sufficient data, 146 funds remain, of which 133 are open-end funds and 13 are closed-end funds. According to the rules of the China Securities Regulatory Commission (CSRC), funds publicize their composition in the portfolio at the end of each quarter. Therefore, the time horizon starts from the last quarter of 2003 to the first quarter of 2009. The reason for choosing this period is there were only close-end funds in China until the first open-end fund: Hua’an Innovations, was established on the 21st of September 2001. The Chinese fund market began to undergo vigorous development only as late as 2003.

The data of this paper are mainly derived from 2 sources: the main Chinese fund websites and the quarterly reports from fund companies. Chinafund.com (one of the biggest Chinese fund portals) provides very detailed information o n funds’ established dates and daily prices on net asset values. And the investment distribution in 22 industries, the holding of top 10 stocks, the market value, the expense ratio and turnover are collected from the quarterly report of fund companies. The investment style information is sourced from the website of Morningstar China.

3.2 Summary Statistics

Panel A of Table 1 shows descriptive statistics for the whole equity fund sample. The equity funds under this research have a mean industry concentration index of 5.81%, and the average stock concentration is 15.26%，23.04% and 37.37% for the Top3,

Top5 and Top10, respectively. The industry concentration index varies from 1.83% to

concentration indices and other variables. It is obvious that there exist statistic ally significant positive or negative correlations between these variables. Overall, there is some evidence that concentration funds have higher expense ratios and turnover, and they tend to be younger and smaller than diversified funds.

Table 1

Sample Descriptive Statistics

The sample comes from Hexun mutual fund database and inc ludes all Chinese equity funds existed during the period from December 2003 to March 2009, except for the funds without data or those having limited observations. We compute the equally weighted average for each fund, through the time series of the 22 quarterly figures. Panel A presents the summary statistics of the equity funds. Panel B reports the contemporaneous correlation between the main var iables included in this paper. The industry concentration Index is defined as , where is the weight of investment in industry i over the whole investment at time t, and is the market average weight of industry i. The stock concentration indexes of the Top3, Top5 and Top 10 are defined as , , and , respectively, in which is the weight of security i, which has the top3, top5 and top10 largest weight in the whole fund portfolio at time t. Age of fund is the number of years a fund has existed. The expense ratio is determined as the funds’ operating expenses divided by the value of assets under management, and turnover is the aggregate purchases of sales of securities divided by the fund TNA, all on a quarterly basis.

Panel A: Fund Characteristics

M ean M edian M inimum M aximum

Number of funds 146

Number of holdings 78.54 61 19 308

Industry concentration (ICI) -% 5.81 5.29 1.83 18.2 Stock concentration

(Top3) -% 15.26 14.58 7.7 30.67

(Top5) -% 23.04 22.41 10.60 41.91

(Top10) -% 37.37 36.71 15.98 64.51

Total net assets (TNA)-￥mil 5,941.13 4,388.79 226.83 23,416.16

Age of funds (AGE)-yrs 3.86 3.02 1.03 11.02

Expense ratio-% 1.38 1.34 0.05 12.85

Turnover-% 79.67 73.98 0.71 859.54

Panel B: Correlation Structure

Variables ICI Top3 Top5 Top10 Expense Turnover Age TNA ICI 1.00 Top3 0.29*** 1.00 Top5 0.30*** 0.95*** 1.00 Top10 0.23*** 0.78*** 0.88* 1.00 Expense 0.13*** 0.15** 0.16* 0.21* 1.00 Turnover 0.14** 0.07** 0.10** 0.15** 0.08*** 1.00 Age -0.11** -0.12** -0.09* -0.04* -0.14** -0.06** 1.00 TNA -0.03** -0.06* -0.04 -0.07** -0.12** -0.05** -0.18** 1.00 ***1% significance, **5% signif icance, *10% signif icance

4. Empirical Evidence

In this section, the main empirical results are presented. We apply a portfolio approach, a cross sectional regression approach, and a panel regression approach to examine the impact of investment concentration on fund performance. We first examine the influence of concentration on fund performance with concentration quintiles, and then we consider the potential external influences on the observed concentration-performance relation, using size and style portfolios in turn for control. Second, we adopt the cross sectional regression model defined in equation (1) to explore the relation between investment concentration and fund performance. Finally, the panel regression model defined in equation (2) is applied to further investigate the concentration-performance relation, with panel information fully used.

4.1 Portfolio Approach

over time series and Fama-French 3-factoer alpha. For this portfolio approach, we use all 272 equity funds to analyze, instead of the consolidated 146 funds, aiming to reduce selection bias.

4.1.1 Concentration Portfolios

Table 2 summarizes the portfolio performance of each quintile based on different concentration levels. With respect to raw returns, the most industry concentrated portfolio outperformed the most industry diversified portfolio significantly by 2.9% (t=2.13). Sorted with stock concentration index Top3, the raw return of the highest stock concentrated portfolio exceeded that of the most stock diversified portfolio by about 2.8% (t=2.64), different from zero at 1% significance level. Noteworthy results are found for quintiles segregated with another stock concentration index: Top10, but not for the quintiles segregated by stock concentration Top5. The differences between the mean return of bottom 2 quintiles and the mean return of top 2 quintiles are also statistically significant with quintiles sorted by the industry concentrated index (ICI) and stock concentrated indices. Overall, when performance is evaluated with raw returns, concentrated portfolios have a superior performance relative to diversified portfolios, although some of the excess returns are not statistically significant.

Table 2

Concentration Portfolios

This table presents the performance of portfolios segregated into deciles based on the equally weighted average industry concentration index, the industry concentration indices (Top3, Top5 and Top10, respectively), for each fund over the whole sample period. Fund performance is on the same principle, evaluated by the equally weighted average raw returns and the Fama-French 3-factoer alpha on a quarterly basis. The first quintile is the most diversified portfolio and the fifth quintile is the most concentrated portfolio. The last two rows display the differences between the mean returns of the top 2 and bottom 2 quintiles, and the mean returns of top and bottom quintiles. Their t-statistics are given in parentheses.

Concentration quintiles

ICI Top3 Top5 Top10

RR  RR  RR  RR  1 0.026** (1.74) 0.014 (1.22) 0.021 (1.23) 0.005 (1.33) 0.017 (1.40) 0.009 (1.21) 0.025** (1.77) 0.007 (1.03) 2 -0.002 (1.18) 0.001 (0.10) 0.004 (0.96) 0.007 (1.22) 0.017* (1.68) 0.009 (1.15) 0.026 (1.31) 0.010 (1.17) 3 0.015 (1.28) 0.004* (1.70) 0.019** (1.92) 0.019 (1.17) 0.026** (2.23) 0.010 (1.13) 0.014* (1.51) 0.011 (1.09) 4 0.037*** (2.77) 0.012 (1.16) 0.036 (1.34) 0.015* (1.11) 0.026 (1.28) 0.015 (1.27) 0.029* (1.35) 0.014 (1.16) 5 0.042* (1.69) 0.020* (1.30) 0.036* (1.45) 0.017 (1.19) 0.031** (1.63) 0.016 (1.27) 0.038** (1.74) 0.016* (1.44) Bottom 2- Top 2 0.001 (1.29) -0.002 (1.07) 0.006* (1.39) 0.003** (1.94) 0.007** (1.86) 0.005** (2.18) 0.013* (1.37) 0.004* (1.45) 5th quintile- 1st quintile 0.016* (1.72) 0.006* (1.55) 0.015*** (2.64) 0.012*** (2.63) 0.014** (2.13) 0.007** (2.05) 0.013** (1.88) 0.009* (1.48) ***1% significance, **5% signif icance, *10% signif icance

Table 3

Fama-French regression statistics

This table displays the estimated coefficients of 3 factors in the Fama-French model in each concentration quintile. All funds are included. The concentration of funds is measured with the industry concentration index and stock concentration indices separately. The first quintile is the most diversified and the fifth quintile is the most concentrated. For each quintile, the Fama-French 3-factor model is estimated. The standard errors of regression are given in parentheses, except the parentheses of the last row, which includes the t-statistics that show the difference between extreme portfolios.

Concentration quintiles

ICI Top3 Top5 Top10

4.1.2 Size Portfolios

The total net assets of funds from our sample are widely distributed, ranging from ￥ 226.83 million to ￥ 23,416.16 million up until the end of March 2009. Diseconomies of scale, argued by Chen, Hong and Kubik (2004), suggest that smaller funds easily outperform larger funds.

Therefore, to control the influence of size on funds in the concentration-performance relation, we report the performance of size quintiles in table 4. We sort the funds into different size quintiles according to the total net assets (TNA) of funds, and compare the performance of concentrated and diversified portfolios within each size quintile, based on the funds’ industry and stock concentration indices. The average TNA of the first quintile is ￥121,8.89 million and the average TNA of the last quintile is ￥13,109.06 million.

The result is reported in table 4. Consistent with the findings of Chen, Hong and Kubik (2004), smaller funds on average have superior performance over larger funds. For example, the smallest funds have an excess raw return of 4.4% over the largest funds, sorted by ICI. The difference of performance is statically significant at the 1% significance level.

Regarding the influence of size on the concentration-performance relation, we look at the effect of concentration in each size quintile. A positive difference between concentrated funds and diversified funds is found within all size quintiles, with various concentration and performance measures. It suggests that the impact of concentration on performance is not, at least not significantly, influenced by size factors. This result is in the line with that of Kacpertczyk et al (2005).

Table 4 Size Portfolios

quintile are further grouped into two portfolios, based on their industry concentration index and stock concentration indices respectively. The returns are measured by the equally weighted quarterly raw returns and the Fama-French alphas. The last row gives the difference between the equally weighted average returns of extreme quintiles : quintile 1 and quintile 5. t-statistics are given in parentheses.

Size

quintiles Concentration

ICI Top3 Top5 Top10

4.1.3 Style Portfolios

Another factor with potential influence on the concentration-performance effect is the investment style. Since the pioneering research of Basu (1997) and Banz (1981), managers begun to be aware of the influence from investment style-related attributes on fund performance. Fu and Ma (2001) find fund performances showed a parentally regulative pattern when the investment style effects were taken into account. The difference of funds performance results from the differences of the fund investment style, through the study of 51 close-end funds in China. Therefore, we take investment style to control the concentration-performance relation in this section.

The investment style of all Chinese funds can be dividend into 9 classes : small- growth, small-balanced, small- value, middle- growth, middle-balanced, middle- value, large-growth, large-balanced and large-value, according to the categorization of Morningstar China3. We use the classification of the Morningstar in our style portfolio segregation. For example, the small- growth portfolio includes funds whose size score, measured as the weighted average of net asset value of top 10 stocks held by the fund, are below-average, and whose value score, measured as the weighted average P/E ratio of top 10 stocks held by the fund, are above-average. The other 8 investment styles are defined in a similar manner. Then we divide each of the 9 portfolios into 2 sub- groups, according to their industry and stock concentration indices, respectively.

The performance of these sub-groups within each style portfolios are given in table 5, with different concentration and performance measures. The last rows from each style portfolio present the differences between concentration and diversified sub- group. We find that portfolios invested principally in small and growth stocks have superior performance over other portfolios. In contrast, portfolios which mainly focus on large-value stocks have the worst performance with respect to all concentration and performance measures. The last row shows the difference of average performance between the extreme style portfolios Small- Growth and Large-Value. It reaches a gap

3

of 2.8% at the 5% significance level, classified by the industry concentration index and the quarterly raw return measure. This finding confirms the previous result in Chen et al. (2004).

Table 5

Style Portfolios

All funds are divided by their investment styles into 9 style portfolios, according to the categorization by Morningstar China. SG, SB, SV, MG, MB, MV, LG, LB, LV stands for small-growth, small-balanced, small-value, middle-growth, middle-balanced, middle-value, large-growth, large-balanced and large-value respectively. Within each style portfolio, two equally sized sub-groups are sorted by funds’ concentration level, measured with the industry concentration index (ICI) and the stock concentration indices（Top3, Top5 and Top10）separately. The equally weighted raw return and the Fama-French alpha are applied on a quarterly basis to evaluate the performance of these sub-groups. The last row of this table gives the difference between the average return of extreme sub-groups Small-Growth and Large-Value. t-statistics are given in parentheses.

Style Concentration

ICI Top3 Top5 Top10

High-Low 0.032*** (3.32) 0.003 (0.91) 0.013** (2.41) 0.006* (1.42) 0.002* (1.88) 0.001 (0.89) 0.002** (2.39) -0.001 (1.39) M B Low _0.017 (1.04) 0.014 （1.34） 0.024 （1.03） 0.011 （1.15） 0.021 （1.27） 0.013* （1.62） 0.023 （1.19） 0.011 （0.95） High 0.046* （1.85） 0.013 （1.32） 0.026** （1.96） 0.016 （1.02） 0.025 （1.33） 0.009 （0.86） 0.032 （1.21） 0.013* （1.48） High-Low 0.029* （1.86） -0.001 （0.93） 0.002* (1.69) 0.005** (2.44) 0.004* (1.44) -0.004 (0.92) 0.009*** (2.97) 0.002 (0.99) M V Low 0.020 (1.20) 0.013* (1.76) 0.023* (1.90) 0.010 (1.16) 0.019 (1.28) 0.012 (1.17) 0.019 (1.33) 0.011 (1.24) High 0.037 (1.38) 0.015 (1.14) 0.022 (1.30) 0.015 (1.27) 0.021** (1.86) 0.012 (1.22) 0.028* (1.96) 0.014 (1.13) High-Low _0.017** (2.88) 0.003* (1.73) -0.001 (0.79) 0.005* (1.45) 0.002 (0.96) 0.000 (0.87) 0.009* (1.60) 0.003** （2.68） LG Low 0.016 (1.27) 0.012 (1.16) 0.017 (1.13) 0.006 (1.05) 0.014 (1.30) 0.012* (1.40) 0.021 (1.22) 0.009* (1.54) High 0.028 (1.06) 0.014 (1.19) 0.015* (1.41) 0.014 (1.21) 0.021 (1.17) 0.008 (1.02) 0.024** (1.97) 0.015 (1.13) High-Low 0.012* (1.54) 0.002* (1.53) -0.002 (1.28) 0.008** (1.64) 0.007* (1.57) -0.004 (1.18) 0.003* (1.57) 0.006** (1.95) LB Low 0.016 （1.37） 0.009 （1.10） 0.015 （1.29） 0.008 （1.02） 0.015 （1.31） 0.010 （0.92） 0.019* （1.66） 0.010 （1.12） High 0.031* （1.69） 0.013 （1.04） 0.019 （1.23） 0.014 （1.27） 0.019* （1.51） 0.009 （0.93） 0.022 （1.19） 0.016 （1.22） High-Low 0.015*** （3.46） 0.004** （2.81） 0.004* （1.43） 0.006* (1.58) 0.004** (1.55) -0.001 (1.29) 0.003* (1.62) 0.006** (2.29) LV Low 0.015 (1.26) 0.010 (1.20) 0.009 (1.02) 0.009 (1.29) 0.016 (1.22) 0.008 (1.14) 0.014 (1.21) 0.007 (1.18) High 0.011 (1.11) 0.011 (1.18) 0.016* (1.49) 0.012 (1.31) 0.013 (1.27) 0.013 (1.15) 0.019 (1.33) 0.018 (1.05) High-Low -0.004 (1.17) 0.001* (1.62) 0.007** (1.93) 0.003** (2.09) -0.003 (0.98) 0.005* (1.64) 0.005** (3.16) 0.011** (2.41) SG-LV 0.028** (2.05) 0.007* (1.72) 0.021** (1.97) 0.007 (1.34) 0.018*** (3.11) 0.004* (1.43) 0.013** （2.38） 0.006* （1.76） ***1% significance, **5% signif icance, *10% signif icance

concentrated peer by 0.8% at the 5% significance level. This concentration effect is more significant when we use raw return instead of the Fama-French alpha. Although some of these style portfolios statistically free themselves from the general concentration effect, such as the Small- Value category segregated by the ICI and the Fama-French alpha, the average return of less concentrated sub-portfolio exceeds the more concentrated one by 0.2%, yet is not significant. However, these minority groups do not affect the overall impact of concentration. In summation, the concentration-performance relation does not differ significantly between different style portfolios. The result is consistent with Kacpertczyk et al (2005).

4.2 Cross Sectional Regression

The portfolio approach confirms our hypothesis that more concentrated funds outperform less concentrated funds in an intuitive way. However, it has several limitations. First, the portfolio approach does not control for other factors with a potential influence on fund performance at the same time. Second, it tends to have the small sample bias when segregating funds into groups. Third, it does not take time effect into consideration, except when performance is measured with the Fama-French alpha. However, the time series information for concentration and other variables are missing. In fact, as we know, fund characteristics vary much over time and this variation might cause the change of interrelationships between different factors. Hence, we use both the cross sectional and panel regression method next to the portfolio approach to further investigate the concentration effect on fund performance. This thereby allows for the controlling of other fund characteristics, which are age, size, expense ratio and turnover, at the same time.

industry concentrated funds, this concentration-performance relation is not statistically significant. Generally speaking, the positive relationship is consistent with our previous portfolio analysis.

Table 6

Concentration and fund pe rformance: cross sectional regression

Table 6 presents the estimated coefficients of the regression model defined in equation (1):

i i i i i i

i CI Size Age EXP TU

Per 01 2ln( ) 3ln( ) 4 5ln( )  , using cross

sectional data. The sample covers 146 equity funds in China and has a time span from December 2003 to March 2009, on a quarterly basis. The dependent variable fund performance, expressed asPer_i,_t, is evaluated with the Fama-French alpha. The concentration level is measured by the

industry concentration index, defined as 2 , , )

(wit wit

ICI





 3 1 , i wit,





i wit ) separately. Besides the

expense ratio (EPX), we use the natural logar ithms of fund age (LnAge), fund size (LnSize) and turnover (LnTU) as control variables. The estimated coefficients are all expressed in thousands. The last row reports the overall R2 s of cross sectional regressions. Standard errors are presented in parentheses.

Alpha

ICI Top3 Top5 Top10

Constant 11.018** (0.14) 23.042*** (0.13) 8.012** (0.02) 33.036*** (0.10) CI 3.177 (0.10) 2.264** (0.13) 1.661*** (0.23) 1.072** (0.11) LnAge -1.572** (0.11) -1.623*** (0.18) -1.319** (0.04) -1.426** (0.11) LnSize -1.002*** (0.06) -1.137*** (0.12) -2.015** (0.09) -1.251*** (0.13) Expense ratio -4.062 (0.22) -2.014* (0.15) -3.539 (0.13) -4.255 (0.16) LnTU 0.078 (0.19) 0.081* (0.14) 0.104 (0.17) 0.093 (0.21) Overall R2 _{0.16 0.19 0.22 0.18}

***1% significance, **5% signif icance, *10% signif icance

smaller funds on average have superior performance. The effects from age and size on fund performance are all statistically and economically significant. Furthermore, the relation between expense ratio and performance are negative, and in contrast, fund turnover has a positive influence on fund performance. However the effect from fund expense ratio and turnover are both not statistically significant.

4.3 Panel Regression

As cross sectional method may yield to bias due to the loss of time series information, in this section, we apply the panel regression approach to further investigate the relationship between concentration and performance, using the unbalanced panel data. We employ the Hausman test4 and find that the random effects estimation is more appropriate in our study. More over, since the raw return measure does not reflect information on risks from Fama-French 3 factors, we have to include these 3 factors as our control variables when we apply the panel approach.

Table 7 reports the estimated coefficients of the panel regression model defined in equation (2). Their standard errors are presented below the estimates. Again, the coefficients of stock concentration indices are all positive and significant, yet the coefficients of industry concentration index are only positive but not significant, indicating stock concentration have a more significant effect than the industry concentration on fund performance. This suggests that industry concentration contributes less than stock concentration on fund performance. This finding is consistent with our previous result in the cross sectional approach and Zhu, Li (2006). Specifically, evaluated with Top3, every 1% increment of concentration index increases funds’ raw return by 0.34% on average. Overall, funds with a higher performance are more concentrated, younger, smaller, and have a lower expense ratio and higher turnover. The effect from industry concentration, expense ratio and turnover are not statistically significant, which confirms the results in the cross sectional approach. Furthermore, the coefficients of the Fama-French 3 factors are all

4 _{The null hypothesis of the Hausman test is that there is no correlation between the e xp lanatory}

positive and significant, indicating fund performance is strongly exposed to the market, size and value risks.

Table 7

Concentration and fund pe rformance: panel regression

This table presents the estimated coefficients in the panel regression model specified in equation (2):Peri,t=α0+β1*CIi,t+β2*ln(Size)i,t+β3*ln(Age)i,t+β4*EXPi,t+β5*ln(TU)i,t+β6*(Rm,t-Rf,t)+β7*SMBt+

β8*HMLt+ei,t, using random effects estimation. The unbalanced data covers 146 equity funds

in China and has a time span from December 2003 to March 2009, on a quarterly basis. The dependent variablePer_i,t, is evaluated in the funds’ raw returns. The concentration level is measured by the industry concentration index, defined as 2

, , )

(w_it wit

ICI 





 3 1 , i wit,





separately. Expense ratio (EPX), the natural logarithms of fund age (LnAge), fund size (LnSize), turnover (LnTU), the 3 Fama-French factors (market factor (Rm,t-Rf,t), size factor (SMB), and

Value factor (HML)) are used as control variables. The estimated coefficients are expressed in thousands, except that of the Fama-French 3 factors. The last row reports the overall R2 of panel regressions. Standard errors are presented in parentheses.

Raw Return

ICI Top3 Top5 Top10

Constant 41.042*** (0.08) 35.995** (0.02) 28.680* (0.13) 30.152** (0.12) CI 6.044 (0.06) 3.423*** (0.04) 3.873** (0.03) 4.489*** (0.06) LnAge -3.013** (0.10) -3.338* (0.01) -3.044* (0.08) -2.727** (0.11) LnSize -1.253* (0.02) 0.978* (0.00) -0.953* (0.07) -0.890 (0.10) Expense ratio -3.007* (0.21) -2.747 (0.13) -1.676 (0.13) -1.341* (0.09) LnTU 2.714 (0.14) 1.126 (0.11) 1.714** (0.11) 1.225 (0.08) Rm-Rf 0.741*** (0.04) 0.739*** (0.03) 0.735*** (0.06) 0.719*** (0.04) SM B 0.176*** (0.05) 0.175*** (0.04) 0.177*** (0.05) 0.176*** (0.09) HM L 0.195*** (0.04) 0.189*** (0.03) 0.175* (0.04) 0.166* (0.06) Overall R2 0.80 0.72 0.64 0.71

4.4 Robust Test

As the Chinese fund market rapidly upgraded since the second half of 2006, when numerous new funds have come into existence. The size of funds also changed dramatically. At the end of 2006, the average total net asset of Chinese equity funds was only approximately ￥2,376.59 million, while by the end of 2008 almost doubled in size, reaching ￥4,130.82 million. On top of that, as already emphasized in the introduction section, Chinese funds have strengthened their investment concentration level by a wide range. Besides, most funds have also shown much variation for other characteristics such as investment style, turnover, etc., as well as their market performance, since the end of 2006. The relation between concentration and fund performance might also change during the latter period. Therefore, for a robust check, we further examine the concentration effect on fund performance in two separated sub-periods: the fourth quarter of 2003 to the fourth quarter of 2006, and the first quarter of 2007 to the first quarter of 2009, using the same 146 equity funds.

From table 8, we can see that very similar results are presented for the two sub-periods. The concentration-performance relation is both positive for the two periods, when measured with stock concentration indices, and only positive but not significant for the industry concentration index. Besides, the age and size effect are negative, and size effect is much more significant in the panel regression model, in which raw return is taken as the performance measurement. The signs and magnitude of the estimated coefficients are all quite consistent with the previous regression. Furthermore, none of the coefficients of industry concentration index is significant, also confirming the previous result that industry concentration contribute less than stock concentration to fund performance.

Table 8 Sub-Periods

quarterly raw return and alternatively with the Fama-French alpha. Panel A presents the results for the cross sectional regression model, and Panel B presents the results for the panel regression model. The last rows of each panel report the overall R2 of the panel regressions. Standard errors are presented in parentheses.

Panel A: cross sectional regression on Fama-French 

2003(Q4)-2006(Q4) 2007(Q1)-2009(Q1)

ICI Top3 Top5 Top10 ICI Top3 Top5 Top10

Constant 9.242** (0.15) 31.643*** (0.12) 6.157** (0.06) 33.642** (0.12) 14.536*** (0.10) 19.641** (0.13) 9.053* (0.07) 32.627 (0.13) CI 2.647 (0.09) 2.183** (0.13) 1.260* (0.09) 1.254*** (0.11) 3.523 (0.11) 2.327** (0.15) 2.315** (0.10) 0.982** (0.14) LnAge -1.228** (0.08) -1.643** (0.09) -1.427* (0.08) -1.332* (0.10) -1.621*** (0.09) -1.478** (0.10) -1.263** (0.09) -1.537** (0.13) LnSize -1.352 (0.07) -1.304* (0.08) -1.252 (0.14) -1.147 (0.12) -0.363 (0.14) -0.982 (0.10) -1.116* (0.09) -1.322 (0.11) EXP -4.648* (0.09) -4.015 (0.12) -3.541 (0.14) -4.523* (0.10) -3.521 (0.11) -4.127* (0.11) -3.536 (0.13) -4.152* (0.14) LnTU 0.083 (0.10) 0.069* (0.07) 0.096 (0.16) 0.080 (0.12) 0.091 (0.13) 0.082* (0.11) 0.125 (0.17) 0.099* (0.10) Overall R2 _{0.15 0.12 0.25 0.13 0.14 0.18 0.26 0.18}

Panel B: panel regression on raw return

2003(Q4)-2006(Q4) 2007(Q1)-2009(Q1)

ICI Top3 Top5 Top10 ICI Top3 Top5 Top10

Constant 43.537** (0.13) 28.633*** (0.09) 23.767 (0.12) 33.647** (0.11) 39.396*** (0.13) 38.643** (0.09) 30.155** (0.05) 28.264** (0.14) CI 5.093 (0.08) 2.856** (0.10) 3.553* (0.16) 4.014** (0.05) 7.359 (0.11) 4.356** (0.08) 4.132** (0.15) 4.972** (0.14) LnAge -2.642** (0.08) -3.566** (0.10) -3.419*** (0.16) -2.878* (0.13) -3.638** (0.15) -3.242* (0.11) -2.982** (0.08) -2.647*** (0.12) LnSize -1.244*** (0.10) -1.024** (0.11) -0.982*** (0.08) -0.902*** (0.14) -1.268 (0.09) -0.915*** (0.05) -0.978** (0.20) -0.824*** (0.09) EXP -2.932 (0.12) -2.532* (0.14) -2.117 (0.03) -1.464 (0.12) -3.229 (0.09) -2.924* (0.13) -1.452 (0.12) -1.252 (0.08) LnTU 2.536 (0.12) 1.251 (0.10) 1.832 (0.15) 1.357 (0.06) 2.890* (0.12) 1.053 (0.08) 1.642 (0.17) 1.351 (0.12) Rm-Rf 0.743*** (0.04) 0.740*** (0.06) 0.732*** (0.06) 0.708*** (0.04) 0.736*** (0.05) 0.737*** (0.04) 0.743*** (0.07) 0.742*** (0.04) SM B 0.173*** (0.05) 0.171*** (0.04) 0.179*** (0.04) 0.173*** (0.12) 0.178*** (0.05) 0.179*** (0.05) 0.174*** (0.03) 0.177*** (0.08) HM L 0.187*** (0.03) 0.184*** (0.04) 0.173*** (0.05) 0.162*** (0.06) 0.199*** (0.04) 0.192*** (0.05) 0.176*** (0.05) 0.170*** (0.07) Overall R2 0.74 0.71 0.70 0.68 0.77 0.74 0.61 0.74

5. Conclusion and Discussion

To provide some empirical evidence for the worldwide discussion on the puzzle of investment concentration and give some ideas both for investors and Chinese fund managers, this study examines the relationship between investment concentration and fund performance with a sample of equity funds in China market.

The concentration of funds in this paper is measured with the industry concentration index from Kacperczyk et al. (2005) and some stock concentration indices, which are the percentage of the top 3, top 5 and top 10 most weighted stocks held in funds. We evaluated the performance of funds with the quarterly raw return and alpha from the Fama-French 3 factor model as an alternative. Using a sample period from December 2003 to March 2009, we first apply a portfolio approach to examine the relationship between concentration level and fund performance. We find that the equity funds’ performance has a significant positive relationship with the degree of concentration and this concentration-performance relation is free from size and style variation, although the fund performance itself is significantly affected by fund size and investment style. We also observe that more concentrated funds are more exposed to

HML factor, suggesting the superior performance of higher concentrated funds may

result from more value stocks. Then we applied the cross sectional regression and panel regression approaches separately to test the relationship between concentration and performance. After controlling for age, size, expense ratio and turnover, positive results for concentration effect are found as well, and a significant negative relationship was found for both age and size effect, yet the influence from expense ratio and turnover are not significant for Chinese funds. Finally, we then applied a robust test on 2 sub-periods. We find the significantly positive relationship between concentration and fund performance not to be affected by the change of macro environment.

Acknowledgements

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