Why are Some Diversified U.S. Equity Funds Less Diversified Than Others? A Study on the Industry Concentration of Mutual Funds

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1 Why are Some Diversified U.S. Equity unds Less Diversified Than Others? A Study on the Industry Concentration of Mutual unds Binying Liu Advisor: Matthew C. Harding Department of Economics Stanford University Abstract Some diversified U.S. equity fund managers hold investments concentrated in one or a few specific industries. This paper investigates why some fund managers hold more concentrated portfolios. Using data on actively managed U.S. mutual funds from 2003 to 2010, I find that managers of more concentrated funds have their skills vary more across different industry sectors. Consequently, they earn a premium by overweighing their portfolios in industries they have comparative advantages in after controlling for risk and style differences using various benchmarks. My results also suggest that managers of more concentrated funds are more skilled, but also on average less responsive to macroeconomic opportunities. inally, I find a manager s choice of industry concentration is also influenced by her investment style and the size of her fund. I would like to thank Prof Matt Harding for his exceptional help as a mentor throughout the entire process. I would like to Prof Jonathan Berk and Prof Jules van Binsbergen for introducing me to mutual fund research, and for all the knowledge I gained about finance working with them over the past two years. I would not have been able to write a honor thesis on a finance topic otherwise.

2 1 Introduction A diversified U.S. equity fund is a mutual fund that invests the majority of its asset in U.S. stocks and is not obliged to focus its investments in a specific industry or type of firms. Consequently, they often benchmark themselves against the market portfolio. To please risk-averse investors, such a fund should reduce volatility in its performance through making diversified investments across industry sectors. However, in practice, diversified U.S. equity funds greatly differ in the industry concentration of their portfolios. Some funds evenly spread out their assets into every industry, while others only invest in one or a few specific industry sectors. In this paper, I study how industry concentration relates to a manager s skill and investment style, and whether a manager s choice of industry concentration is affected by the other characteristics of her fund. Despite the prevalence of academic literature addressing questions related to mutual funds, to the best of my knowledge, only two works have studied questions related to portfolio concentration, and both works focused on investigating how concentration relates to fund performance. These are (Kacperczyk, Sialm, and Zheng; 2007) and (Pollet and Wilson; 2008), and their results are not consistent with each other. Based on the Herfindahl Index, which is commonly used in Industrial Organization to measure the concentration of companies in an industry, Kacperczyk, Sialm, and Zheng (2007) create the Industry Concentration Index (ICI) as a measure for a mutual fund s level of diversification across different industry sectors. That is, a fund with a high ICI has its investments concentrated into one or a few industries, while an ICI of zero indicates the fund has the exact same industry structure as the market portfolio. Their research shows that mutual fund managers holding more concentrated portfolios have stronger risk-adjusted performance. They find doubling the ICI leads to a 2-4 basis points increase in abnormal returns. Their results also suggest that more concentrated funds follow distinctive investment styles by overweighing small and growth stocks. rom these findings they conclude that managers who hold portfolios that are concentrated in a few 1

3 industries have stronger investment ability. However, using a different measure of portfolio concentration based on the number of holdings, Pollet and Wilson (2008) find that riskadjusted performance is higher for more diversified funds. or example, their results suggest that on average a fund with 100 holdings has 1.5% higher annualized risk-adjusted return when compared to an otherwise identical fund with only 20 holdings. Although it still remains a question why some managers choose to bias their investments into stocks belonging to a few specific industries, a related topic that has been more thoroughly studied is the geographic bias in the portfolio choice of some managers. Using mutual fund data from 1975 to 1994, Coval and Moskowitz (2001) find that a fund manager on average earns substantial abnormal returns from geographically proximate investments. More specifically, their research suggests that the average fund manager gains 2.7% more per year from investments in firms located within 100 kilometers of the fund headquarter. However, despite the benefits of local investments, they find the average fund to only exhibit a modest bias towards local stocks. One possible reason for this phenomenon is that overweighing local stocks forces a fund to deviate from the market benchmark and increases risk. Consequently, a significant premium is needed to compensate for the added risk of more local investments. Consistent with this argument, they find the small fraction of funds that choose to heavily overweigh in local stocks are those best at selecting local stocks. unds that devote as much as percent to stocks of local firms generate the largest gains from local investments, while funds that do not exhibit a local bias generate no abnormal performance in their local holdings. In this paper, I investigate whether a similar conclusion can be made regarding the industry concentration of mutual funds. That is, whether managers who hold more concentrated portfolios are also those who gain greater benefits by having such portfolios that deviate from the market. In their work, Kacperczyk et al briefly surveyed two possible explanations for why managers holding more concentrated portfolios perform better. One argument is that the superior performance comes from managers who can identify hot and superior industries. 2

4 Consequently, these fund managers invest more heavily in industries that they expect will outperform the overall market, resulting in a more concentrated portfolio. Another possible explanation is that managers hold more concentrated portfolios because they have special informational advantages in specific industries. That is, these managers have significantly more skill in some industries than in others. As a result, they overweigh their portfolios in sectors they have comparative advantages in. However, there is little empirical evidence in support of either argument. In this paper, I evaluate the two hypotheses and investigate what motivates some fund managers to hold more concentrated portfolios. Mutual fund characteristics such as fund size and family size are found to have significant effects on fund performance and investment style. The term family refers to the parent investment company of a fund. In an empirical study using mutual fund data from 1962 to 1999, Chen, Hong, Huang, and Kubik (2004) regress monthly fund returns on lagged fund size and other observable characteristics. They find that a fund one log order of magnitude larger earns risk-adjusted returns that are 2 to 3 basis points per month lower. One explanation for this relationship is the liquidity hypothesis. It argues that larger funds give weaker performance because of the increasing trading costs associated with liquidity and price impact. Another explanation is the organizational diseconomies hypothesis, which argues that hierarchial costs increases with fund size. A larger fund has to hire more managers and research staff. Consequently, with more agents fighting to get their ideas implemented, it becomes harder to promote good ideas involving soft information (i.e. information not based on hard facts but on other factors such as personal relations with CEOs) in a larger fund. Chen et al have empirical evidences supporting both arguments. urther, they find the size of fund family to have a positive effect on performance. That is, funds hosted by larger investment companies perform better. In this paper, I investigate whether fund characteristics such as fund size, family size, and investment style also affect a fund manager s choice of industry concentration. I present three sets of findings. irst, I show that the choice of some managers to hold more concentrated portfolios is rational. That is, the average fund manager is able 3

5 to gain a premium for holding concentrated portfolios to compensate for the higher risk associated with less diversification. The more concentrated the portfolio is, the higher the risk premium the average manager is able earn. urther, my findings suggest that the rate at which this premium rises also increases with industry concentration. These findings suggest that some mutual fund managers are not only skilled, but also aware of their skill and exploit their comparative advantages. Second, I investigate the possible hypotheses on why some managers gain from holding more concentrated portfolios. I find managers with concentrated investments have skills that vary more across industry sectors. That is, these managers perform significantly better in some industries than in others. On the other hand, performances of fund managers holding more diversified portfolios tend to be more even across different industries. urther, I find managers of more concentrated portfolios to have stronger stock-picking skills. These results support the hypothesis that managers hold more concentrated portfolios because they have superior knowledge to select stocks in specific industries. I find industry-picking skill first increases but then falls with increasing industry concentration. This suggests that managers are only willing to deviate from the market s industry structure moderately to chase hot and growing industries. Third, I find the effect of fund size on industry concentration to be negative and statistically significant. So a larger fund diversifies more when compared to a smaller fund that is otherwise identical. urther, I find that investment style also affects industry concentration. Holding all other fund characteristics equal, a small-cap fund tends to be more diversified. This relationship can also be generalized: funds that invest more in stocks of smaller market capitalizations hold less concentrated portfolios. These relationships are consistent with what the liquidity hypothesis would predict. Larger funds and funds investing in smaller stocks have higher liquidity constraints, making it more expensive for these funds to hold concentrated portfolios. Although not the focus of my investigation, I also find that size of the parent investment company, or family size, is positively correlated with industry concentration 4

6 as well as the fund manager s variation in skill across different industry sectors. That is, larger investment companies tend to hire more specialized managers who hold more concentrated portfolios. These findings serve as empirical evidence for the theory work of Messa (1998), which rationalizes product proliferation as a marketing strategy of fund managing companies to attract investors with heterogenous objectives and avoid internal competition. The rest of this paper is organized as follows. Section 2 and 3 describes the data and terminologies used in this study. Section 4 examines whether the decision of some fund managers to hold portfolios of high industry concentration is rational. That is, whether fund managers are able to gain higher risk premiums for holding more concentrated portfolios. Section 5 and 6 evaluate two possible explanations of why holding more concentrated portfolios can be optimal for some managers. Section 7 studies the relationship between industry concentration and other fund characteristics. Section 8 concludes. 2 Data This paper uses mutual fund data from two sources. The main data set used is the Center for Research in Security Prices (CRSP) Survivorship Bias ree Mutual und Database. The database includes information on monthly fund returns, total net assets, different types of fees, and investment objectives of mutual funds and spans the period from January 1962 to December CRSP also has holdings data for mutual funds from 2003 to A fund releases its holdings either quarterly or semi-annually. However, CRSP do not identify index funds. To exclude all index funds from my analysis and concentrate on active management, I merge the subsets of CRSP and the Morningstar s Principia database by NASDAQ ticker, fund name, total net assets, and monthly returns to make use of Morningstar s label for index funds. I remove all index funds from my database. urther, using information on investment objective from CRSP, I also exclude 5

7 balanced funds, bond funds, commodity funds, sector funds, and foreign equity funds from the combined database. This allows me to limit my study to actively managed, diversified U.S. equity funds. Next, I add holdings data into the combined database. Since U.S. equity funds have vast majority of their holdings in companies listed on the NYSE, NASDAQ, or AMEX stock exchanges, I am able to identify over 99% of the holdings of mutual funds from 2003 to 2010 using the CRSP stock database. There are funds with holdings I cannot find in CRSP. However, the missing data only constitute less than 1% of all holdings. inally, because the most frequent release of holdings data is quarterly, I collapse my database from monthly observations to quarterly observations. urther, in this paper I do not directly study the performance and style of the mutual funds. This is because from the fund characteristics alone I cannot recover how a fund manager s portfolio performs in each industry sector. Consequently, I study the set of corresponding copycat funds. That is, for each fund identified in the combined database, I create a corresponding copycat to replace the primitive fund. Current regulation requires mutual funds to disclose their portfolio holdings at least twice a year. However, a large fraction of funds chooses to disclose their holdings every quarter. The copycat fund strategy make use of the holdings information released either quarterly or semi-annually. On the first day of every quarter, the copycat invests in assets that exactly match those in the latest publicly disclosed holdings of the primitive fund. The copycat then holds on to these assets until last day of the quarter. In other words, the copycat is created by assuming that a fund only buy or sell assets on the first day of every quarter. Table I presents the summary statistics for the matched database of copycat funds from 2003 to Row 2 and row 3 provides the number of funds and fund families at the start of each labeled period. und families refer to investment companies organizing the mutual funds. Row 4 and 5 report the average natural logarithms of total net assets for mutual funds and the fund families. Row 6 gives the average number of holdings per fund. Row 7 to Row 10 provide the averages of other fund characteristics, including turnover ratio, age, expense ratio, and total loading. Turnover ratio refers to the percentage of 6

8 a mutual fund s holdings that have been replaced with other holdings in the given year. Age is defined as the number of years the fund has survived since its inception date. The expense ratio is determined through an annual calculation, where a fund s operating expenses are divided by the average dollar value of its assets under management. Total loading is computed as the sum of front and rear loadings, which are one-time fees that need to be paid when funds are bought or sold. As in Pollet and Wilson (2008) as well as other works, we organized all shared classes of a fund into one observation. The statistics are consistent with general trends in the mutual fund industry. rom row 2 and row 3 I observe that there have been a steady expansion in the industry over the past 8 years. Row 4 and row 5 show that the average size of a mutual fund and a fund family also have been on an increasing trend between 1990 and The statistics suggest that expense ratio remains stable over the eight year period. I recognize that the recent financial crisis has many several effects on mutual fund characteristics. There is a moderate dip in average fund size in 2008 and 2009, and a dip in average family size in urther, turnover rate is also significantly lower between 2007 and 2009, a sign that managers have become more conservative during this period. Table II gives the correlation matrix of the important fund characteristics that are relevant to this study, including the natural logarithms of fund size and the size of the fund s parent investment company, turnover rate, age, expense ratio, and total loading. We observe that expense ratio and total loading are negatively correlated with fund size and family size. Economies of scale in management fees is well known among practitioners. Both expense ratio and total loading are also negatively correlated with turnover rate. This is consistent with the fact that more actively managed funds have higher management costs than funds following passive investment strategies. urther, fund size is negatively correlated with the fund s turnover ratio. This observation corresponds to recent findings suggesting smaller funds tend to be more active, overweigh growth and small-cap stocks, and invest more heavily in local firms, while larger funds have more value based and balanced investment styles (see Coval and Moskowitz, 2001; Pollet and Wilson, 2008; 7

9 and Kacperczyk et al, 2005). Age is positively correlated with fund size and family size, suggesting larger funds tend to be the more successful funds that have survived longer. 3 Industry Classification Before I start my analysis, I need to first formally define three terminologies that will be used throughout this paper. I start by defining industry sectors and the sector performances of copycat funds. In this study, I divide all U.S. stocks included in the CRSP stock database into 10 main industry sectors: consumer non-durables, consumer durables, healthcare, manufacturing, energy, utilities, telecommunication, business equipment and services, wholesale and retail, and finance. Details on the industry classification and each industry s weight in the market portfolio are provided in Table III. An unique advantage of studying copycat funds is that it allows me to not only measure a fund s overall performance, but also its performance in each sector. Let S denote the set of all 10 industries and J t be the set of all holdings of fund during quarter t, I define the fund s return in a sector s S as the average return of the stocks in its holdings that belong to sector s during quarter t, weighted by their weights in the fund s portfolio at the end of the previous quarter w j,t 1. r s,t1 = j J t 1 s w j,t 1 r j j J t 1 s w j,t 1 (1) J t s is the set of stocks that both belong to sector s S and are in the holdings of fund at the end of the quarter t 1. r j,t is the return of stock j during quarter t. I define r s,t as the return of fund in sector s, or the sector s performance of the fund. I say that a fund s performance in sector s is not observable if the fund does not hold any investments in that sector, making J t s an empty set. Next, I define the sector indices. Analysis in this paper make use of sector indices as benchmarks for performance. or each industry sector s, I compute quarterly return of 8

10 the sector index (idx s,t ) as the average returns of all equities in sector s that are included in the CRSP stock database, weighted by their weights in the market portfolio at the end of the previous quarter w M j,t 1. idx s,t = j s r j,t w M j,t 1 j s wm j,t 1 (2) r j,t is the quarterly return of equity j during quarter t, where j is a stock in sector s. w M j,t 1 is the weight of stock j in the market portfolio at the end of the quarter previous to t. Lastly, I define the Industry Concentration Index. I will use the Industry Concentration Index (ICI), first proposed by Kacperczyk et al (2007), as the measure of industry concentration in this research. The ICI of a fund during quarter t is defined as the sum of squared deviations of the value weights for each sectors s held by the fund, ws,t, relative to the industry weights of the market portfolio, ws,t. M ici t = s S(w s,t w M s,t) 2 (3) The ICI measures how much a fund s portfolio deviates from the industry structure of the market portfolio. If a fund has exactly the same industry composition as the market, the index gives a value of zero. On the other hand, if a fund concentrates all of its investments into one industry, the index gives a value close to one. The reason I use the definition of industry concentration in Kacperczyk et al (2007), who based their industry classification on the work of ama and rench (1997), is to make my results comparable to works done by earlier researchers. Another measure that is also widely used by researchers is the Herfindahl Index. In this context the Herfindahl Index (HI) is defined as follows. ici t = s S(w s,t) 2 (4) 9

11 The underlying assumption of using HI instead of ICI is that diversified funds benchmark themselves against the risk-free rate rather than the market portfolio. Although analysis done in this paper are based on the ICI, using HI instead of ICI does not change any of my findings. 4 Industry Concentration and Risk Premium Some diversified mutual fund managers choose to hold portfolios that are highly concentrated. A quick survey through the CRSP mutual fund data shows that during an average quarter, only 36.2% of all funds hold investments in all of the ten industries I categorized in Table III. In comparison, 23.9% of all funds invest in five or fewer than five industry sectors. or fund managers who have diversified investment objectives, more concentration brings greater risk. Instead, holding a diversified portfolio allows the manager to fully exploit her own investment skill without having to worry about systematic risks that usually affect entire industries. So why do some fund managers still choose to only invest in a few specific industry sectors? I start my analysis by demonstrating that their decision to hold more concentrated portfolios is rational. That is, a fund manager who chooses to deviate her portfolio from the market s industry structure should expect a premium to compensate for the higher risk associated with less diversification. The higher the industry concentration, the higher the premium should be in order to rationalize the manager s choice of higher industry concentration. To carry out this analysis, I construct a measure of the premium a manager gets from her choice of industry concentration. irst, for each fund, I construct a unique benchmark whose performance in every sector is equivalent to the sector performance of the fund. However, the benchmark portfolio has an Industry Concentration Index (ICI) of zero. That is, the weight of each sector in the benchmark portfolio is exactly identical to its weight in the market portfolio. So the quarterly return of this benchmark idx t can be 10

12 written as follows. idx t = s S(w M s,t 1 r s,t ) (5) The weight of sector s in the market portfolio at the end of the quarter t 1 is denoted by w M s,t 1. r s,t is the performance of the fund in sector s during quarter t. Intuitively, the benchmark s return idx t captures the return of the fund assuming that while retaining all investment abilities, the fund holds a portfolio whose industry structure exactly matches that of the market. Consequently, a fund whose return r t exceeds the benchmark return idx t benefits from its choice of industry concentration, whereas a fund that underperforms its corresponding benchmark is hurt by its choice of industry concentration. Creating the benchmark outlined above assumes that a fund s performance in every sector can be observed. However, as shown in Table IV, in an average quarter 63.8% of all funds do not have investments in one or more industry sectors. So if a fund does not have investments in a sector s, then I cannot observe its performance in that sector. Consequently, when a fund s performance in one or more sectors is missing, I proportionally increase the weights of the remaining sectors so they still sum up to one. Let S t be the set of sectors in which fund s performance is observable during quarter t, then the benchmark return can be generalized as follows. idx t = (w M s,t 1 r s,t ) s St s S w M t s,t 1 (6) 1 A multiplier s S t w M s is applied to the weights of the remaining sectors in S t of the remaining weights still sum up to one. By construction, S t so all S always hold. So when performance is not missing in any of the ten sectors, equation X can be simplified into equation Y. urther, observations in which the fund only has investments in a single industry are dropped from this analysis. Using a CAPM-based regression framework, I measure a fund s abnormal return 11

13 resulting from its choice of industry concentration as follows. r t rf t = α + β 1 (idx t rf t ) + ɛ t (7) I use rf t to denote the risk-free rate. r t is the fund s return and idx t is the return of the corresponding benchmark. or any fund, if α is significantly positive, then holding the concentrated portfolio is adding value to the fund. To ensure robustness of my results, I also estimate a fund s abnormal return α resulting from its choice of industry concentration using the ama-rench 3-factor and the Carhart 4-factor model. r t = α + β 1 (idx t rf t ) + β 2 smb t + β 3 hml t + ɛ t (8) r t = α + β 1 (idx t rf t ) + β 2 smb t + β 3 hml t + β 4 mom t + ɛ t (9) The two models add extra variables to explain performance. ama and rench (1969) document that small stocks tend to outperform large stocks and high book-to-market stocks tend to outperform low book-to-market stocks. So they find that CAPM overestimates the abnormal returns of funds with a focus on small or high book-to-market stocks. In the ama-rench 3-factor model, two additional variables are added into the regression framework to control for smb t (return difference between small stocks and large stocks) and hml t (return difference between high book-to-market stocks and low book-tomarket stocks). Carhart (1997) finds that stock s past performance tend to be positively correlated with future performance, so in the Carhart 4-factor model an additional variable mom t is added to distinguish skill from simple momentum chasing strategies. Using the estimated abnormal returns α and residuals from regressions ɛ, I compute the risk premium a fund gains from its industry concentration, which I will refer to as the 12

14 Industry Concentration Premium (ICP), during a quarter t as follows. icp t = α + ɛ t (10) To study whether managers with more concentrated portfolios gain higher premium from their choice of industry concentration, I regress ICP on one-quarter lagged industry concentration and other fund characteristics. As I mentioned earlier, in many cases the ICP is not computed from the fund s performances in all of the ten industry sectors because some funds do not always invest in all ten industry sectors. Consequently, in this regression I also add fixed effects to control for the number of sector performances used to compute ICP. These results are presented in Table V. The regression set up is as follows. icp t = β 0 + β 1 ici t 1 + β 2 X t 1 + β 3 Y t + ɛ t (11) X t 1 denotes a set of one-quarter lagged fund characteristics, including the natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loading as the sum of front and rear loadings. Y t is the set of fixed effect variables on the number of sectors performances used to compute icp t. To add more reliability to my results, I repeat the regressions without using fixed effects. Instead, I make the assumption that a fund manager does not invest in an industry sector because she has no knowledge in the industry. Consequently, she does not expect any abnormal return from that industry. Under this assumption, the optimal strategy for the manager if she were to invest in a sector she does not invest in would be to replicate the sector index, which gives her the least risk exposure. Consequently, under this approach, when the sector return of a fund is missing during any quarter, I fill it in using the return of the sector index during that quarter. I estimate the abnormal return by regressing fund returns against the corresponding benchmarks and compute the ICP using the procedure outlined earlier. I then regress ICP on industry concentration 13

15 and other fund characteristics. No fixed effect dummy variables are needed because fund performances in every sector during every quarter is made observable by filling in the sector indices wherever the real sector returns are missing for the fund. The regression results are reported in Table VI, and the set up of this regression is as follows. icp t = β 0 + β 1 ici t 1 + β 2 X t 1 + ɛ t (12) Again, X t 1 is a set of one-quarter lagged fund characteristics that include the natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loading. Using results from Table V and Table VI, I find that across all six regressions used, industry concentration has a positive and statistically significant effect on the ICP. This means that managers who hold more concentrated portfolios are able to gain higher premiums from their choice of industry concentration. Moreover, I look at if there is a clear nonlinear trend in the relationship between industry concentration and the ICP. If the managers are risk averse, I should observe that as risk increases, the additional premiums required for the managers to take on even more risks should also increase. So I add a squared industry concentration term (ici t 1) 2 to the regressions. This allows me to look at if the rate at which the ICP increases also increases as the portfolio becomes more concentrated. The new regression set ups, based on (eqn. 11 and eqn. 12), are as follows. icp t = β 0 + β 1 ici t 1 + β 2 (ici t 1) 2 + β 3 X t 1 + ɛ t (13) icp t = β 0 + β 1 ici t 1 + β 2 (ici t 1) 2 + β 3 X t 1 + β 4 Y t + ɛ t (14) The results from these two sets of regressions are shown in Table XII. These results suggest that, consistent with my conjecture, the rate at which risk premium increases also increases with industry concentration. 14

16 5 Industry Concentration and Variation in Performance Across Industries What enables some mutual fund managers to gain a premium for holding concentrated portfolios? One possible explanation is that these managers have informational advantages in specific industries. or example, a manager with a background in chemical engineering may have a better understanding of manufacturing firms that produce chemical products. Consequently, these managers hold portfolios that deviate from the market s industry structure because they invest more in industries they have comparative advantages in. If this argument is valid, then I should observe managers holding more concentrated portfolios to have skills that vary more across industry sectors. On the other hand, for managers who expect themselves to perform roughly equally well across all industries, they cannot expect additional abnormal returns by investing more in one sector over another sector. As a result, they should set their portfolio s industry structure to closely match that of the market in order to minimize risk. To empirically investigate the validity of this argument, I construct the Cross-sector Variation in Skill Index (CVSI) as a proxy for how much a fund manager s skill varies across different industries. irst, I estimate a manager s skill in each sector using three factor-based regression models: 1) CAPM, 2) the ama-rench 3-factor model, and 3) the Carhart 4-factor model. The CAPM model used in this context is defined as follows. r s,t rf t = α s + β s,1 (idx s,t rf t ) + ɛ s,t (15) The parameter of interest is α s, an estimation of the fund s risk-adjusted performance in sector s. r s,t is the return of the fund in sector s, and idx s,t is the return of the sector index. rf t is the risk-free rate. The 3-factor model and the 4-factor model can be written 15

17 as follows. r s,t rf t = α s + β s,1 (idx s,t rf t ) + β s,3 smb t + β s,4 hml t + ɛ s,t (16) r s,t rf t = α s + β s,1 (idx s,t rf t ) + β s,3 smb t + β s,4 hml t + β s,5 mom t + ɛ s,t (17) Variables smb t, hml t, and mom t account for return differences between small and large stocks, between high book-to-market stocks and low book-to-market stocks, and between past-winning and past-losing stocks. I do not observe the abnormal returns of every fund in every one of the ten sectors. There are two reasons why a fund manager s skill in an industry sector cannot be estimated: 1) the fund never invests in that sector, or 2) the fund only has investment in that sector for a few quarters, making accurate estimation impossible. or these reasons, I consider a fund manager s skill in sector s as non-determinant, or missing, if the fund never holds stocks from sector s, or has equities from that sector in its portfolio for a total of fewer than eight quarters. rom the sector alpha estimates α s and the residuals from regressions ɛ s,t, I estimate a fund manager s risk-adjusted performance in sector s during each quarter t as follows. α s,t = α s + ɛ s,t (18) However, α s,t will not be observable if either α s or ɛ s,t is not observable. This means that in order to observe α s,t, the fund must have 8 or more quarters with investments in sector s (for α s to be observable) and must also have investments in sector s during the given quarter t (for ɛ s,t to be observable). Let St be the set of sectors in which α s,t is observable for fund during quarter t. Then for each fund and during each quarter t, I define the Cross-sector Variation in Skill Index (CVSI) as the variance of risk-adjusted performances ( α s,t) across all sectors 16

18 from which performances are observable (s S t ). cvsi t = variance s S t ( α s,t) (19) Intuitively, a large CVSI indicates that the fund is doing comparatively well in some sectors but poorly in others, while a CSVI close to zero suggests that the fund does roughly equally well (or poorly) in all sectors it is involved in. To study if there exists a statistically significant relationship between industry concentration and CSVI, I regress CSVI against one-quarter lagged industry concentration and other fund characteristics including the natural logarithms of fund and family size, turnover rate, age, and expense ratio. urther, a set of fixed effect variables Y t is added to control for the number of observable sector risk-adjusted performances used to compute CSVI for each fund during each quarter t. The results from these regressions are summarized in Table VII. The regression set up is as follows. cvsi t = β 0 + β 1 ici t 1 + β 2 X t 1 + β 3 Y t + ɛ t (20) X t 1 is a set of one-quarter lagged fund characteristics, including the natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loading as the sum of front and rear loadings. As another check for robustness, rather than using fixed effects, I assume that a fund manager does not invest in an industry sector because she does not expect any abnormal return from that industry. In this case, the optimal strategy for the manager if she were to invest in a sector she does not invest in would be to hold the sector index, which gives her the least risk exposure. Consequently, when the sector return of a fund is missing during a quarter, I fill it in using the return of the sector index during that quarter. I then estimate the risk adjusted sector performances and the CVSI using the procedure outlined earlier, and regress CSVI on one-quarter lagged industry concentration and other fund 17

19 characteristics. Under this approach, I no longer need to add any fixed effect variables. This is because whenever a sector performance is missing, I am filling it in using the return of the sector index. The regression results are reported in Table VIII. The regression set up is as follows. cvsi t = β 0 + β 1 ici t 1 + β 2 X t 1 + ɛ t (21) X t 1 is a set of one-quarter lagged variables that include the natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loading. Using the results reported by Table VII and Table VIII, I find that across all six regression frameworks, the relation between industry concentration and CVSI is positive and statistically significant. This means that the skills of managers having more concentrated portfolios vary more greatly across industry sectors. In other words, it supports the hypothesis that managers concentrate their investments into a few industry sectors because they have informational advantages in these specific sectors. My results also show that fund size negatively correlates with CVSI. So managers of larger funds are more well-rounded, having their skills more evenly distributed across different industry sectors. A possible explanation for this phenomenon is that more well-rounded managers have a comparative advantage in managing larger funds. The reasoning is as follows. A more well-rounded manager tend to spread her asset more evenly across different industries and thus faces a weaker liquidity constraint. Consequently, the diseconomies of scale associated with managing a larger fund is weaker for more a wellrounded manager, giving less incentive for such a fund manager to control the size of asset under her management (for example, many funds put a cap on their assets under management and will not expand their sizes beyond that cap). I find family size to be positively correlated with CVSI. This means that large investment companies have a tendency to hire more specialized managers. Two possible explanations can be used to rationalize this relationship. In a theory paper, Massa (1998) 18

20 argues that product proliferation is used as a marketing strategy for fund managing companies to exploit investors heterogeneity and avoid competition among its own funds. Applying the same reasoning, I conjecture that a larger investment company has more funds and consequently needs to specialize its funds more in order to avoid its own funds competing for the same investors. Knowledge spillovers can be another reason why larger investment companies hire more specialized fund managers. The more specialized a manager is, the more other managers in the same company can benefit from her. Consequently, because a larger fund family has more fund managers, the cumulative spillovers benefit of hiring a specialized manager is higher, giving larger funds more incentive to hire managers with specialized skills. 6 Industry Concentration and Investment Skill If managers holding more concentrated portfolios are those who have informational advantages in certain industries, they should be able to pick the best stocks in those industries, and consequently demonstrate stronger overall stock-picking skills. I proceed to investigate whether this relationship holds. That is, whether managers having concentrated investments are superior stock-pickers. I construct three factor-based measurements of stock-picking skill. irst, for each fund, I construct a corresponding benchmark that has the exactly identical industry structure as the fund. However, rather than investing in individual stock, the benchmark holds a portfolio of sector indices. idx t = idx s,t ws,t 1 (22) s S idx s,t is the return of the sector s index. w s,t 1 is the the weight of sector s in the fund at the end of the quarter previous to t. Constructing this benchmark allows me to differentiate a manager s stock-picking skill from her ability to pick superior industries. Intuitively, if 19

21 the fund outperforms its benchmark, I know it is because the stocks the manager chooses in every industry sectors on average outperform their corresponding sector indices. If the fund underperform its benchmark, I know it is because the stocks the manager picks are inferior compared to their industry averages. I derive my first measurement of average stock-picking skill from the standard CAPM. r t rf t = α + β 1 (idx t rf t ) + ɛ t (23) The parameter of interest is α, which estimates a fund s average stock-picking skill over time. rt is the fund s return and rf t is the risk-free rate. idx t is the return of the corresponding benchmark outlined above. To account for additional factors affecting fund performance, I also apply a 3-factor model and a 4-factor model to my analysis of stockpicking skill: r t rf t = α + β 1 (idx t rf t ) + β 2 smb t + β 3 hml t + ɛ t (24) r t rf t = α + β 1 (idx t rf t ) + β 2 smb t + β 3 hml t + β 4 mom t + ɛ t (25) In the 3-factor model, two additional variables are added into the regression framework to control for smb t (return difference between small stocks and large stocks) and hml t (return difference between high book-to-market stocks and low book-to-market stocks). In the 4-factor model, another variable mom t is added to distinguish skill from simple momentum chasing strategies. Using estimated average stock-picking abilities α and the regression residuals ɛ, I compute a fund s stock-picking skill in each quarter (sps t ) as follows. sps t = α + ɛ t (26) To study the association between industry concentration and stock-picking ability, I 20

22 regress sps t against one-quarter lagged industry concentration (ici t 1) and other fund characteristics. sps t = α + β 1 ici t 1 + β 2 X t 1 + ɛ t (27) The fund characteristics (X t 1) used as explanatory variables include natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loadings as the sum of front and rear loadings. Results from this regression are presented in Table IX. Consistent with my prediction, increases in ICI is associated with increases in stock-picking skill. That is, managers of more concentrated funds are superior stock-pickers. The positive effect of ICI on stockpicking ability is statistical significant across all three benchmarks used. Although my research uses different methodology and benchmarks, these results are consistent with the work of Kacperczyk et al, who find that more concentrated funds give stronger overall performance, as well as performance after adjusting for average industry performance. Results from Table IX also show a positive relationship between stock-picking skill and family size. So larger investment companies are able to hire fund managers who are better at picking stocks. This finding is consistent with the results obtained by Chen et al, who find family size to be positivley correlated with overall fund performance. Another possibility is that large investment company provides more shared resources and allows more knowledge spillovers among its fund managers, thus enhancing the stock-picking skill of each manager. The negative relationship between fund size and stock-picking skill is consistent with the findings of earlier works. Chen et al, Pollen and Wilson, and others find fund size to have a negative affect on overall performance. Next, I identify potential nonlinearity in the relationship between ICI and stockpicking skill. My results from the earlier section suggests that as industry concentration increases, the rate at which the Industry Concentration Premium increases also increase. If managers holding concentrated portfolios earn their premiums through their informational advantages in specific industries, I should observe the rate at which stock-picking ability 21

23 increases also increase with rising industry concentration. To verify my conjecture, I add a squared ICI term to the regression (eqn. 27). The new regression set up is as follows. sps t = α + β 1 ici t 1 + β 2 (ici t 1) 2 + β 3 X t 1 + ɛ t (28) Again, (X t 1) a set of fund characteristics including natural logarithms of fund size and family size, turnover rate, age, expense ratio, and total loadings. Results from these regressions are provided in Table XII. I observe that the estimated coefficient on the squared ICI term is positive and statistically significant across all three benchmarks used. So consistent with my prediction, as industry concentration increases, the rate at which stock-picking ability increases also increases. The second possible explanation for why some managers hold more concentrated portfolios is that they cluster their investments into industries which they expect will outperform the market. This argument implies that managers of concentrated portfolios are superior industry-pickers. That is, these managers must be more confident about their abilities to choose superior industries in order for them to take on the additional risk associated with a more concentrated portfolio. To analyze the association between industry concentration and industry-picking ability, I construct three factor-based measurements of industry-picking skills. The first model based on the CAPM is as follows. idx t rf t = α + b 1 (mkt t rf t ) + e t (29) α is the desired measurement for a fund s average industry-picking skill over time. idx t is the return from the benchmark that has the exactly identical industry structure as the fund but only invest in sector indices. Details on the construction of this benchmark is described earlier when it is used to measure stock-picking skills. mktr t is the return of the market portfolio in quarter t. The intuition behind this measurement is straightforward. The 22

24 performance of the benchmark idx t in each of the ten sectors is equivalent to performance of the sector index. However, the benchmark retains the industry structure of the original fund. This way, this benchmark erases the manager s ability to pick individual stocks while retaining the industry composition of the manager s portfolio. So if the benchmark outperforms the market, it is because the fund overweighs in hot and growing industries. If the benchmark underperforms the market, then the fund must be overweighing in declining industries. Consequently, a higher α implies the manager s greater ability in picking industries that outperforms the market. To check for robustness, I also estimate a fund s average industry-picking skill using a 3-factor and a 4-factor model. idx t rf t = α + b 1 (mkt t rf t ) + b 2 smb t + b 3 hml t + e t (30) idx t rf t = α + b 1 (mkt t rf t ) + b 2 smb t + b 3 hml t + b 4 mom t + e t (31) In the 3-factor model, smb t is added to control for return difference between small stocks and large stocks and hml t is added to control for return difference between high bookto-market stocks and low book-to-market stocks. In the 4-factor model, another variable mom t is added to account for momentum. Using estimates on abnormal returns from industry-picking α and regression residuals (ɛ t ), I compute a fund s industry-picking skill in each quarter (ips t ) as: ips t = α + ɛ t (32) To study the effect of industry concentration on the ability to select superior industries, I regress industry-picking skill (ips t ) against one-quarter lagged industry concentration (ici t 1) and other fund characteristics (X t 1) including natural logarithms of fund size and family size, turnover rate, age, and expense ratio. ips t = α + β 1 ici t 1 + β 2 X t 1 + ɛ t (33) 23

25 Results from this regression are summarized in Table X. According to the hypothesis that managers hold concentrated portfolios to chase superior industries, I should expect a positive relationship between ICI and industry-picking skill. However, across all three benchmarks used, the ability to pick strong industries is negatively correlated with industry concentration. So my results do not support this hypothesis. I do not find fund size to have an effect on industry-picking skill. This is consistent with intuition. Earlier in this section, I concluded that stock-picking skill is negatively affected by fund size because of higher liquidity constraints and increasing trading costs that are associated with a larger fund. However, the trading of large fund is unlikely to be able to make an impact on the entire industry. So the liquidity hypothesis does not apply to mutual funds ability to select industries that they expect will outperform the market. There is still a positive effect of family size on industry-picking skill. Earlier this section I find that large family size is also associated with stronger stock-picking skill. The two observations together suggest larger investment companies on average are able to attract fund managers of higher quality. This is consistent with the findings of Chen et al. They find in their work that funds from larger investment companies have stronger overall performance. Next, I investigate potential nonlinear trend in the relationship between ICI and industry-picking skill. I add a squared ICI term to regression (eqn. 33). The new regression has its set up as follows. ips t = α + β 1 ici t 1 + β 2 (ici t 1) 2 + β 3 X t 1 + ɛ t (34) Results from the regressions are reported in Table XII. I find that across all three benchmarks used, the estimated coefficient on squared ICI is negative while the estimated coefficient on ICI is positive. This suggest that holding everything else constant, as industry concentration increases, industry-picking skill first increases but then falls. The results show that managers are only willing to deviate from the market s industry structure 24

26 moderately to chase superior industries. The managers who are holding portfolios that significantly deviate from the industry composition of the market (i.e. invest only in a single industry) are not trying to capture macroeconomic trends that affect entire industries. Instead, as my results earlier suggest, they hold highly concentrated portfolios to take advantage of their informational advantages in one or a few specific industry sectors. Both sets of my results, linear and nonlinear, suggest that once industry concentration reaches certain level, higher industry concentration becomes negatively correlated with industry-picking skill. Why do managers highly skilled in specific industries have weaker industry-picking ability. A likely explanation is that, because these managers are highly skilled in specific industries, it makes them less willing to respond to macroeconomic opportunities, which usually requires them to invest heavily into industries they are less familiar with. Because these managers are less responsive to macroeconomic trends, they demonstrate weaker industry-picking skill. 7 Industry Concentration and the Other und Characteristics In this section I investigate the effect of other fund characteristics such as fund size, family size, and investment style on industry concentration, and whether these relationships are consistent with the finding I made so far. In a work that is widely cited, Chen, Hong, Huang and Kubik (2004) find fund size to be negatively correlated with risk-adjusted performance. One argument made to account for diseconomies of scale in the mutual fund industry is the liquidity hypothesis. Liquidity constraint refers to the negative price impact resulting from buying or selling a large volume of the same stock. The larger the fund is, the more trading cost the fund has to pay because of liquidity constraint. I argue that a similar conjecture can be made on the relationship between fund size and industry concentration. A large fund that wants to concentrate its investments has to accept higher trading costs, while a small fund can concentrate its portfolio without increasing its impact 25

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