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Idiosyncratic Risk in Mutual Fund Jia-Hui Lin∗ Department of International Business Management, Tainan University of Technology, Taiwan Min-Hsien Chiang∗∗ Institute of international Business, National Cheng Kung University, Taiwan ∗ Address correspondence to Jia-Hui Lin, Assistant Professor of Department of International Business Management, Tainan University of Technology, 529 Jhongjheng Rd., Yongkang, Tainan 71002, Taiwan. Tel: +886-6-2422609; Fax: +886-6-2530313; e-mail: t90041@mail.tut.edu.tw. ∗∗ Min-Hsien Chiang, professor of Institute of international Business, National Cheng Kung University, Taiwan, No. 1, University Road, Tainan City, 701, Taiwan. Tel: +886-6-2757575; Fax: +886-6-2376811; e-mail:mchiang@mail.ncku.edu.tw. No 1 Idiosyncratic Risk in Mutual Fund Abstract The innovation in our paper is to look at the idiosyncratic risk of mutual fund in addition to the volatility of mutual fund returns. If idiosyncratic risk can be eliminated by a well-diversified portfolio, then there is no or little idiosyncratic risk in mutual fund. We find the idiosyncratic risk can not be eliminated and when the returns of mutual fund are negative and they also have higher idiosyncratic risk. The evidence shows that the variance of the market has no forecasting power for the mutual fund return, but we find a negative relation between the idiosyncratic risk and next year returns of mutual fund. We also find returns and the yearly idiosyncratic risk of aggressive-growth funds even larger than other groups. The estimates also suggest that younger funds have higher returns and the lowest idiosyncratic risk. When we use some factors to explain what causes the difference of idiosyncratic risk. We find high turnover ratio and old funds may have high idiosyncratic risk and reduce fund’s return. We also find older managers and manager with longer tenure have lower idiosyncratic risk, so they can earn lower returns. If we consider the momentum effect, the evidence show that funds following momentum strategies may have high idiosyncratic risk and reduce next year return. Keywords: idiosyncratic risk; mutual fund; momentum strategies 2 Idiosyncratic Risk in Mutual Fund Most asset pricing models suggest a positive relation between risk and return for the aggregate stock market. Goyal and Santa-Clara (2003) find a significant positive relation between average stock variance (largely idiosyncratic) and the return on the market, but market variance has no forecasting power for the market return. Barberis and Huang (2001) offer a different type of asset pricing model based on prospect theory, where investors are loss averse over the fluctuations of individual stocks that they own. They also obtain a relation between expected returns and idiosyncratic risk. Campbell, Lettau, Malkiel and Xu (2001) and Morck, Yeung and Yu (2000a) find a long-term rise in idiosyncratic variation in U.S. stock returns. One of the most noticeable recent changes in the stock market is the increased share of institutional ownership, particularly in large stocks. Institutional investors (pension funds and mutual funds) form a small, relatively homogeneous group whose sentiment may be influenced by a few common factors. This suggests that shocks to institutional sentiment might be important in explaining the increased idiosyncratic volatility of stock returns. Malkiel and Xu (1999) explore this effect in a sample of S&P 500 stocks and find that the proportion of institutional ownership is correlated with volatility. The rapid growth in the share of assets held by institutional investors and their virtual domination of trading volume could have an impact on the volatility of stock prices. Some investors who do try to diversify do so by holding mutual fund. Conventional wisdom holds that such a portfolio closely approximates a well-diversified portfolio in which all idiosyncratic risk is eliminated. However, the adequacy of this approximation depends on the level of idiosyncratic volatility in the stocks making up the portfolio. In this paper, we want to know if idiosyncratic risk can be eliminated by a well-diversified portfolio, then there is no or little idiosyncratic risk in mutual fund. In general, US studies of mutual (and pension) funds suggest little or no superior performance but somewhat stronger evidence of underperformance (e.g. Carhart (1997),Wermers (2000),Pastor and Stambaugh (2002)). There is little empirical research to examine the idiosyncratic risk of mutual fund. Kosowski, A., Wermers and White (2005) apply a new bootstrap statistical technique to examine the performance of the U.S. mutual fund and find that clustering in idiosyncratic risk-taking, among funds, also induces important non-normalities in the cross-section of alphas. The innovation in our paper is to look at the idiosyncratic risk of mutual fund in addition to the volatility of mutual fund returns. We first measure the idiosyncratic risk of mutual fund in each year similarly to Goyal and Santa-Clara (2003). So we can test if 3 there is a long-term rise in idiosyncratic variation in U.S. mutual fund returns. Then we run predictive regressions to explore the linkage of the mutual fund’s idiosyncratic risk and next year mutual fund return. Furthermore, Campbell, Lettau, Malkiel and Xu (2001) have found that average stock variance is countercyclical. Evidence also show that the stock market can be predicted by variables related to the business cycle, such as the dividend-price ratio, the relative Treasury bill rate, the term spread, and the default spread (Campbell (1991), Ferson and Harvey (1991)and Goyal and Santa-Clara (2003)).So we confirm the predictability of market returns with idiosyncratic volatility after controlling for variables proxying for business cycle fluctuations. Goyal and Santa-Clara (2003) show that that Fama-French variance is even stronger than traditional variance in predicting the next period’s value-weighted returns. Malkiel and Xu (2001) also present evidence of the importance of idiosyncratic risk in explaining the cross section of expected stock returns, even after controlling for size. So we also construct measures of pure idiosyncratic risk using residuals from the Fama-French (FF) three-factor model and Carhart (1997) four-factor model. The four-factor model using Fama and French (1993) 3-factor model plus an additional factor capturing Jegadeesh and Titman (1993) one-year momentum anomaly. Carhart (1997) describes the 4-factor model in greater detail and finds it prices passively-managed portfolios formed on size, book-to-market equity and one-year return momentum considerably better than the CAPM or Fama and French’s (1993) 3-factor model. Chan, Jegadeesh and Lakonishok (1996) also suggest that the momentum anomaly is market inefficiency due to slow reaction to information. However, the effect is robust to time-periods (Jegadeesh and Titman (1993)).Wermers (1996), who suggests that it is the momentum strategies themselves that generate short-term persistence, and Grinblatt, Titman and Wermers (1995), who find that funds following momentum strategies realize better performance before management fees and transaction expenses (these investment strategies are called “momentum-investing” or “trend-following” strategies). Furthermore, the idiosyncratic risk may be difference in different investment-objective. And we want to test if there are difference in the returns and the yearly idiosyncratic risk of young and old funds. Some literatures argue that expense differences between funds seem to be associated with performance differences. One potential explanation is that there are systematic differences in the jobs held by different types of managers, which result in their having different expense ratios (Chevalier and Ellison (1999)).We then examine whether the idiosyncratic risk of mutual fund is related to portfolios characteristics. So this paper will examine the changes of idiosyncratic risk by the mutual fund portfolios characteristics, such as portfolio of fund age, total net assets, expense ratio, turnover and maximum load fees. Carhart (1997) demonstrates that expenses have negative impact on 4 fund performance, and that turnover also negatively impacts performance. In addition, he also finds that fund performance and load fees are strongly and negatively related, probably due to higher total transaction costs for load funds. Chevalier and Ellison (1999) take a new approach to the question of whether some mutual fund managers are better than others by looking at the relationship between performance and manager characteristics. So this paper we also examine the changes of idiosyncratic risk by the mutual fund portfolios characteristics, such as manager CFA, manager age, manager tenure, manager Sex, manager MBA and manager PHD. Funds that earn higher one-year returns do not because fund managers successfully follow momentum strategies, but because some mutual funds just happen by chance to hold relatively larger positions in last year’s winning stocks. Grinblatt, Titman and Wermers (1995) who find that funds following momentum strategies realize better performance before management fees and transaction expenses. But Carhart (1997) finds that individual mutual funds follow one-year momentum strategy earn significantly lower abnormal returns after expenses, so he think transaction costs consume the gains from following a momentum strategy in stocks. Finally, we follow Carhart (1997) and form portfolios of mutual funds on lagged one –year idiosyncratic risk to test the momentum effect. Our sample period is January 1995 to December 2006.We use two major mutual fund databases in our analysis, including Morningstar and Center for Research in Security Prices (CRSP) database. In this paper, we find when the returns of mutual fund are negative and they also have higher standard deviation and idiosyncratic risk. But we can not find a long-term rise in idiosyncratic variation in U.S. mutual fund returns. Like Goyal and Santa-Clara (2003), we find that the variance of the market has no forecasting power for the market return, but we find a negative relation between the idiosyncratic risk and next year returns of mutual fund. We also find returns and the yearly idiosyncratic risk of aggressive-growth funds even larger than other groups. This may be aggressive-growth funds invest in high risk investment-objective and present a positive relation between risk and return. The estimates also suggest that younger funds have higher returns and the lowest idiosyncratic risk. Then we use fund portfolios characteristics and manager characteristics to test what cause the difference of idiosyncratic risk. We find high turnover ratio and old funds may have high idiosyncratic risk and reduce fund’s return. Carhart (1997) finds that expense ratios, portfolio turnover, and load fees are significantly and negatively related to firm’s performance. But our expense ratio and load fees are not significant. We also find older managers and longer tenure have lower idiosyncratic risk, so they can earn lower returns. 5 The remainder of the paper proceeds as follows. In section I we describe our data. In section II we calculate returns and time-varying idiosyncratic risk of mutual fund. Then we run predictive regressions to explore the linkage of the mutual fund’s idiosyncratic risk and next year mutual fund return. And we also confirm the predictability of market returns with idiosyncratic volatility after controlling for variables proxying for business cycle fluctuations. We also test the difference of the yearly idiosyncratic risk in different investment-objective and survivorship period funds. Section III, we use some factors to explain what causes the difference of idiosyncratic risk, including portfolios characteristics and manager characteristics. In Section IV we test if funds follow momentum strategies, can they get better performance? Section V concludes. I. Data Our sample period is January 1995 to December 2006.We use two major mutual fund databases in our analysis of mutual fund idiosyncratic risk. The first is the database of Morningstar, Inc. From the December 2006 CD we obtain monthly returns and manager characteristics: including manager CFA, manager age, manager tenure, manager sex, manager MBA and manager PHD. For each fund, Morningstar gives the name(s) of the fund's manager(s) along with a brief biographical sketch that includes the manager's start date, all undergraduate and graduate degrees received, the years in which the degrees were granted, and the names of the degree granting institutions. We use the data from the biographical sketches to create six manager characteristic variables The second database is Center for Research in Security Prices (CRSP). Mutual fund portfolios characteristics: including total net asset, expense ratio, turnover ratio and maximum load fees all from this database. The most widely used mutual fund databases in recent studies are those provide by these two databases. Because they have different identifier for each mutual fund, so we must match them carefully. We combine these two databases by fund name and ticker (the NASDAQ ticker symbol). We first get 12,328 diversified equity funds and 864,126 monthly returns from Morningstar and calculate the yearly idiosyncratic risk by regressing each mutual fund’s month returns within each year on the market portfolio. Second, the manager characteristics and portfolios characteristics, we can only get yearly data, come from two different databases. We get 7,993 yearly manager observations and 25,389 yearly mutual portfolios characteristics. Finally, we match them and get 11,7431 observations. 1. There are only 7,993 yearly manager observations. But one manager may manage several funds, each fund has its portfolios characteristics. So when we match manager characteristics and portfolios 6 We also calculate the idiosyncratic risk in different investment-objective funds. Our sub-sample consists of aggressive-growth funds, growth and income funds, long-term growth, and balanced or income funds. We identify a fund’s investment strategy by CRSP ICDI’s fund objective code. II. Idiosyncratic risk matter A. Calculation of time-varying idiosyncratic risk We first calculate the yearly idiosyncratic risk by regressing mutual fund i’s month returns within year t on the market portfolio, Rm,m,t is the excess return on the CRSP value-weighted portfolio of all NYSE, Amex, and Nasdaq stocks: Ri ,m ,t = α i ,0 +bi , m Rm ,m ,t + ε i ,m ,t (1) Then, the idiosyncratic risk of mutual fund i for year t is measured by the following equation: 1 ⎡ Mt 2 Mt ⎤ Vi ,t (ε ) = ⎢∑ ε i ,m ,t + 2 ∑ ε i ,m,t ε i ,m −1,t ⎥ (2) M t ⎣ m =1 m=2 ⎦ Where ε i ,m,t are the residuals obtained from the market model (1), M t is the number of trading months applicable in year t. The average idiosyncratic risk for the entire mutual fund may be found by the following equation: Nt 1 Vew,t (ε ) = Nt ∑V i =1 i ,t (ε ) (3) Table I reports the returns and idiosyncratic risk of mutual fund. Our sample includes a total of 12,328 diversified equity funds and 864,126 monthly returns. We can find hundreds of new funds are launched every year, a surprise rise in the number of mutual fund from 1995 to 2006. We also can find the returns of mutual fund are strongly, positively correlated with the stock market returns, although our samples not all invest in stock market. When the returns of mutual fund are negative and they also have higher standard deviation. This means that the fluctuation and risk of mutual fund returns larger when the market condition is bad. In this paper we want to know if idiosyncratic risk can be eliminated by a well-diversified portfolio, there is no or little idiosyncratic risk in mutual fund. But we find the idiosyncratic risk can not be eliminated. From column 5 of Table I, we find monthly idiosyncratic risk reach the highest in 2001 and 2002. Campbell, characteristics, we can get 11,743 yearly observations total. 7 Lettau, Malkiel and Xu (2001) and Morck, Yeung and Yu (2000a) find a long-term rise in idiosyncratic variation in U.S. stock returns. Because mutual fund is a portfolio of stocks, when idiosyncratic variation in U.S. stock returns rise, idiosyncratic variation of mutual fund may be rise except when idiosyncratic risk can be eliminated by a well-diversified portfolio. High-risk funds may often hold concentrated portfolios that load on similar industries or individual stocks, so the idiosyncratic risk can not be eliminated. Furthermore, there is a potential agency conflict between mutual fund investors and mutual fund companies. Investors would like the fund company to use its judgment to maximize risk-adjusted fund return. A fund company, however, in its desire to maximize its value as a concern, has an incentive to take actions that increase the inflow of investments. This also results the rise of idiosyncratic variation in mutual fund. Grinblatt and Titman (1992), Elton, Gruber, Das and Hlavka (1993), and Elton, Gruber, Das and Blake (1996) document mutual fund return predictability over longer horizons of five to ten years, and attribute this to manager differential information or stock-picking talent. However, funds that earn higher one-year returns do so not because fund managers successfully follow momentum strategies, but because some mutual funds just happen by chance to hold relatively larger positions in last year's winning stocks(Carhart (1997)). Our primary focus is to examine the evolution of the idiosyncratic risk in response to the cross-listing of the mutual fund. In order to control for alternative explanations for the changes of idiosyncratic risk, we will find the residual returns with the following extended regression equation. Fama and French (1993) find that a three factor model including Rm ,t , SMBt and HMLt factors, provides significantly greater power than the CAPM. In addition, Carhart (1997) finds that momentum is statistically significant in explaining returns on US mutual funds. Ri ,t = α i ,0 +bi ,1 Rm,t + bi ,2 SMBt + bi ,3 HMLt + ε i ,t (4) Ri ,t = α i ,0 +bi ,1 Rm,t + bi ,2 SMBt + bi ,3 HMLt + bi ,4 MOM t + ε i ,t (5) Where SMBt and HMLt are factor mimicking portfolios for size, book-to-market value effects. MOM t as the equal-weight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal equal-weight average of firms with the lowest 30 percent eleven-month returns 8 lagged one month. The idiosyncratic risk for fund-i is again calculated by plugging in the residuals from Equation (4) and (5) into Equation (2) and (3). Carhart (1997) suggests the 4-factor model can explain sizeable time-series variation, because the relatively high variance of the SMB, HML, and MOM portfolios and their low correlations with each other and the market proxies. He also finds the 4-factor model substantially improves on the average pricing errors of the CAPM and the 3-factor model. The idiosyncratic risk of column 6 of Table I is calculated by the 3-factor model, and Column 7 of Table I is calculated by the 4-factor mode. We can find most idiosyncratic risks calculated by the 4-factor mode are smaller than 3-factor model, this mean momentum can statistically significant explain returns. Figure 1 plots the time series volatility of average mutual fund returns for our sample. The top panel of this figure plots the raw time series while the bottom panel plots its 12-month moving average. The figure also plots the NBER recession months as shaded bars. A remarkable feature of this graph is that the mutual fund volatility was high in the 2000 to 2002 years. We also can find in this period that stock market return and mutual fund return are all negative from Table 1. Figure 2 gives a graphical illustration of the volatility of idiosyncratic risk on mutual fund. This Figure also shows that the volatility of idiosyncratic risk was high in the 2000 to 2002 year. We can find the volatility of idiosyncratic risk is small except that period. Campbell, Lettau, Malkiel and Xu (2001) and Morck, Yeung and Yu (2000a) find a long-term rise in idiosyncratic variation in U.S. stock returns. But we can not get the same result. This may a surprise rise in the number of mutual fund from 2000 year. There are lager samples, so the volatility was reduced. Another reason may be the idiosyncratic risk eliminated by a well-diversified portfolio, there is no or little idiosyncratic risk in mutual fund. If we compare Figure 1 and Figure 2, we also can find when the volatility of mutual fund return is highly, the volatility of idiosyncratic risk will be larger. B. Predictive regression Our paper is to look at each mutual fund’s idiosyncratic risk in addition to all mutual fund risk. Goyal and Santa-Clara (2003) find that market variance has no forecasting power for the market return, but they find a significant positive relation between average stock variance and the return on the market. We measure the idiosyncratic risk of each mutual fund in each year similarly to Goyal and Santa-Clara (2003) and run the predictive regressions to explore the linkage between average mutual fund’s idiosyncratic risk and mutual fund return. So we regress 9 realized excess returns on the lagged volatility measures. The fitted value of this regression gives the expected return conditional on the lagged volatility. The forecasting regression is rt +1 = α + β X t + ε t +1 (6) Where r is the simple excess return on the mutual fund, and X includes different combinations of the volatility of mutual fund return and the variance of average idiosyncratic risk of mutual fund. Table II presents the results of regressions for the monthly mutual fund return. Model 1 regression runs the classic regression of mutual fund return on lagged mutual fund variance. The literature presents conflicting results on the sign of the coefficient in stock market, but no related literature in mutual fund. Goyal and Santa-Clara (2003) find a negative but insignificantly coefficient. Campbell (1987) and Glosten, Jagannathan and Runkle (1993) find a significantly negative relation, whereas Campbell and Hentschel (1992) and French, Schwert and Stambaugh (1987) find a significantly positive relation. For our data and sample, we find a positive but insignificantly coefficient. Like Goyal and Santa-Clara (2003) find that market variance has no forecasting power for the market return. Model 2 shows that average idiosyncratic risk of mutual fund is negatively and significant in predicting mutual fund returns. This means highly idiosyncratic risk may reduce next year mutual fund returns. But Goyal and Santa-Clara (2003) find positive relation in stock market. From equation 6, we test whether the average idiosyncratic risk of mutual fund can be a predictor of subsequent mutual fund return. We also run regressions of mutual fund returns on lagged standard deviations and lagged log of variances. One potential problem with the regressions on the variance measures is the nonsphericity of residuals. Goyal and Santa-Clara (2003) find that the times series of the variance measures display large kurtosis and skewness. This can potentially affect the distribution of standard errors. Andersen, Bollerslev, Diebold and Ebens (2001) and Goyal and Santa-Clara (2003) find that the square root and log transformations of the variance measures are closer to normally distributed than the variances themselves. Model 3 to 4 of Table 2 report the regressions on standard deviations and Model 5 to 6 are the regression on logs of variances. With these transformed variables, the relation between mutual fund returns and the average idiosyncratic risk of mutual fund remains negative and significant. C. Controlling for the Business Cycle Campbell, Lettau, Malkiel and Xu (2001) and Goyal and Santa-Clara (2003) 10 have found that average stock variance is countercyclical. The stock market can be predicted by variables related to the business cycle, such as the dividend-price ratio, the relative Treasury bill rate, the term spread, and the default spread. To test this “proxy” hypothesis, we examine the relation between the mutual fund returns and the average mutual fund idiosyncratic risk using macro variables as controls for business cycle fluctuations. The dividend-price ratio is calculated as the difference between the log of the last 12 month dividends and the log of the current level of the CRSP value weighted index. The three-month Treasury bill rate is obtained from Ibbotson Associates. The relative Treasury bill stochastically detrends the raw series by taking the difference between the Treasury bill rate and its 12-month moving average. The term spread is calculated as the difference between the yield on long-term government bonds and the Treasury bill rate, also obtained from Ibbotson Associates. The default spread is calculated as the difference between the yield on BAA- and AAA-rated corporate bonds, obtained from the FRED database. Like Goyal and Santa-Clara (2003), we include the lagged mutual fund return on the equation to control for the serial correlation in returns that might spuriously affect the predictability results2. Table III examines the forecasts of the mutual return controlling for the business cycle. Our results show that the lagged return is significant positively to the excess mutual fund return. The dividend-price ratio is significant negatively for explaining returns. Goyal and Santa-Clara (2003) find that the relative treasury bill rate is strongly significant with a negative coefficient in their sample. Both the term spread and the default spread are strongly significant in explaining returns. But in our samples the three variables are not significant. This may our samples period only 12 years. There is only one NBER recession in 2001 March to November. The other reason may that these variables can explain in stock market not in mutual fund market. Previous researchers examine the relation between the stock market returns and the average stock variance using macro variables as controls for business cycle fluctuations. So we can not get the same result with earlier research. When we include the volatility measures along with the control variables in the regression, the evidence also show that the variance of the market has no forecasting power for the mutual fund return, but we can not find a significantly negative relation between the idiosyncratic risk and returns of mutual fund. D. Idiosyncratic risk in different Investment-objective category and survivorship 2.Lewellen(2001) suggests using the lagged 12-month return as a correction for the mean reversion in the stock market. 11 period We have calculated the yearly idiosyncratic risk of the full sample of funds in Table I, but the yearly idiosyncratic risk may be difference in different investment-objective funds. Our sub-sample consists of aggressive-growth funds,3 growth and income funds,4 long-term growth,5 and balanced or income funds.6 Table IV reports returns and idiosyncratic risk of funds in each investment-objective category. We can find the returns and the yearly idiosyncratic risk of aggressive-growth funds even larger than other groups. This may be aggressive-growth funds invest in high risk investment-objective and present a positive relation between risk and return. This is consistent with the hypothesis of asset pricing models. We also can find the returns and the yearly idiosyncratic risk of balance or income funds even smaller than other groups. Because balanced and income funds contain portfolios of both fixed income and equity securities with variable mix capabilities and try to provide stability of net asset value through changing market conditions. We find the returns and the yearly idiosyncratic risk are significant difference in different investment-objective funds from last section. And we are interested in the yearly idiosyncratic risk may be difference in different survivorship period funds. People may say young fund may be more active, and it may be has high return and risk. Next, we will test if there are difference in the returns and the yearly idiosyncratic risk of young and old funds. The survivorship period divided 3 parts, less than 5 year (< 5 year), between 5 ~ 10 year, and larger than 10 year ( >10year). When the survivorship period less than 3. Aggressive Growth Fund’s investment objective is described in the prospectus as capital appreciation or similar working and it also meets at least one of the following criteria: (1) A portfolio turnover rate of 100% or more per year is permitted by prospectus; (2) The fund can borrow more than 10% of the value of its portfolio; (3) The prospectus permits short selling; (4) The fund can purchase options; (5) The fund may invest in unregistered securities; (6) The fund invests primarily in new, speculative or unproven securities. 4. Growth and Income Funds provide growth of capital with income or income with some capital growth as the primary objective. Historically, dividend payments have been made on a fairly regular basis. 5. Long Term Growth Funds are those where long-term growth of capital is the primary objective and income is a secondary consideration. 6. Income funds and balanced funds are combined in our study, as the number in each category is relatively small, and because funds in these two categories make similar investments. 12 5 year, we define it is a young fund. But when the survivorship period larger than 10 year, we define it is an old fund. Table V reports the returns and idiosyncratic risk of different survivorship period funds. The estimates suggest that younger funds have higher returns. Chevalier and Ellison (1999) find positive significant coefficient of excess returns indicates as expected that better performing funds are more likely to survive. They also find that fund survival is more performance sensitive for funds managed by younger managers. The young funds have longer survivorship ahead of them, so fund manager may like higher risk and they also have shorter tenure. But if we measure of pure idiosyncratic risk using residuals from the Carhart (1997) four-factor model, we can find young funds have the lowest idiosyncratic risk (1.3895). From Table V, we can find four-factor model substantially improves on the average pricing errors of the CAPM and the 3-factor model. III. What cause the difference of idiosyncratic risk A. Measurement of the mutual fund portfolios characteristics Mutual fund managers claim that expenses and turnover do not reduce performance, since investors are paying for the quality of the manager's information, and because managers trade only to increase expected returns net of transactions costs. Thus, expenses and turnover should not have a direct negative effect on performance, but rather a neutral or positive effect(Carhart (1997)). Some literatures argue that expense differences between funds seem to be associated with performance differences. One potential explanation is that there are systematic differences in the jobs held by different types of managers, which result in their having different expense ratios (Chevalier and Ellison (1999)). This section we will estimate the relationship between idiosyncratic risk and mutual fund portfolios characteristics. We use some factors to explain what causes the difference of idiosyncratic risk. Q Vi ,t (ε ) = α 0,i + ∑ cq ,iWq ,i ,t + ei ,t (7) q =1 Where Vi ,t denotes the idiosyncratic risk (calculated by the 4-factor mode) for mutual fund i in month t, α o ,i is the intercept term, Wq ,i ,t denotes q-the mutual fund portfolios characteristics variable that may affect the time-varying idiosyncratic risk of the mutual fund. The explanatory variables ( Wq ,i ,t ) in equation (7) are ln(TNA), expense ratio, turnover ratio, mutual fund age, and maximum Load. Ln(TNA)is the log of total net 13 assets, which is the closing market value of securities owned, plus all assets, minus all liabilities. TNA is lagged one year to avoid spurious correlation (Granger and Newbold (1974)). Expense ratio is total month management and administrative expenses divided by average total net assets. Turnover ratio is the minimum of aggregate purchases of securities or aggregate sales of securities, divided by the average total net assets of the fund. Age is live in operation at the end of the sample. Maximum Load is the sum of maximum front-end, back-end and deferred sales charges. Table VI summarizes the mean and standard deviation of mutual fund portfolios characteristics. The mean ln(TNA) value of the total sample is 364 millions, compare to Carhart (1997), the average ln(TNA) is 218.7 millions, his sample period is from 1962 to 1993, we can find a large rise in the size of mutual fund recent year. The mean of expense ratio is 1.323%, near the value (1.352%) of Chevalier and Ellison (1999), his sample period is from 1988 to 1994, but larger than Carhart (1997). The mean of turnover ratio is 84.275%, larger than Carhart (1997) and Chevalier and Ellison (1999), this may imply that funds following momentum strategies for better performance, so increase the turnover ratio. But Carhart (1997) finds turnover ratio is significantly and negatively related to performance. Grinblatt, Titman and Wermers (1995) find that funds following momentum strategies realize better performance before management fees and transaction expenses. The mean of fund age (7.315 years) is smaller than the age (18.1years) of Carhart (1997), this may be the faster rise of mutual fund recent year, so many young funds in our sample. In Table VII, we use three different methods to test the relationship between mutual fund performance, idiosyncratic risk and mutual fund portfolios characteristics. Newey –West standard errors are used throughout in section III, because we expect residuals for a single fund for different years to be serially correlated (Chevalier and Ellison (1999). In Model 1, simple excess return is regressed on fund portfolios characteristics. We find ln(TNA) and fund age are significantly and negatively related to performance. This mean large company and old company may reduce fund’s return. In Model 2, we measure systematic risk. We calculate a beta for each mutual fund-year in our sample by regressing the fund's monthly returns in that year minus the risk-free rate on the monthly return of the market minus the risk-free rate, HML, SMB, and MOM. We also find ln(TNA) and fund age are significantly and negatively related to market risk. But turnover ratio is significantly and positively related to market risk. In Model 3, Idiosyncratic Risk is regressed on fund portfolios characteristics. Idiosyncratic Risk is calculated by 4 14 Factor model from equation (5). We find ln(TNA) is significantly and negatively related to idiosyncratic risk. But turnover ratio and fund age are significantly and positively related to idiosyncratic risk. This mean high turnover ratio and old funds may have high risk and reduce fund’s return. Carhart (1997) finds that expense ratios, portfolio turnover, and load fees are significantly and negatively related to firm’s performance. But our expense ratio and load fees are not significant. B. Measurement of the mutual fund manager characteristics Chevalier and Ellison (1999) take a new approach to the question of whether some mutual fund managers are better than others by looking at the relationship between performance and manager characteristics. In this paper, we want to test what factors will inference the idiosyncratic risk. We not only look the mutual fund portfolios characteristics, but also look the mutual fund manager characteristics. Our goal in this section is to present a simple look at whether manager characteristics predict the cross-sectional distribution of mutual fund idiosyncratic risk and to see whether differences in “ability” may also play a role. We use the following equation to test idiosyncratic risk. M Vi ,t (ε ) = α 0,i + ∑ bm ,i Z m ,i ,t + ei ,t (8) m =1 Where Vi ,t denotes the idiosyncratic risk (calculated by the 4-factor mode) for mutual fund i in month t, α o ,i is the intercept term, Z m,i ,t denotes the m-th variable in the fund managers characteristics. We examine whether the fund’s idiosyncratic risk in year t is related to the characteristics of the manager who is charge of the fund on December 31 of year t-1.7 The explanatory variables ( Z m,i ,t ) in equation (8) are manager CFA, manager age, manager tenure, manager Sex, manager MBA and manager PHD. A dummy variable that takes the value of one if the manager has a CFA, the manager is man, the manager has a MBA degree, the manager has a PHD degree and zero otherwise. Manager tenure is live in operation from he begin to manager the fund until the end of the sample year. The mean of manager MBA is 58.7%, near the value (59.6%) of Chevalier and Ellison (1999), manager age (46.976)is larger than the value(44.176) of Chevalier and Ellison (1999), and our manager tenure (5.83)is larger than them (3.793). The regression results are reported in Table VIII. We also use three different 7. We follow Chevalier and Ellison(1999). If the manager of the fund changes during year t, we do not ascribe the fund’s performance to the new manager until year t+1. Because we do not want to use a methodology that introduce look-ahead bias. 15 methods to test the relationship between mutual fund performance, idiosyncratic risk and mutual fund manager characteristics. In Model 1, simple excess return is regressed on fund manager characteristics. We find manager age and manager tenure are significantly and negatively related to performance. This mean older manager and longer tenure may reduce fund’s return. But when manager with MBA or PHD, he may earn higher returns. Model 2 regresses systematic risk on fund manager characteristics. The estimate indicates that older managers choose higher betas, because they don’t like risk. We get the same result as Chevalier and Ellison (1999). In Model 3, Idiosyncratic Risk is regressed on fund manager characteristics. The estimates suggest that older managers and longer tenure have lower idiosyncratic risk, so they can earn lower returns. From Model 1 and Model 3, we get the consistent results. Chevalier and Ellison (1999) also find that younger managers outperform older managers. One explanation for why such performance differences might exist is that younger managers may work harder, both because they are more likely to be fired for poor performance and because they have longer careers ahead of them, so younger managers like higher risk and they also have shorter tenure. Chevalier and Ellison (1999) find that a manager who has an MBA outperforms a non-MBA manager and more likely to manage higher beta funds. In our paper, we also find manager who has an MBA outperforms a non-MBA manager. This may they are more overconfidence and seek for higher return. From our four Models, we find the variables of manager sex or managers with CFA are not important factors to inference marker return or risk. C. Measurement of the mutual fund portfolios characteristics and manager characteristics This section we not only consider mutual fund portfolios characteristics, we also consider manager characteristics. So we combine section III.A and section III.B. We also use four different methods to test the relationship between mutual fund performance, idiosyncratic risk and mutual fund characteristics. The regression results are reported in Table IX. The sample number is 11,743 yearly observations. In Model 1, simple excess return is regressed on fund characteristics. We find turnover ratio, manager age and manager with CFA are significantly and negatively related to performance. This mean higher turnover ratio, old manager and manager with CFA may reduce fund’s return. Model 2 regresses systematic risk on fund characteristics. The estimate indicates that firms with maximum load fees choose lower betas, so they have lower excess returns. In Model 3, Idiosyncratic Risk is regressed on fund characteristics. The estimates suggest that larger firms, older managers and longer tenure have lower idiosyncratic risk, so they can earn lower 16 returns. From section III.A to section III.C, we get the consistent results. IV. Momentum Effect Grinblatt, Titman and Wermers (1995) who find that funds following momentum strategies realize better performance before management fees and transaction expenses. But Carhart (1997) finds that individual mutual funds follow one-year momentum strategy earn significantly lower abnormal returns after expenses, so he think transaction costs consume the gains from following a momentum strategy in stocks. Funds that earn higher one-year returns do not because fund managers successfully follow momentum strategies, but because some mutual funds just happen by chance to hold relatively larger positions in last year’s winning stocks. From Table I, we find the returns of mutual fund are strongly, positively correlated with the stock market returns. In this section, we first follow Carhart (1997) and form portfolios of mutual funds on lagged one–year returns, then estimate performance on the resulting portfolios. On January 1 of each year, we form ten equal-weighted portfolios of mutual fund, using reported returns minus one-month T-bill return. Reported returns are net of all operating expenses (expense ratios) and security-level transaction cost, but do not include sales charges. We hold the portfolios for one year, then re-form them. This yields a time series of monthly returns on each decile portfolio from 1995 to 2006. Funds that disappear during the course of the year are included in the equal-weighted average until they disappear, then the portfolio weights are readjusted appropriately. The portfolios of mutual funds sorted on one-year past returns shown in Table X. Carhart (1997) finds the returns on the top decile funds are strongly, positively correlated with the one-year momentum factor, while the returns in the bottom decile are strongly, negatively correlated with the factor. But we can’t get the same result. His samples period is from1963 to 1993. But our samples are from 1995 to 2006. So we get many new finds. First, the post-formation monthly excess returns on the decile portfolios decrease monotonically in portfolio rank. Portfolio 1, which contains the top of funds, outperforms Portfolio 10, the bottom of funds, by 18 percent per month. It is so amazing, but Carhart (1997) only get a spread of 0.67 percent per month. Our sample includes a total of 12,328 diversified equity funds and 864,126 monthly returns. But only 1,892 diversified equity funds in Carhart (1997) samples. So we can get so large return spreads. Second, the CAPM betas on the top deciles are all strongly, negatively correlated with mutual returns. And we also find that if individual mutual funds follow one-year momentum strategy earn significantly lower abnormal returns after expenses. So in our paper, if funds follow momentum strategies can’t get realize better performance. Because our paper is to look at the idiosyncratic risk of mutual fund in addition to 17 the volatility of mutual fund returns. We also follow Carhart (1997) and form portfolios of mutual funds on lagged one–year idiosyncratic risk, then estimate variation on the resulting portfolios. The portfolios of mutual funds sorted on one-year past idiosyncratic risk shown in Table XI. Portfolio 1, which contains the highest idiosyncratic risk of funds, outperforms Portfolio 10, the bottom of funds, by 2.54 percent per month. There are many outlier data in Portfolio 1(high idiosyncratic risk) and Portfolio 10(low idiosyncratic risk), so we get very small Adj R square and large standard deviation. From this Table, we also can find if individual mutual funds follow one-year momentum will have larger idiosyncratic risk. Most asset pricing models suggest a positive relation between risk and return for the aggregate stock market. But in our paper, we find that funds following momentum strategies may have high idiosyncratic risk and reduce next year return. V. Conclusion The innovation in our paper is to look at the idiosyncratic risk of mutual fund in addition to the volatility of mutual fund returns. We want to know if idiosyncratic risk can be eliminated by a well-diversified portfolio, then there is no or little idiosyncratic risk in mutual fund. We find the idiosyncratic risk can not be eliminated and when the returns of mutual fund are negative and they also have higher standard deviation and idiosyncratic risk. Although Campbell, Lettau, Malkiel and Xu (2001) and Morck, Yeung and Yu (2000a) find a long-term rise in idiosyncratic variation in U.S. stock returns. We can not find a long-term rise in idiosyncratic variation in U.S. mutual fund returns. Then we document a link between idiosyncratic risk and returns in the mutual fund market. We find that the variance of the market has no forecasting power for the market return, but we find a negative relation between the idiosyncratic risk and next year returns of mutual fund. We also find returns and the yearly idiosyncratic risk of aggressive-growth funds even larger than other groups. The estimates also suggest that younger funds have higher returns and the lowest idiosyncratic risk. Then we use some factors to explain what causes the difference of idiosyncratic risk, including portfolios characteristics and manager characteristics. Some literatures argue that expense differences between funds seem to be associated with performance differences. One potential explanation is that there are systematic differences in the jobs held by different types of managers, which result in their having different expense ratios. We find high turnover ratio and old funds may have high idiosyncratic risk and reduce fund’s return. We also find older managers and longer tenure have lower idiosyncratic risk, so they can earn lower returns. If we consider the momentum effect, we find that funds following momentum strategies may have high idiosyncratic risk and reduce next year return. 18 The idiosyncratic risk of mutual funds can not be eliminated in our paper. We discuss three possible explanations. First, because mutual fund is a portfolio of stocks or bonds, when idiosyncratic variation in U.S. stock returns rise, idiosyncratic variation of mutual fund may be rise except when idiosyncratic risk can be eliminated by a well-diversified portfolio. High-risk funds may often hold concentrated portfolios that load on similar industries or individual stocks, so the idiosyncratic risk can not be eliminated. Second, there is a potential agency conflict between mutual fund investors and mutual fund companies. Investors would like the fund company to use its judgment to maximize risk-adjusted fund return. A fund company, however, in its desire to maximize its value as a concern, has an incentive to take actions that increase the inflow of investments. This also results the rise of idiosyncratic variation in mutual fund. Third, manager differential information or stock-picking talent, these factors also result the rise of idiosyncratic variation. 19 Reference Andersen, Torben G., Tim Bollerslev, Francis X. Diebold, and Heiko Ebens, 2001, The distribution of realized stock return volatility, Journal of Financial Economics 61, 43-76. Barberis, Nicholas, and Ming Huang, 2001, Mental accounting, loss aversion, and individual stock returns, Journal of Finance 56, 1247-1292. Campbell, John, Martin Lettau, Burton G. Malkiel, and Yexiao Xu, 2001, Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk, Journal of Finance 56, 1-43. Campbell, John Y., 1987, Stock returns and the term structure, journal of Financial Economics 18, 373-399. Campbell, John Y., 1991, Avariance decomposition for stock returns, Economic Journal 101, 157-179. Campbell, JohnY., and Ludger Hentschel, 1992, No news is good news: An asymmetric model of changing volatility in stock returns, Journal of Financial Economics 31, 281-318. Carhart, M., 1997, On Persistence in Mutual Fund Performance, Journal of Finance 52, 57-82. Chan, Louis K.C., Narasimhan Jegadeesh, and Josef Lakonishok, 1996, Momentum strategies, Journal of Finance 51, 1681-1713. Chevalier, Judith, and Glenn Ellison, 1999, Are Some Mutual Fund Managers Better than Others? Cross-Sectional Patterns in Behavior and Performance, Journal of Finance 54, 875-899. Elton, Edwin J., Martin J. Gruber, Sanjiv Das, and Christopher R. Blake, 1996, The persistence of risk-adjusted mutual fund performance, Journal of Business 69, 133-157. Elton, Edwin J., Martin J. Gruber, Sanjiv Das, and Matt Hlavka, 1993, Efficiency with costly information: a reinterpretation of evidence from managed portfolios, review of financial studies 6, 1-21. Fama, E.F. , and K.R. French, 1993, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33, 3-56. Ferson, Wayne E., and Campbell R. Harvey, 1991, The variation of economic risk premiums, Journal of Political Economy 99, 385-415. French, Kenneth R., William Schwert, and Robert F. Stambaugh, 1987, Expected stock returns and volatility, Journal of Financial Economics 19, 3-29. Glosten, Lawrence R, Ravi Jagannathan, and David E. Runkle, 1993, On the relation between the expected value and the volatility of the nominal excess return on stocks, journal of finance 48, 1779-1801. 20 Goyal, Amit, and Pedro Santa-Clara, 2003, Idiosyncratic risk matters！, Journal of finance 58, 975-1007. Granger, C. , and P. Newbold, 1974, Spurious regressions in econometrics, Journal of Econometrics 2, 111-120. Grinblatt, Mark, and Sheridan Titman, 1992, The persistence of mutual fund performance, Journal of Finance 47, 1977-1984. Grinblatt, Mark, Sheridan Titman, and Russ Wermers, 1995, Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior, American Economic Review 85, 1088-1105. Jegadeesh, Narasimham, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 48, 65-91. Kosowski, R., Timmermannm A., R. Wermers, and H. White, 2005, Can Mutual Fund "Stars"? Really Pick Stocks? New Evidence from a Bootstrap Analysis, Journal of Finance 61, 2551-2595. Malkiel, Burton G., and Yexiao Xu, 1999, The structure of stock market volatility, Working paper, Princeton University. Malkiel, Burton G., and Yexiao Xu, 2001, Idiosyncratic risk and security returns, Working paper, University of Texas at Dallas. Morck, Randall, Bernard Yeung, and Wayne Yu, 2000a, The Information Content of Stock Markets: Why Do Emerging Markets Have Comoving Stock Price Movements, Journal of Financial Economics 58, 215-238. Pastor, L. , and R. Stambaugh, 2002, Mutual Fund Performance and Seemingly Unrelated Assets, Journal of Financial Economics 63, 315-350. Wermers, R., 2000, Mutual Fund Performance : An Empirical Decomposition into Stock Picking Talent, Style, Transactions Costs, and Expenses, Journal of Finance 55, 1655-1703. Wermers, Russ, 1996, Momentum investment strategies of mutual funds, performance persistence, and survivorship bias, Working paper, Graduate School of Business and Administration, University of Colorado at Boulder, Boulder, Col. . 21 Table I Returns and Idiosyncratic Risk of Mutual Fund : 1995-2006 This table presents returns and idiosyncratic risk of mutual fund. The sample period is January 1995 to December 2006 (864,126 monthly observations). The variable Market returns is the CRSP value-weighted portfolio of all NYSE, Amex, and Nasdaq stocks. The variable Mutual fund returns is the equal-weighted portfolio of Morningstar. Monthly Idiosyncratic Risk from equation (1) to (3). Monthly Idiosyncratic Risk by 3 Factor model from equation (4). Monthly Idiosyncratic Risk by 4 Factor model from equation (5). year Monthly Market Mutual Fund Returns Yearly Yearly Yearly return returns (%) (%) (Standard Idiosyncratic Idiosyncratic Risk Idiosyncratic Risk 3 number Deviation) Risk (Mean*10 ) by 3 Factor model by 4 Factor model 3 (Mean*10 ) (Mean*103) 1995 22,762 2.59 2.2982 (2.6736) 1.1338 0.7140 0.6982 1996 28,662 1.66 1.6014 (3.9135) 1.7013 1.2073 1.1775 1997 37,041 2.32 1.8888 (4.8037) 2.0741 1.0678 1.2089 1998 47,162 1.90 1.3689 (7.3634) 7.3817 4.9269 5.1012 1999 57,136 1.97 2.1816 (5.8846) 7.0280 2.5297 1.9481 2000 70,990 -0.83 -0.0013 (8.8520) 5.1245 4.3326 4.7225 2001 87,465 -0.81 -0.8037 (8.9204) 9.2708 5.3420 4.0314 2002 95,590 -1.78 -1.9677 (8.6496) 9.1041 8.8495 3.5370 2003 99,062 2.46 2.4539 (3.9202) 2.7764 3.0628 2.6364 2004 101,731 1.05 1.0318 (3.4265) 1.4788 1.0857 1.2549 2005 105,561 0.62 0.6351 (3.2767) 0.4687 0.3080 0.4521 2006 110,964 0.06 1.0296 (3.0092) 1.0070 0.4144 0.5384 Total 864,126 22 Standard Deviation 20 16 12 Pr e t ec n 8 4 0 1996 1998 2000 2002 2004 2006 Year Standard Deviation (MA) 7 6 5 e et P rc n 4 3 2 1 1996 1998 2000 2002 2004 2006 Year Figure I The Volatility of Mutual Fund Returns This figure plots the average standard deviation of mutual fund for the period January 1995 to December 2006. The bottom panel uses a 12-month simple moving average of the top panel. NBER recessions are represented by shaded bars. 23 Standard Deviation 90 80 70 60 Pr e t 50 ec n 40 30 20 10 0 1996 1998 2000 2002 2004 2006 Year Standard Deviation (MA) 20 16 12 Pr e t ec n 8 4 0 1996 1998 2000 2002 2004 2006 Year Figure II The Volatility of Idiosyncratic Risk on Mutual Fund This figure plots the average standard deviation of idiosyncratic risk of mutual fund for the period January 1995 to December 2006. Monthly Idiosyncratic Risk by 4 Factor model from equation (5) and (1) to (3). The bottom panel uses a 12-month simple moving average of the top panel. NBER recessions are represented by shaded 24 Table II Predictive Regression This table presents the results of a one-month-ahead predictive regression of the excess mutual fund return on lagged explanatory variables. The variable V is the average mutual fund variance, and Vidi is the variance of average idiosyncratic risk of mutual fund. Both are calculated using monthly data. The sample period is January 1995 to December 2006 (864,126 monthly observations). Where Newey-West adjusted t value in parentheses. Level of significance: 1%***; 5%**; 10%* Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Constant 0.5690 -0.0769 0.5387 0.8349** 0.8465 1.6536*** (1.3766) (-0.2917) (0.0562) (2.2108) (1.1171) (4.1621) Variance V 0.0093 (0.8684) Vidi -0.0005*** (-4.6834) Standard V 0.0562 (0.3272) Deviation Vidi -0.0046* (-1.9081) Ln V -0.0578 (-0.1454) Variance Vidi -0.2842** (-1.9903) Adjust R2 -0.0017 -0.0015 -0.0062 0.0007 -0.0069 0.0242 25 Table III Predictive Regression Controlling for Business Cycle Variables This table presents the results of a one-month-ahead predictive regression of the excess mutual fund return on lagged explanatory variables. The variable V is the average mutual fund variance, and Vidi is the variance of average idiosyncratic risk of mutual fund. Both are calculated using monthly data. The sample period is January 1995 to December 2006 (864,126 monthly observations). DP is the logged dividend price ratio calculated as the difference between the log of last 12 month dividends and the log of the current price index of the CRSP value-weighted index. RTB is the relative three-month Treasury bill rate calculated as the difference between T-bill and its 12- month moving average. Term Spread is the difference between the yield on long-term government bonds and T-bill. Default Spread is the difference between the yield on BAA- and AAA rated corporate bonds. Where Newey-West adjusted t value in parentheses. Level of significance: 1%***; 5%**; 10%* Model 1 Model 2 Model 3 Model 4 Constant 6.0591** 5.9962** 5.9623** 5.9064** (2.4524) (2.3067) (2.3617) (2.2188) Returnt-1 0.1788** 0.1828** 0.1767** 0.1808** (2.3809) (2.4911) (2.3048) (2.4210) V 0.0153 0.0153 (1.5564) (1.5527) Vidi -0.0002 0.0001*** (0.6517) (-0.5988) DP -17.954*** -17.562** -17.829*** -17.448*** (-2.3007) (-2.1961) (-2.2794) (-2.1775) RTB 0.6036 0.7141 0.5622 0.6753 (1.2134) (1.4542) (1.0432) (1.2688) Term Spread 0.5039 0.5584 0.5092 0.5631 (1.2589) (1.3011) (1.2580) (1.2980) Default Spread -1.1906 -1.6627 -1.1052 -1.5818 (-0.6277) (-0.8338) (-0.5557) (-0.7588) Adjust R2 0.0265 0.0330 0.0200 0.0264 26 Table IV Returns and Idiosyncratic Risk of Mutual Fund : by Investment-Objective Category This table presents returns and idiosyncratic risk of mutual fund by investment-objective category. The sample period is January 1995 to December 2006 (13,779 yearly observations). The investment-objective category consist aggressive growth funds, growth and income funds, long-term growth, and balance or income fund. The variable Mutual fund returns is the equal-weighted portfolio of Morningstar. Yearly Idiosyncratic Risk from equation (1) to (3). Yearly Idiosyncratic Risk by 3 Factor model from equation (4). Yearly Idiosyncratic Risk by 4 Factor model from equation (5). Yearly return Mutual fund Yearly Yearly Yearly number return (%) Idiosyncratic Idiosyncratic Idiosyncratic (Standard Risk (Mean*103) Risk by 3 Factor Risk by 4 Factor Deviation) model model (Mean*103) (Mean*103) Aggressive growth 4,317 1.11664 4.0176 3.0736 2.6847 (1.6144) Growth and income 3,774 0.9349 1.7878 1.6472 1.1867 (1.2966) Long-term growth 5,028 0.9471 2.5855 2.1205 1.7715 (1.5197) Balance Fund & 660 0.9264 1.3579 1.2809 0.9237 Income Fund (1.0775) Total 13,779 27 Table V Returns and Idiosyncratic Risk of Mutual Fund : by Survivorship Period This table presents returns and idiosyncratic risk of mutual fund by Survivorship Period. The sample period is January 1995 to December 2006 (19,309 yearly observations). The Survivorship Period divided 3 parts, less than 5 year (< 5 year), between 5 ~ 10 year, and larger than 10 year ( >10year). The variable Mutual fund returns is the equal-weighted portfolio of Morningstar. Yearly Idiosyncratic Risk from equation (1) to (3). Yearly Idiosyncratic Risk by 3 Factor model from equation (4). Yearly Idiosyncratic Risk by 4 Factor model from equation (5). Survivorship Period Yearly return Mutual fund Yearly Yearly Yearly Number (%) return (%) Idiosyncratic Idiosyncratic Idiosyncratic (Standard Risk (Mean*103) Risk by 3 Factor Risk by 4 Factor Deviation) model model (Mean*103) (Mean*103) > 10 year 4,250 0.9214 2.4922 2.1309 1.8892 (1.4016) 5~10 year 6,509 0.9106 2.7000 2.3594 1.9225 (1.4443) < 5 year 8,550 1.2321 2.5303 1.7251 1.3895 (1.3929) Total 19,309 28 Table VI Summary Statistics Summary statistics for all of the variables used in the analysis are presented. The observations are fund-years. The portfolios characteristics are log of TNA, expense ratio, turnover ratio, maximum load fees and Age. TNA is total net assets. Expense ratio is management, administrative expenses divided by average TNA. Turnover represents the minimum of aggregate purchases of securities or aggregate sales of securities, divided by the average total net assets of the fund. Maximum load is the sum of maximum front-end, back-end and deferred sales charges. Fund Age is live funds are those in operation at the end of the sample. The manager characteristics variables include the manager CFA, age, tenure, sex, MBA and PHD. A dummy variable that takes the value of one if the manager has a CFA and zero otherwise. A dummy variable that takes the value of one if the manager is man and zero otherwise. A dummy variable that takes the value of one if the manager has a MBA degree and zero otherwise. A dummy variable that takes the value of one if the manager has a PHD degree and zero otherwise. Variable # of Obs Mean Std. Dev TNA (millions) 25,389 364.928 1964.793 Expense ratio (%) 25,389 1.323 0.972 Turnover ratio (%) 25,389 84.275 104.551 Maximum load fees (%) 25,389 1.067 1.983 Fund Age 25,389 7.315 9.384 Manager CFA (%) 7,993 0.531 0.499 Manager Age 7,993 46.976 9.442 Manager Tenure 7,993 5.833 4.779 Manager Sex (%) 7,993 0.914 0.280 Manager MBA (%) 7,993 0.587 0.492 Manager PHD (%) 7,993 0.135 0.342 29 Table VII Mutual Fund Performance, Idiosyncratic Risk and Portfolios Characteristics This table estimates the relationship between mutual fund performance, idiosyncratic risk and mutual fund portfolios characteristics. The sample period is January 1995 to December 2006 (25,389 yearly observations). Model 1, simple excess return is regressed on fund portfolios Characteristics. Model 2, Beta4 is regressed on fund portfolios Characteristics. Beta4 is the coefficient of the market portfolio in a regression of the fund's monthly returns minus the risk-free rate on the monthly returns of the market portfolio minus the risk-free rate, HML, SMB, and MOM. Model 3, Idiosyncratic Risk is regressed on fund portfolios Characteristics. Idiosyncratic Risk is calculated by 4 Factor model from equation (5). The observations are fund-years. Where Newey-West adjusted t value in parentheses. Level of significance: 1%***; 5%**; 10%* Dependent Variables Independent Variables Model 1 Model 2 Model 3 Return Beta4 Idiosyncratic Risk4 Constant 1.0645*** 3.0164*** 1,7830*** (49.9108) (28.0434) (23.5781) ln TNA -0.00001*** -0.00001** -0.00001** (-2.6442) (-2.0386) (-2.3255) Expense ratio 0.2514 -4.8759 -2.9461 (0.3386) (-1.1223) (-0.8861) Turnover ratio -0.0090 0.1075** 0.0594** (-0.9199) (2.4114) (2.1154) Maximum load fees -0.0552 1.6892 0.4968 (-0.1083) (0.6195) (0.2741) Fund Age -0.0118*** -0.0134** 0.0096*** (-10.3286) (-2.9062) (3.1153) Adjust R2 0.0054 0.0011 0.0014 30 Table VIII Mutual Fund Performance, Idiosyncratic Risk and Manager Characteristics This table estimates the relationship between mutual fund performance, idiosyncratic risk and mutual fund manager characteristics. The sample period is January 1995 to December 2006 (7,993 yearly observations). Model 1, simple excess return is regressed on fund manager characteristics. Model 2, Beta4 is regressed on fund manager characteristics. Beta4 is the coefficient of the market portfolio in a regression of the fund's monthly returns minus the risk-free rate on the monthly returns of the market portfolio minus the risk-free rate, HML, SMB, and MOM. Model 3, Idiosyncratic Risk is regressed on fund manager characteristics. Idiosyncratic Risk is calculated by 4 Factor model from equation (5). The observations are fund-years. Where Newey-West adjusted t value in parentheses. Level of significance: 1%***; 5%**; 10%* Dependent Variables Independent Variables Model 1 Model 3 Model 4 Return Beta4 Idiosyncratic Risk4 Constant 1.4308*** -1.6125*** 2.0275*** (13.1636) (-5.1191) (16.8322) Manager CFA -0.0644 0.1239 0.0068 (-1.5553) (0.8823) (0.1614) Manager Age -0.0069*** 0.0112* -0.0052** (-3.2065) (1.8913) (-2.2044) Manager Tenure -0.0202*** -0.0035 -0.0127*** (-4.2251) (-0.2094) (-2.4171) Manager Sex 0.0465 0.0765 -0.0777 (0.6594) (0.4271) (-1.1063) Manager MBA 0.0949** 0.2125 -0.0009 (2.3295) (1.4526) (-0.0226) Manager PHD 0.1023* -0.0653 0.0313 (1.8443) (-0.3391) (0.5369) Adjust R2 0.0072 0.0001 0.0024 31 Table IX Mutual Fund Performance, Idiosyncratic Risk, Portfolios Characteristics and Manager Characteristics This table estimates the relationship between mutual fund performance, idiosyncratic risk and mutual fund portfolio, manager characteristics. The sample period is January 1995 to December 2006 (11,743 yearly observations). Model 1, simple excess return is regressed on fund portfolio and manager characteristics. Model 2, Beta4 is regressed on portfolio and fund manager characteristics. Beta4 is the coefficient of the market portfolio in a regression of the fund's monthly returns minus the risk-free rate on the monthly returns of the market portfolio minus the risk-free rate, HML, SMB, and MOM. Model 3, Idiosyncratic Risk is regressed on fund portfolio and manager characteristics. Idiosyncratic Risk is calculated by 4 Factor model from equation (5). The observations are fund-years. Where Newey-West adjusted t value in parentheses. Level of significance: 1%***; 5%**; 10%* Dependent Variables Model 1 Model 3 Model 4 Independent Variables Return Beta4 Idiosyncratic Risk4 Constant 1.3770*** -1.4265*** 2.6700*** (8.9492) (-3.3065) (14.8360) ln TNA -0.00002 0.0001 -0.00003*** (-1.3956) (0.8849) (-3.2204) Expense ratio -0.0252 -10.1034 -6.5451* (-0.0084) (-0.4667) (-1.8374) Turnover ratio -0.0377* 0.0756 0.0023 (-1.8827) (1.0563) (0.1086) Maximum load fees 0.2502 -9.7006* -1.0736 (0.2515) (-1.9063) (0.9576) Fund Age -0.0027 0.0031 -0.0093*** (-1.4932) (0.3242) (-4.0704) Manager CFA -0.1403*** 0.0173 -0.0341 (-2.6473) (0.0713) (-0.5774) Manager Age -0.0073** 0.0092 -0.0096*** (-2.4892) (1.1523) (-2.9440) Manager Tenure -0.0036 -0.0444 -0.0248*** (-0.5938) (-1.3277) (-3.7216) Manager Sex -0.0165 0.4522 -0.1524 (-0.1898) (1.6017) (-1.4421) Manager MBA 0.0130 0.4112 -0.0208 (0.2449) (1.3939) (-0.3602) Manager PHD -0.0303 0.1362 0.0342 (-0.3832) (0.4129) (0.4044) Adjust R2 0.0039 0.0027 0.0167 32 Table X Portfolios of Mutual Funds on Lagged 1-Year Return This table estimates the momentum effect. Mutual funds are sorted on January 1each year from 1995 to 2006 into decile portfolios based on their previous calendar year's return. The portfolios are equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the highest past one-year return comprise decile 1and funds with the lowest comprise decile 10. Rm is the excess return on the CRSP value-weighted portfolio of all NYSE, Amex, and Nasdaq stocks. Where SMBt and HMLt are factor mimicking portfolios for size, book-to-market value effects. MOM as the equal-weight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal equal-weight average of firms with the lowest 30 percent eleven-month returns lagged one month. The t-statistics are in parentheses. Portfolio Monthl Std CAPM 4-Factor Model y excess Dev Alpha Rm Adj Alpha Rm SMB HML MOM Adj return (%) R-sq R-sq (%) 1 (high) 9.31 8.48 7.74 -5.61 0.010 7.64 -5.07 -0.05 0.25 -0.07 0.022 (124.6) (-28.66) (105.5) (-24.14) (-5.02) (24.04) (-15.23) 2 5.43 1.61 5.23 -0.72 0.005 4.84 -1.19 0.10 0.13 -0.04 0.076 (451.2) (-20.33) (372.4) (-31.83) (50.93) (69.27) (-47.26) 3 3.73 1.09 3.57 -0.57 0.007 3.55 -0.66 0.02 -0.01 -0.01 0.012 (465.9) (-23.94) (425.9) (-26.86) (12.69) (-6.22) (-7.24) 4 2.27 0.91 2.08 -0.67 0.014 2.24 -0.63 -0.04 -0.09 -0.01 0.117 (326.2) (-34.29) (344.4) (-32.97) (-39.38) (-89.00) (-23.30) 5 1.06 1.03 1.13 0.25 0.002 1.33 0.34 -0.05 -0.13 -0.02 0.166 (153.2) (11.36) (183.3) (16.09) (-46.84) (-116.2) (-28.06) 6 -0.09 1.29 0.30 1.34 0.025 0.38 0.89 -0.01 -0.13 -0.05 0.202 (31.98) (46.57) (42.28) (32.55) (-11.12) (-88.79) (-66.76) 7 -1.31 1.68 -0.98 1.16 0.011 -1.13 0.002 0.07 -0.07 -0.05 0.145 (-80.58) (30.62) (-97.92) (0.07) (49.44) (-35.79) (-46.96) 8 -2.74 2.19 -2.81 -0.24 0.0003 -2.85 -1.16 0.15 0.02 -0.03 0.106 (-183.6) (-4.95) (-189.7) (-23.85) (81.65) (7.87) (-20.38) 9 -4.46 2.75 -4.61 -0.57 0.001 -4.81 -1.82 0.15 -0.03 0.03 0.050 (-242.6) (-9.36) (-241.4) (-27.59) (58.91) (-8.10) (13.19) 10 (low) -8.84 5.58 -9.30 4.51 0.004 -9.69 -2.98 -0.03 -0.17 0.08 0.010 (-229.3) (35.21) (-219.9) (-19.76) (-5.43) (-25.62) (16.17) Total monthly returns 839,530 numbers 33 Table XI Portfolios of Mutual Funds on Lagged 1-Year Idiosyncratic Risk This table estimates the momentum effect. Mutual funds are sorted on January 1each year from 1995 to 2006 into decile portfolios based on their previous calendar year's idiosyncratic risk. The portfolios are equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the highest past one-year return comprise decile 1and funds with the lowest comprise decile 10. Rm is the excess return on the CRSP value-weighted portfolio of all NYSE, Amex, and Nasdaq stocks. Where SMBt and HMLt are factor mimicking portfolios for size, book-to-market value effects. MOM as the equal-weight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal equal-weight average of firms with the lowest 30 percent eleven-month returns lagged one month. The t-statistics are in parentheses. Portfolio idiosyncrati Std CAPM 4-Factor Model c risk Dev Alpha Rm Adj Alpha Rm SMB HML MOM Adj 3 (Mean*10 ) (%) R-sq R-sq 1 (high) 20.78 306.4 2.38 1.14 2E-05 2.74 3.96 -0.13 0.12 0.07 0.001 (11.09) (1.64) (12.55) (5.25) (-5.50) (3.60) (3.62) 2 4.82 3.16 -0.44 -0.16 0.006 0.48 0.09 -0.02 0.01 0.01 0.113 (197.9) (-23.13) (220.2) (12.70) (-57.53) (41.14) (36.70) 3 3.73 1.09 -0.01 0.10 0.147 -0.008 0.08 0.0002 -0.003 -0.001 0.267 (-30.68) (120.3) (-32.99) (106.1) (5.07) (-88.0) (-21.31) 4 1.52 0.97 0.16 0.02 0.001 0.16 0.04 -0.002 0.003 -0.0004 0.029 (219.6) (6.84) (218.1) (18.53) (-21.27) (32.05) (-6.31) 5 0.81 0.59 0.09 0.03 0.008 0.09 0.05 -0.001 -0.002 -0.001 0.037 (212.8) (26.00) (209.7) (34.25) (-18.00) (33.44) (-17.34) 6 0.33 0.33 0.05 0.05 0.067 0.05 0.06 -0.0001 0.001 -0.001 0.080 (211.6) (77.65) (204.4) (77.50) (-3.02) (18.96) (-29.70) 7 -0.01 0.21 0.02 0.06 0.206 0.02 0.06 0.0001 -0.001 -0.001 0.247 (127.4) (147.7) (126.1) (136.9) (2.93) (-33.77) (-40.01) 8 -0.36 0.39 -0.01 0.10 0.147 -0.01 0.08 0.0002 -0.003 -0.001 0.267 (-30.68) (120.3) (-32.99) (106.1) (5.07) (-87.98) (-21.31) 9 -0.94 0.79 -0.05 0.16 0.10 -0.05 0.13 0.002 -0.005 0.002 0.164 (-94.23) (95.50) (-105.3) (76.83) (24.65) (-62.32) (34.89) 10 (low) -4.71 85.48 -0.41 0.21 3E-06 -0.46 -0.05 0.01 -0.03 0.02 3E-04 (-7.10) (1.13) (-7.78) (-0.27) (1.51) (-2.95) (4.13) Total monthly idiosyncratic 839,530 risk numbers 34