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idiosymcraticriskinmutualfund

VIEWS: 2 PAGES: 34

									                                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
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                                            20
Goyal, Amit, and Pedro Santa-Clara, 2003, Idiosyncratic risk matters!, Journal of
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 .




                                          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

								
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