This document provides a 3-sentence summary of a research paper that develops a multifactor model to forecast the 1-year returns of actively managed equity mutual funds. The model uses forecasts of a fund's manager skill, style (based on factors like market, size, value, and momentum), and expected factor returns. When tested on German equity funds, the multifactor model substantially improved forecasts compared to a naive model, reducing the mean squared error by up to 30% and yielding returns over 200 basis points higher for top-decile funds.

1. Original Article
Predicting returns of equity
mutual funds
Received (in revised form): 18th September 2008
Olaf Stotz
holds the BHF-BANK Endowed Chair of Private Wealth Management at Frankfurt School of Finance & Management, Germany. His
research interests include wealth management, empirical finance, asset pricing and behavioural finance. His research has been
published by various international academic journals, has been discussed in the financial press and is also applied in the financial
industry. Before his academic career he also worked in the fund management industry for several years.
Correspondence: Frankfurt School of Finance & Management, Sonnemannstrae 9-11, D-60314 Frankfurt, Germany
ABSTRACT This paper investigates 1-year-ahead forecasts of actively managed equity
mutual funds. A multifactor forecast model is developed that employs forecasts on the
manager’s skill, the fund’s style and the expected factor returns. On the basis of a sample of
German equity funds, we show that this forecast model substantially improves forecast
power in relation to a naıve forecast model, which just extrapolates past returns into the
¨
future. In particular, the multifactor model reduces the mean-squared error (mean absolute
¨
error) by up to 30 per cent compared to the naıve model. More importantly, from the
perspective of a mutual fund investor, the return of top-decile funds chosen by the multifactor
model exceeds the average return of all funds by more than 200 basis points per year.
Journal of Asset Management (2009) 10, 158–169. doi:10.1057/jam.2009.7
Keywords: out-of-sample return forecasting; mutual funds; multifactor model
naıve investor
¨
INDRODUCTION The return of a fund is dependent on two
Over the past few decades, private investors sources. The first source is the return of the
have allocated an increasing amount of fund’s underlying stocks, which can be
money to mutual funds, thus making this explained by various risk factors. Four factors
financial innovation a sweeping success. have been identified by theoretical and
Mutual fund investors face the problem of empirical research that are successful in
having to select appropriate funds out of a explaining stock returns (in excess of the
universe of several hundred individual funds. risk-free rate): market, size, value and
Financial theory guides the investor through momentum (for example Fama and French,
this choice by looking at each fund’s 1993; Jegadeesh and Titman, 1993). The
expected return and risk, as measured by the market factor is based on the capital asset
covariance matrix of returns (Markowitz, pricing model, and predicts that high beta
1952). The optimal selection of funds then stocks should produce higher returns than
crucially depends on good estimates of low beta stocks. The size factor refers to the
expected returns (for example Best and empirical observation that, on average, stocks
Grauer, 1991; Chopra and Ziemba, 1993). with a small market capitalisation perform
Financial theory, however, is silent about the better than stocks with a large market
estimation of expected returns. capitalisation. The value factor captures the
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
www.palgrave-journals.com/jam/

2. Predicting returns of equity mutual funds
difference in returns between stocks with a valuation ratios (for example book-to-market
high book-to-price ratio (value stocks) and ratio, dividend yield) are able to predict the
stocks with a low ratio (growth stocks). The stock market’s excess return. Predictability of
momentum effect is related to a stock’s past the remaining three factors (size, value,
1-year return. Stocks with a high return in momentum), however, has been rarely
the past year perform better over the next investigated. However, the book-to-market
year than stocks with a low return do. These ratio seems to predict the return on the size
factors have been found to explain the cross- and value factor (in addition to the market
section of stock returns in various countries return), as the empirical evidence of Kothari
and over different samples. and Shanken (1997), Pontiff and Schall
The second source of a fund’s return is the (1998), Lewellen (1999) and Cohen et al
decision of a fund manager as to which (2003) demonstrates. Therefore, the book-
securities she or he holds in a fund. This to-market ratio seems to be an appropriate
decision can be classified into management conditioning variable for predicting factor
style, selection skill and timing skill. A returns. The management style is an
preference for certain stock characteristics is important issue in fund management (for
described by the fund’s management style. example Sharpe, 1992, and Brown and
Stock characteristics refer to the four factors Goetzmann, 1997). Fund tracking
mentioned above. For example, a value companies regularly report the fund’s style
manager tends to invest in stocks with high (see, for example, the style box created by
book-to-price-ratios (value stocks). Selection Morningstar). Managers tend to hold the
skill describes the fund manager’s ability to style of their fund relatively steady over time,
find stocks that outperform a benchmark and the style can therefore be derived from
index on a risk-adjusted basis. Timing skills the correlation between past fund returns
characterise the ability of whether a fund and factor returns (for example Davis, 2001;
manager is able to buy and sell stocks (with Chan et al, 2002). Selection skills are found
certain characteristics) at favourable times. to be persistent over a horizon of up to 2
For example, a fund manager can follow an years (for example Hendricks et al, 1993;
active timing strategy by switching between Zheng, 1999; Bollen and Busse, 2004).
stocks and cash or between styles (for Therefore, these can also be derived from past
example, from value to growth). A manager fund returns. Timing decisions, however, do
with good timing skills in value stocks will not seem to enhance the performance of
buy value stocks before they outperform funds. It is found that parameters measuring
growth stocks. Management style, selection timing skills are usually not significant (for
skills and timing skills then characterise a example Jiang, 2003; Bollen and Busse, 2004),
fund manager’s investment decisions. and, in addition, they seem difficult to predict.
To predict a fund’s return, an investor has This paper, therefore, will pay particular
to forecast the returns on the risk factors and attention to this issue.
the investment decisions (management style We combine the prediction of factor
and manager’s skills in selection and timing). returns and the information on a fund’s style
Predictability of factor returns has been and a manager’s skills within a multifactor
largely confined to the market return (see, model. We then compare the prediction
for example, Fama and Schwert, 1977; Keim results with that of a naıve forecast, which
¨
and Stambaugh, 1986; Campbell, 1987; simply extrapolates the past return into the
Fama and French, 1988; Lewellen, 1999). In future. We have chosen the naıve model as
¨
general, it is found that standard macro- the benchmark model because empirical
economic variables (for example term research implies that mutual fund investors
structure of interest rates, credit spread) and base their estimates of expected returns
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 159

3. Stotz
primarily on past returns. As a result, In specifying equation (1), we rely on
investors put more money into funds with a empirical and theoretical research that has
high return in the past year than into funds shown that the following four factors
with a low return (for example Chevalier and describe the cross-section of stock returns
Ellison, 1997; Sirri and Tufano, 1998). (for example Fama and French, 1993;
Gruber (1996) shows that newly invested Jegadeesh and Titman, 1993):
money slightly outperforms the average
the return of the stock market in excess of
mutual fund. This outperformance, however,
the risk-free rate: market factor ‘MAR’;
can be largely attributed to a higher risk of
the return of small stocks (small market
the fund (Carhart, 1997). Therefore, it seems
capitalisation) in excess of large stocks
questionable as to whether investors should
(large market capitalisation): size factor
rely solely on past returns when making
‘SMB’;
investment decisions and predict mutual fund
the return of value stocks (high book-to-
returns.
market stocks) in excess of growth stocks
This paper is organised as follows. The
(low book-to-market stocks): value factor
multifactor model is presented in the next
‘HML’;
section. Estimation details of the prediction
the return of good performing stocks
model are discussed in the third section. This
(high past-year return) in excess of bad
model is then used to predict fund returns.
performing stocks (low past-year return):
Performance results of the prediction model
momentum factor ‘1YR’.
are given in the fourth section. The last
section concludes. According to the four-factor model, the
excess return of stock j is then
THE MODEL ~j;t ¼ aj þ bMAR Á ~tMAR þ bSMB Á ~tSMB
r r r
j j
This section derives the multifactor model
of fund returns via three steps. The first step þ bHML Á ~tHML þ b1YR Á ~t1YR þ ~j;t :
j r j r e
relates a stock’s return to various risk factors
within a multifactor approach. The second
step models the selection decision of stocks by
the fund manager. This step also allows the Selection decision of the fund
characterisation of the fund’s management manager and management style
style. The third step finally introduces the
A fund manager now combines various
timing strategy of the fund manager.
stocks within a fund portfolio, which then
yields a return of
Multifactor model of stock returns
!
The multifactor model states the stock’s X
Nt X
4
excess return as ~p;t ¼
r wj;t Á
~ aj þ bk Á ~tk þ ~j;t
j r e
j¼1 k¼1
X
n
!
~j;t ¼ aj þ
r bk
j Á ~tk
r þ ~j;t ;
e (1Þ X
Nt X
Nt X
4
k¼1 ¼ wj;t Á aj þ
~ wj;t Á
~ bk
j Á ~tk
r
j¼1 j¼1 k¼1
where
X
Nt
rj,t ¼ return of stock j in excess of the
˜ þ wj;t Á ~j;t
~ e
risk-free rate j¼1
rt k ¼ return of factor k
˜ X
4
aj ¼ risk-adjusted return ¼ ap;t þ ~ r
bk Á ~tk þ ~p;t ;
e ð2Þ
p;t
bk ¼ factor loading of stock j to factor k.
j k¼1
160 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

4. Predicting returns of equity mutual funds
where well compared to growth stocks, she or he
would buy more stocks with a high load on
wj;t ¼ weight of stock j in fund p
~
the value factor r t HML, thereby increasing the
˜
ðfund manager’s investment decisionÞ fund’s value beta bHML. As a result, betas are
p,t
Nt ¼ number of stocks in fund p random variables that change taking
~p;t ¼ return of fund p in excess of the
r expectations of equation (2) as follows:
risk free rate X h
4 i  Ã
 Ã
E ~p;tþ1 ¼ ap þ ~
E bk k
X
Nt r p;tþ1 Á E ~
rtþ1
ap;t ¼ wj;t Á aj ¼ risk adjusted return
~ k¼1
(4Þ
j¼1 X
4 h i
þ ~
cov bk ; ~tþ1 :
rk
ðmeasures selection skillÞ k¼1
p;tþ1
X
Nt
~
bk ¼ wj;t Á bk ¼ factor loading of fund
~ ~p,t
p;t j cov(bk þ 1,rt k 1) then measures the fund
˜þ
j¼1
manager’s ability to time the return on factor
p to factor k ðmeasures fund’s styleÞ k. We follow Treynor and Mazuy (1966),
This four-factor model has also been who assume that the fund’s exposure to the
applied by Carhart (1997) to evaluate the (market) factor depends linearly on the
performance of fund returns, and will be used factor’s return:
in this paper to predict fund returns. a1 is ~
bk ¼ bp þ gp Á ~tk :
r (5Þ
p;t
interpreted as a parameter that measures the
stock selection skill of the fund manager. This Then gi characterises the timing skill of
k
is usually assumed to be constant through time the fund manager. Replacing bp,t þ 1 in
(see Christopherson et al, 1998, for an equation (2) with equation (5) yields
exception). bs are the sensitivities of the fund’s
X
4 X
4
return on the risk factors, from which the ~p;t ¼ ap þ
r bk Á ~tk
r þ gk Á ð~tk Þ2
r
p p
investment style of the fund can be deduced. k¼1 k¼1
For example, a value manager is characterised
þ ep;t: (6Þ
by a high bHML. In deriving expected fund
p
returns, we distinguish between a constant Taking expectations then results in
investment style (bk ¼ const.) and a time-
p,t
varying investment style (bk ¼ time-varying). X
4
p,t
E½~p;tþ1 Š ¼ ap þ
r bk Á E½~tþ1 Š
p rk
On the basis of constant selection skill and k¼1
investment style, the expected fund return can
X
4
then be estimated by þ gk Á E½ð~tþ1 Þ2 Š
rk
p
X
4 k¼1
 à Âk Ã
E ~p;tþ1 ¼ ap þ
r bk Á E ~tþ1 :
p r (3Þ X
4
k¼1 ¼ ap þ bk Á E½~tþ1 Š
p rk
k¼1
X
4
Timing decision of the fund þ gk Á ðE½~tþ1 Š2 þ Var½~tþ1 ŠÞ:
p rk rk
k¼1
manager
(7Þ
However, fund managers can vary the
exposure of their fund to the four factors in We estimate a fund’s expected return by
anticipation of predictable future factor equations (3) and (7). Details of the
returns. For example, if a fund manager determination of each component are
expects value stocks to perform exceptionally described below. We compare the prediction
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 161

5. Stotz
of these models with a naıve estimator that
¨ capitalisation). The return on the factor-
uses only information on the past year’s fund mimicking portfolio HML is the return
return. This naıve estimator seems to be
¨ difference between a value-weighted
applied by mutual fund investors, as portfolio of stocks with the highest book-to-
suggested by the mutual fund literature market ratio and a value-weighted portfolio
mentioned in the introduction. of stocks with the lowest book-to-market
ratio. The return on the factor-mimicking
portfolio 1YR is computed as the return
ESTIMATION DETAILS difference between a value-weighted
portfolio of stocks with the highest past-year
Data return and a value-weighted portfolio of
We compare the performance of prediction stocks with the lowest past-year return.4
models on the basis of equations (3) and (7) We predict 1-year-ahead returns at the
for a large sample of actively managed equity beginning of January of each year from 1991
mutual funds in Germany. The sample is to 2005, inclusive, for each existing fund.
taken from the database of BVI Thus, we have 15 prediction periods. As
(Bundesverband Investment und Asset funds are closed or newly created, not all 133
Management e.V.),1 and includes all funds funds exist in each prediction period. As a
that have an investment objective that is result, 1246 predicted fund return years are
focused on German equities. We exclude obtained. Applying equation (3) or (7) for
funds that (i) primarily invest in specific return prediction, the following parameters
sectors, (ii) have a performance guarantee, have to be estimated:
(iii) have a limited duration and (iv) are index
Stock selection coefficient alpha: ap
funds. This leaves 133 active funds. The
Style coefficient beta: bk
p
sample is free of a survivorship bias, as BVI’s
Timing coefficient gamma: gk p
database contains surviving and defunct
Expected factor returns: E[rt k 1]
˜þ
funds.2 Net return data of funds, which
Variance of factor returns: Var[rt k 1].
˜þ
account for management and administrative
costs, are from Datastream. We use the
1-month LIBOR-offered rate yield as a Alpha, betas and gammas
proxy for the risk free-rate, which is The fund’s alpha, betas and gammas are
subtracted from net returns to obtain excess estimated by an OLS regression, based on
returns. equation (3) and (7). ^, b and ^ then,
a ^ l,
The return on the market factor is symbolise OLS estimates. The estimation
proxied by the return of a stock market index period starts in January 1990 and ends in the
in excess of the risk-free rate (MSCI3 month before the prediction date (which is
Germany minus 1-month LIBOR-offered the beginning of January of each year). For
rate); the returns for the factors size, value example, when returns are forecasted at the
and momentum are constructed similarly to beginning of 1995, the estimation period
Fama and French (1993). Therefore, factor- covers the period from January 1990 up to
mimicking portfolios are computed. For December 1994. This rolling forecasting
example, the return on the factor-mimicking scheme uses only lagged information to
portfolio SMB is constructed as follows: the predict future returns. If the return series of a
value-weighted return of all stocks with the specific fund starts later (because the fund has
lowest market capitalisation (below median been created after January 1990), a minimum
market capitalisation) minus the value- of 52 weeks are required for parameter
weighted return of all stocks with the highest estimation. To obtain precise estimates,
market capitalisation (above median market weekly returns are used.
162 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

6. Predicting returns of equity mutual funds
Factor returns We use information variables that are
Expected factor returns are estimated both based on the empirical evidence of Kothari
unconditionally and conditionally, whereby and Shanken (1997), Pontiff and Schall
we can investigate whether or not fund (1998), Lewellen (1999) and Cohen et al
managers are able to exploit the predictability (2003). They demonstrate that the book-to-
of factor returns. In both cases, the market ratio (or spread of the ratio) is able to
estimation period starts at the beginning of predict the return in the market, size return
1980, and uses yearly returns because 1-year- and value factor. The return of the
ahead forecasts are made. The unconditional momentum factor will be forecasted on the
estimation approach (that is constant factor lagged momentum return because
returns) uses the average of the realised momentum relies on the notion of return
factor returns over the estimation period continuation. These assumptions result in the
of length T, which is denoted by following information variables:
 k à  à 1 X kT ItMAR ¼ logðBMMAR Þ;
t
E ~tþ1 ¼ AVG rtk ¼ Á
r r : (8Þ
T t¼1 t ItSMB ¼ logðBMS Þ À logðBMB Þ;
t t
Conditional factor returns are assumed to be ItHML ¼ logðBMH Þ À logðBML Þ and
t t
linearly related to information variables It. The
It1YR ¼ rtÀ1 :
1YR
prediction of each factor’s conditional expected
return is then based on the following model: where BMMAR is the book-to-market ratio
t
of the market index at t, BMS (BMB) is the
t t
~tþ1 ¼ f2kÀ1;t þ f2k;t Á Itk þ ~t :
rk ~ e (9Þ
book-to-market ratio of stocks with a small
The estimated OLS regression coefficients (large) market capitalisation, and BMH t
^
fk,t are used to obtain conditional forecasts of (BML) is the book-to market ratio of value
t
1-year ahead returns for each factor: (growth) stocks.
Âk à Finally, the variance of the factor return is
^ ^
E ~tþ1 jIt ¼ f2kÀ1;t þ f2k;t Á Itk :
r (10Þ estimated by the sample variance of realised
Table 1: Details of prediction models
Prediction Prediction of Consideration of Expected return
model factor returns manager’s
investment
decisions
1 Unconditional Management style, P ^k
4
selection skill E½~i;t þ 1 Š ¼ ^i þ
r a bi Á AVG½rtk Š
k¼1
2 Conditional Management style, P ^k ^
4
^
selection skill E½~i;t þ 1 jIt Š ¼ ^i þ
r a bi Á ðfi;2k þ fi;2k þ 1 Á Itk Þ
k¼1
3 Conditional Management style, X4
selection skill, E½~i;t þ 1 jIt Š ¼ ^i þ
r a ^ ^ ^
bk Á ðfi;2k þ fi;2k þ 1 Á Itk Þ
i
timing skill k¼1
X
4
þ ^k Á ððf þ f
^ ^ k 2
^2
li i;2k i;2k þ 1 Á It Þ þ sk Þ
k¼1
4 — Naıve
¨ E½~i;t þ 1 Š ¼ ri;t
r
^
a: selection coefficient.
^
b: style coefficient.
^
l: timing coefficient.
^
f: prediction parameter for conditional factor returns.
I: information variable for conditionally predicted factor returns.
s2: sample variance.
^
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 163

7. Stotz
factor returns, which is denoted by
P important (for example Leung et al, 2000).
s2 ¼ TÀ1 Á T ðrtk À AVGðr k ÞÞ2 .
^k 1
t¼1 t Therefore, we also calculate the average hit
Given these estimation details, Table 1 ratio (HR) as
presents an overview of the resulting models !
and their parameters. 1 X 1 X
T Mt
HR ¼ Á Á hri;tþ1 ; (13Þ
T t¼1 Mt i¼1
EVALUATING PREDICTION where
( Â Ã
MODELS 1 if E ~i;tþ1 Á ri;tþ1 40
r
We evaluate the forecast of each model on hri;tþ1 ¼ Â Ã
the basis of forecast performance (that is 0; if E ~i;tþ1 Á ri;tþ1 p0:
r
statistical perspective) and investment return HR indicates in how many years the
(that is investor’s perspective). The next prediction model will get the correct sign of
section presents the statistical perspective the return.
and the section after this the investor’s Table 2 summarises the forecast
perspective. performance results for each model. As
expected, the naıve prediction model 4
¨
produces the highest prediction error. The
Mean absolute error, mean MSE and MAE criteria show an estimation
squared error and hit ratio error of 27.47 per cent and 25.21 per cent,
The statistical performance of each respectively. This is even higher than the
prediction model is evaluated by the average standard deviation of fund returns,
difference between the return forecast which is about 22 per cent. The use of
and the realised return (that is forecasting information on the fund manager’s
error). Hereby, we compute two common investment decisions (management style and
statistical measures, the mean absolute selection skill) increases the forecast
error (MAE) and the mean-squared error performance. Model 1 reduces the
(MSE). The MAE and the MSE are prediction error by about 24 per cent. The
defined as the average across individual consideration of management style and
funds (Mt denotes the number of available selection skill improves the prediction results
funds in t) and over time (T ¼ 15 prediction substantially.
periods): If factor returns are predicted
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi conditionally (model 2) instead of
u
1 Xu 1 X
T
t Á
Mt
unconditionally (model 1), the prediction
MSE ¼ Â ðE½~i;tþ1 Š À ri;tþ1 Þ2
r
T t¼1 Mt i¼1 error is reduced by additional 10 per cent.
Compared to model 4, the reduction is about
(11Þ
30 per cent. Therefore, the conditional
and prediction of factor returns seems to improve
! `
the forecast performance vis a vis the
1 X 1 X
T Mt
E½~i;tþ1 Š À ri;tþ1 : unconditional prediction. However, fund
MAE ¼ Â Á r
T t¼1 Mt i¼1
(12Þ Table 2: Forecast performance of prediction models
The degree of accuracy of the respective Model MSE(%) MAE(%) HR(%)
forecast does not necessarily translate into
1 21.15 19.04 66.89
large investment returns. To achieve large 2 19.85 17.89 67.31
investment returns, the direction of the 3 20.80 18.68 64.49
4 27.47 25.21 57.17
forecast (positive or negative) can be more
164 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

8. Predicting returns of equity mutual funds
managers do not seem to be able to exploit performance, which will be investigated in
this predictability. Model 3 – which the next section.
models the timing of factor returns of fund
managers – does not improve forecast Decile portfolios
performance compared to model 2. This Return forecast are mainly used to guide
result resembles the empirical evidence of investment decisions. Therefore, we further
other studies that show that fund managers evaluate the forecast models from the
are not successful in timing (for example perspective of an investor, and address the
Chan et al, 2002; Bollen and Busse, 2004). issue of whether forecasts of models 1–3 can
Under the HR evaluation criteria, the be translated into investment decisions that
same conclusions can be drawn. The use of are superior to those of the naıve model 4.
¨
information on the fund manager’s selection This issue is investigated with decile
skill and the fund’s style in general improves portfolios that are formed on the basis of
the HR compared to the naıve model 4.
¨ estimates of each model’s expected returns.
Furthermore, the conditional prediction of Therefore, for each prediction date, funds are
factor returns enhances the HR. Model 2’s ranked into deciles on the basis of their
HR of 67.31 per cent is slightly higher than expected return. Funds with the highest
the HR of model 1. Accounting for factor (lowest) expected returns are designated to
timing by the fund manager (model 3), decile 1 (decile 10). The funds in each decile
however, worsens the HR. portfolio are held constant for the prediction
In summary, model 2 (conditional period (1 year), and are rearranged at the
prediction of factor returns and use of next prediction date according to their new
information on management style and expected returns. In each decile portfolio,
selection skill) is the best forecast model, as funds are equally weighted. The yearly
expected. The prediction error is almost 30 return of each decile portfolio is averaged
per cent lower compared to the naıve model 4.
¨ over the 15 prediction periods. If a model
In addition, model 2 produces an increase in produces good forecasts, the average
the HR of more than 10 percentage points. return should decrease from decile 1 to
The consideration of these observations decile 10, with a large difference between
should result in a better investment decile 1 and 10.
Table 3: Investment returns based on decile portfolios of prediction models
Decile
1 1 2 3 4 5 6 7 8 9 10 10–1
Panel A: mean realized return
1 9.68 9.64 10.25 9.79 8.91 9.68 7.63 8.40 8.00 6.58 3.10
2 11.00 10.30 9.79 10.00 9.65 8.86 8.51 8.33 7.73 4.78 6.22*
3 9.41 10.47 9.66 9.07 7.96 9.22 9.10 9.34 8.27 6.20 3.21
4 9.56 9.53 9.54 9.87 8.81 9.20 8.85 8.26 8.35 6.97 2.59
ALL 8.88
Panel B: Sharpe ratio=(mean realized return–risk-free rate)/standard deviation of realized return
1 18.15 22.20 23.80 21.69 18.42 21.97 13.96 17.34 16.11 9.97 8.18
2 25.55 23.91 22.45 22.30 21.84 18.55 17.38 16.98 14.70 0.79 24.76*
3 19.22 25.18 22.68 18.91 14.72 20.75 19.23 21.39 16.91 7.03 12.19
4 19.15 22.07 23.05 22.55 19.02 20.33 18.46 15.64 17.28 10.01 9.14
ALL 18.81
* significantly greater than zero at 5% level.
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 165

9. Stotz
Results for average returns of decile consideration of factor timing by the fund
portfolios are displayed in Panel A of Table 3. manager, therefore, does not seem to
Four main results can be observed from improve investment results. A likely reason
Table 3. First, prediction model 2 shows the for this puzzling result seems, to us, to be
best investment performance, and, therefore, that either fund managers lack timing skills or
reinforces its superiority from the statistical a timing strategy is not being followed by the
perspective. For example, decile 1 of fund manager. This notion is consistent with
prediction model 2 produces a return, which empirical research that finds that fund returns
is the largest of all prediction models (11.00 are not enhanced through timing (for
per cent per year). This is about 200 basis example Chan et al, 2002; Bollen and Busse,
points higher than the average of all mutual 2004). This issue is explored in more detail
funds (symbolised by ‘ALL’), and almost 150 in the next section.
basis points better than model 4. In addition, Fourth, the investment results for model 4
the difference between decile 1 and decile 10 are not as bad as suggested by its statistical
is also the largest (6.22 per cent per year), and performance. Panel A shows that the naıve ¨
significantly different from zero. The average model 4 is able to select funds that perform
return decreases almost uniformly from slightly better than the average fund. For
decile 1 to decile 10. Thus, the superior example, decile 1 achieves an average return
forecast performance from the statistical of 9.56 per cent per year, whereas the
perspective, displayed in the last section, can average mutual fund delivers just 8.88 per
also be translated into a superior investment cent per year. The difference between the
performance. The use of information on the returns of decile 1 and of decile 10 (displayed
fund manager’s selection skill, the fund’s style in the last column) is 2.59 per cent per year,
and the conditional prediction of factor which indicates that winner funds
returns also results in a good investment outperform loser funds (although the
performance. difference is not statistically greater than zero
Second, the conditional prediction of at the 5 per cent level). This result indirectly
factor returns results in a better investment supports the findings of Elton et al (1996),
performance than the unconditional who provide evidence that the performance
prediction (model 2 is better than model 1). of newly invested money (that is primarily in
The conditional prediction of factor returns funds with high past returns) marginally
increases the performance by an additional outperforms money already invested. A likely
132 basis points per year (decile 1). The reason for this observation seems to be a
predictability of factor returns translates, positive correlation between alpha and the
therefore, into substantial investment gains, past year’s returns. Therefore, the past returns
and investors can benefit from the seem to proxy partly the stock selection skill
conditional prediction of factor returns by (although not as well as alpha itself).
selecting funds that have a high style Panel B shows the corresponding realised
coefficient (that is factor loading) for the Sharpe ratios of each decile portfolio. The
style that is expected to achieve a high results reinforce the forecast power of
return. model 2. For example, decile 1 of model 2
Third, the results of model 3 show that achieves the highest Sharpe ratio, which is
fund managers are not able to exploit the substantially larger than the Sharpe ratio of
predictability of factor returns. Model 3 – the average fund and of model 4 (naıve ¨
which considers the factor timing of fund model). The Sharpe ratio of model 1
managers – leads to inferior investment decreases uniformly from decile 1 to decile
results compared to model 2, and to almost 10, indicating that this model can successfully
the same results as model 1. The discriminate good funds from bad funds. On
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10. Predicting returns of equity mutual funds
the basis of the test statistics of Jobson and decisions. In addition, parameters are
Korkie (1981), the difference in the Sharpe estimated with a large estimation error, and
ratio between decile 1 and decile 10 (last average t-values are small. Only 9 per cent of
column) is significantly greater than zero at all gammas are significantly greater than zero
the 5 per cent level. Therefore, the superior at the 5 per cent level. In contrast, style
investment performance reported before parameters’ betas are estimated with a lower
does not seem to be the result of a larger risk prediction error, resulting in 59 per cent
(measured by the standard deviation of significant betas at the 5 per cent level (not
returns), but instead of superior return reported in Table 4).
forecasts. We additionally investigate the stability of
estimated timing parameters. A positive
relation between past parameters and future
Why does modelling timing of parameters is a necessary condition to infer
fund managers not improve future timing skills from past return data (that
forecasts? is persistency of skills). Therefore, past
Results from the decile analysis summarised parameter estimates are regressed on future
in Table 3 suggest that the modelling of a parameter estimates:
fund manager’s factor timing decision does ^i;t ¼ intercept þ slope Á ^i;tÀ1 þ ei;t
g g
not improve investment performance. In this
section, we explain this result by We regress past parameters (denoted by
investigating timing coefficients in more g g
^i,tÀ1) on future parameters (denoted by ^i,t)
detail. We obtain two results: first, estimated in a pooled regression approach. Past
timing parameters are, on average, not parameters are estimated from 1990 to the
significantly different from zero. This prediction date, and future parameters are
indicates that the average mutual fund estimated over the year following the
manager is not a good market timer. Second, prediction date. A positive slope then
future timing parameters cannot reliably be indicates that timing skills persist. Table 5
derived from past returns, as they display a shows that this is partly not the case. Future
large degree of instability. gammas are not consistently and positively
Table 4 summarises estimates of gamma related to their past estimates. For example,
from equation (6) over the full sample the future timing parameter for the market
period. Parameters are averaged over all factor is positively related to its past value
individual funds. Estimated gammas are, on (slope for ^MAR equals 0.256, t-value ¼
g
average, not significantly different from zero, 4.514), whereas the relation between the
which indicates that fund managers are not future and past parameter on the momentum
successful market timers. Some average factor is negative (slope for ^1YR equals
g
timing parameters are even smaller than zero À0.512, t-value ¼ À3.794). These results
(size, momentum), indicating that fund suggest that timing is not a persistent
managers are losing money with their timing management skill, which further explains the
Table 4: Results for timing parameter estimates Table 5: Results for parameter stability from pooled
regressions
MAR SMB HML IYR
g
^ g
^ g
^ g
^
^MAR
g ^SMB
g ^HML
g ^IYR
g
Average 0.31 À0.381 0.491 À0.242
Average t-value 0.754 À0.565 0.815 À0.241 Intercept 0.058 0.878 0.329 À1.561
t-value 0.372 3.765 1.124 À10.182
The table displays estimated timing parameters from Slope 0.256 0.050 À0.104 À0.512
equation (6), which are based on the estimation period t-value 4.514 0.876 À1.321 À3.794
from 1990 to 2005.
2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 167

11. Stotz
bad investment performance of prediction We investigate various models from the
models that include timing parameters. In statistical perspective and the perspective of a
contrast, stock selection parameters alpha and mutual fund investor. From both
style parameters beta display uniformly a perspectives, we found the most successful
positive and significant relation between past model to be the one that considers the fund’s
and future values with all t-values greater style, the manager’s stock selection skills and
than 4 (not reported in Table 5). conditionally estimates the factor returns.
These results help to explain the findings This model is able to select funds that
of the last sections. Skill and style can be outperform the average mutual fund by more
predicted from past returns (and therefore than 200 basis points per year. Moreover, the
persist), which leads to good forecast results. prediction error of this model is about 30 per
Timing skills cannot be predicted from past cent lower than that of a naıve model that
¨
returns because parameters are (i) not only uses information in the past return.
significantly different from zero and (ii) not The skills in timing should not be
stable through time, resulting in no considered in the forecast model, as they
improvement in investment returns. If mutual lower the forecast power of the respective
fund investors want to exploit the predictability model. It seems that fund managers lack
of factor returns, they should, therefore, not timing skills. Therefore, fund investors have
rely on fund managers’ timing abilities. Instead, to switch between funds with the appropriate
they should predict factor returns by style characteristics if they want to exploit
themselves, and select funds that have – given the predictability of factor returns. The
the conditional return expectations – the empirical results in this study have shown
highest expected returns. For example, if the that such a strategy can be beneficial, as it
conditional expected return for the factor increases the return of an additional 130 basis
HML is exceptionally high, investors should points per year. The gains from conditional
select value funds that have a high loading on forecasts of factor returns are, in practice,
HML. Therefore, investors should follow an largely neglected. For example, fund-
active style-switching strategy (as in model 2) tracking companies, like Morningstar, rank
that replaces the non-existent timing abilities of funds according to measures of past
fund managers. performance but not by expected returns,
thereby neglecting the benefits from factor
return predictability, even though these seem
CONCLUSION to be an important issue, as shown by the
In this paper, a multifactor model for empirical results of this study.
predicting mutual fund returns has been
investigated. The factor model considers four
sources of risk of stock returns: market
return, size return, value return and NOTES
1. BVI is the German mutual fund association.
momentum return. These risk factors have 2. Survivorship bias is an important issue in mutual fund
been found to successfully explain the cross- performance studies, as poorly performing funds disappear
section of stock returns, and have been more frequently from the mutual fund universe than good
extensively used for evaluating fund returns. performing funds do (for example Brown and Goetzmann,
1995). As a result, performance measures based on samples
In terms of mutual fund management, three of surviving funds may be upwardly biased (for example
sources from the multifactor model Brown et al, 1992; Malkiel, 1995; Gruber, 1996; Carhart
contribute, then, to the expected mutual et al, 2002).
3. MSCI ¼ Morgan Stanley Capital International
fund return: the fund’s style, the manager’s 4. As the empirical analysis focuses on the German mutual
skills in stock selection and timing and the fund market, the portfolios include all German stocks that
predictability of factor returns. are in the database of Datastream.
168 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

12. Predicting returns of equity mutual funds
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