Predicting returnsfundmanagers stotz

Original Article

Predicting returns of equitymutual fundsReceived (in revised form): 18th September 2008

Olaf Stotzholds 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, Sonnemannstra�e 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

INDRODUCTIONOver the past few decades, private investors

have allocated an increasing amount of

money to mutual funds, thus making this

financial innovation a sweeping success.

Mutual fund investors face the problem of

having to select appropriate funds out of a

universe of several hundred individual funds.

Financial theory guides the investor through

this choice by looking at each fund’s

expected return and risk, as measured by the

covariance matrix of returns (Markowitz,

1952). The optimal selection of funds then

crucially depends on good estimates of

expected returns (for example Best and

Grauer, 1991; Chopra and Ziemba, 1993).

Financial theory, however, is silent about the

estimation of expected returns.

The return of a fund is dependent on two

sources. The first source is the return of the

fund’s underlying stocks, which can be

explained by various risk factors. Four factors

have been identified by theoretical and

empirical research that are successful in

explaining stock returns (in excess of the

risk-free rate): market, size, value and

momentum (for example Fama and French,

1993; Jegadeesh and Titman, 1993). The

market factor is based on the capital asset

pricing model, and predicts that high beta

stocks should produce higher returns than

low beta stocks. The size factor refers to the

empirical observation that, on average, stocks

with a small market capitalisation perform

better than stocks with a large market

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/

difference in returns between stocks with a

high book-to-price ratio (value stocks) and

stocks with a low ratio (growth stocks). The

momentum effect is related to a stock’s past

1-year return. Stocks with a high return in

the past year perform better over the next

year than stocks with a low return do. These

factors have been found to explain the cross-

section of stock returns in various countries

and over different samples.

The second source of a fund’s return is the

decision of a fund manager as to which

securities she or he holds in a fund. This

decision can be classified into management

style, selection skill and timing skill. A

preference for certain stock characteristics is

described by the fund’s management style.

Stock characteristics refer to the four factors

mentioned above. For example, a value

manager tends to invest in stocks with high

book-to-price-ratios (value stocks). Selection

skill describes the fund manager’s ability to

find stocks that outperform a benchmark

index on a risk-adjusted basis. Timing skills

characterise the ability of whether a fund

manager is able to buy and sell stocks (with

certain characteristics) at favourable times.

For example, a fund manager can follow an

active timing strategy by switching between

stocks and cash or between styles (for

example, from value to growth). A manager

with good timing skills in value stocks will

buy value stocks before they outperform

growth stocks. Management style, selection

skills and timing skills then characterise a

fund manager’s investment decisions.

To predict a fund’s return, an investor has

to forecast the returns on the risk factors and

the investment decisions (management style

and manager’s skills in selection and timing).

Predictability of factor returns has been

largely confined to the market return (see,

for example, Fama and Schwert, 1977; Keim

and Stambaugh, 1986; Campbell, 1987;

Fama and French, 1988; Lewellen, 1999). In

general, it is found that standard macro-

economic variables (for example term

structure of interest rates, credit spread) and

valuation ratios (for example book-to-market

ratio, dividend yield) are able to predict the

stock market’s excess return. Predictability of

the remaining three factors (size, value,

momentum), however, has been rarely

investigated. However, the book-to-market

ratio seems to predict the return on the size

and value factor (in addition to the market

return), as the empirical evidence of Kothari

and Shanken (1997), Pontiff and Schall

(1998), Lewellen (1999) and Cohen et al

(2003) demonstrates. Therefore, the book-

to-market ratio seems to be an appropriate

conditioning variable for predicting factor

returns. The management style is an

important issue in fund management (for

example Sharpe, 1992, and Brown and

Goetzmann, 1997). Fund tracking

companies regularly report the fund’s style

(see, for example, the style box created by

Morningstar). Managers tend to hold the

style of their fund relatively steady over time,

and the style can therefore be derived from

the correlation between past fund returns

and factor returns (for example Davis, 2001;

Chan et al, 2002). Selection skills are found

to be persistent over a horizon of up to 2

years (for example Hendricks et al, 1993;

Zheng, 1999; Bollen and Busse, 2004).

Therefore, these can also be derived from past

fund returns. Timing decisions, however, do

not seem to enhance the performance of

funds. It is found that parameters measuring

timing skills are usually not significant (for

example Jiang, 2003; Bollen and Busse, 2004),

and, in addition, they seem difficult to predict.

This paper, therefore, will pay particular

attention to this issue.

We combine the prediction of factor

returns and the information on a fund’s style

and a manager’s skills within a multifactor

model. We then compare the prediction

results with that of a naıve forecast, which

simply extrapolates the past return into the

future. We have chosen the naıve model as

the benchmark model because empirical

research implies that mutual fund investors

base their estimates of expected returns

Predicting returns of equity mutual funds

159& 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

primarily on past returns. As a result,

investors put more money into funds with a

high return in the past year than into funds

with a low return (for example Chevalier and

Ellison, 1997; Sirri and Tufano, 1998).

Gruber (1996) shows that newly invested

money slightly outperforms the average

mutual fund. This outperformance, however,

can be largely attributed to a higher risk of

the fund (Carhart, 1997). Therefore, it seems

questionable as to whether investors should

rely solely on past returns when making

investment decisions and predict mutual fund

returns.

This paper is organised as follows. The

multifactor model is presented in the next

section. Estimation details of the prediction

model are discussed in the third section. This

model is then used to predict fund returns.

Performance results of the prediction model

are given in the fourth section. The last

section concludes.

THE MODELThis section derives the multifactor model

of fund returns via three steps. The first step

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

characterisation of the fund’s management

style. The third step finally introduces the

timing strategy of the fund manager.

Multifactor model of stock returnsThe multifactor model states the stock’s

excess return as

~rj;t ¼ aj þXn

k¼1

bkj � ~rk

t þ ~ej;t; (1Þ

where

rj,t ¼ return of stock j in excess of the

risk-free rate

rtk ¼ return of factor k

aj ¼ risk-adjusted return

bjk ¼ factor loading of stock j to factor k.

In specifying equation (1), we rely on

empirical and theoretical research that has

shown that the following four factors

describe the cross-section of stock returns

(for example Fama and French, 1993;

Jegadeesh and Titman, 1993):

� the return of the stock market in excess of

the risk-free rate: market factor ‘MAR’;

� the return of small stocks (small market

capitalisation) in excess of large stocks

(large market capitalisation): size factor

‘SMB’;

� the return of value stocks (high book-to-

market stocks) in excess of growth stocks

(low book-to-market stocks): value factor

‘HML’;

� the return of good performing stocks

(high past-year return) in excess of bad

performing stocks (low past-year return):

momentum factor ‘1YR’.

According to the four-factor model, the

excess return of stock j is then

~rj;t ¼ aj þ bMARj � ~rMAR

t þ bSMBj � ~rSMB

t

þ bHMLj � ~rHML

t þ b1YRj � ~r1YR

t þ ~ej;t:

Selection decision of the fundmanager and management styleA fund manager now combines various

stocks within a fund portfolio, which then

yields a return of

~rp;t ¼XNt

j¼1

~wj;t � aj þX4

k¼1

bkj � ~rk

t þ ~ej;t

!

¼XNt

j¼1

~wj;t � aj þXNt

j¼1

~wj;t �X4

k¼1

bkj � ~rk

t

!

þXNt

j¼1

~wj;t � ~ej;t

¼ ap;t þX4

k¼1

~bkp;t � ~rk

t þ ~ep;t; ð2Þ

Stotz

160 & 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169

where

~wj;t ¼ weight of stock j in fund p

ðfund manager’s investment decisionÞNt ¼ number of stocks in fund p

~rp;t ¼ return of fund p in excess of the

risk free rate

ap;t ¼XNt

j¼1

~wj;t � aj ¼ risk adjusted return

ðmeasures selection skillÞ

~bkp;t ¼

XNt

j¼1

~wj;t � bkj ¼ factor loading of fund

p to factor k ðmeasures fund’s styleÞ

This four-factor model has also been

applied by Carhart (1997) to evaluate the

performance of fund returns, and will be used

in this paper to predict fund returns. a1 is

interpreted as a parameter that measures the

stock selection skill of the fund manager. This

is usually assumed to be constant through time

(see Christopherson et al, 1998, for an

exception). bs are the sensitivities of the fund’s

return on the risk factors, from which the

investment style of the fund can be deduced.

For example, a value manager is characterised

by a high bpHML. In deriving expected fund

returns, we distinguish between a constant

investment style (bp,tk ¼ const.) and a time-

varying investment style (bp,tk ¼ time-varying).

On the basis of constant selection skill and

investment style, the expected fund return can

then be estimated by

E ~rp;tþ1

� �¼ ap þ

X4

k¼1

bkp � E ~rk

tþ1

� �: (3Þ

Timing decision of the fundmanagerHowever, fund managers can vary the

exposure of their fund to the four factors in

anticipation of predictable future factor

returns. For example, if a fund manager

expects value stocks to perform exceptionally

well compared to growth stocks, she or he

would buy more stocks with a high load on

the value factor r tHML, thereby increasing the

fund’s value beta bp,tHML. As a result, betas are

random variables that change taking

expectations of equation (2) as follows:

E ~rp;tþ1

� �¼ ap þ

X4

k¼1

E ~bkp;tþ1

h i� E ~rk

tþ1

� �

þX4

k¼1

cov ~bkp;tþ1;~r

ktþ1

h i:

(4Þ

cov(b~p,tþ 1k ,rtþ 1

k ) then measures the fund

manager’s ability to time the return on factor

k. We follow Treynor and Mazuy (1966),

who assume that the fund’s exposure to the

(market) factor depends linearly on the

factor’s return:

~bkp;t ¼ bp þ gp � ~rk

t : (5Þ

Then gi characterises the timing skill of

the fund manager. Replacing bp,tþ 1k in

equation (2) with equation (5) yields

~rp;t ¼ ap þX4

k¼1

bkp � ~rk

t þX4

k¼1

gkp � ð~rk

t Þ2

þ ep;t: (6Þ

Taking expectations then results in

E½~rp;tþ1� ¼ ap þX4

k¼1

bkp � E½~rk

tþ1�

þX4

k¼1

gkp � E½ð~rk

tþ1Þ2�

¼ ap þX4

k¼1

bkp � E½~rk

tþ1�

þX4

k¼1

gkp � ðE½~rk

tþ1�2 þ Var½~rk

tþ1�Þ:

(7Þ

We estimate a fund’s expected return by

equations (3) and (7). Details of the

determination of each component are

described below. We compare the prediction



of these models with a naıve estimator that

uses only information on the past year’s fund

return. This naıve estimator seems to be

applied by mutual fund investors, as

suggested by the mutual fund literature

mentioned in the introduction.

ESTIMATION DETAILS

DataWe compare the performance of prediction

models on the basis of equations (3) and (7)

for a large sample of actively managed equity

mutual funds in Germany. The sample is

taken from the database of BVI

(Bundesverband Investment und Asset

Management e.V.),1 and includes all funds

that have an investment objective that is

focused on German equities. We exclude

funds that (i) primarily invest in specific

sectors, (ii) have a performance guarantee,

(iii) have a limited duration and (iv) are index

funds. This leaves 133 active funds. The

sample is free of a survivorship bias, as BVI’s

database contains surviving and defunct

funds.2 Net return data of funds, which

account for management and administrative

costs, are from Datastream. We use the

1-month LIBOR-offered rate yield as a

proxy for the risk free-rate, which is

subtracted from net returns to obtain excess

returns.

The return on the market factor is

proxied by the return of a stock market index

in excess of the risk-free rate (MSCI3

Germany minus 1-month LIBOR-offered

rate); the returns for the factors size, value

and momentum are constructed similarly to

Fama and French (1993). Therefore, factor-

mimicking portfolios are computed. For

example, the return on the factor-mimicking

portfolio SMB is constructed as follows: the

value-weighted return of all stocks with the

lowest market capitalisation (below median

market capitalisation) minus the value-

weighted return of all stocks with the highest

market capitalisation (above median market

capitalisation). The return on the factor-

mimicking portfolio HML is the return

difference between a value-weighted

portfolio of stocks with the highest book-to-

market ratio and a value-weighted portfolio

of stocks with the lowest book-to-market

ratio. The return on the factor-mimicking

portfolio 1YR is computed as the return

difference between a value-weighted

portfolio of stocks with the highest past-year

return and a value-weighted portfolio of

stocks with the lowest past-year return.4

We predict 1-year-ahead returns at the

beginning of January of each year from 1991

to 2005, inclusive, for each existing fund.

Thus, we have 15 prediction periods. As

funds are closed or newly created, not all 133

funds exist in each prediction period. As a

result, 1246 predicted fund return years are

obtained. Applying equation (3) or (7) for

return prediction, the following parameters

have to be estimated:

� Stock selection coefficient alpha: ap

� Style coefficient beta: bpk

� Timing coefficient gamma: gpk

� Expected factor returns: E[rtþ 1k ]

� Variance of factor returns: Var[rtþ 1k ].

Alpha, betas and gammasThe fund’s alpha, betas and gammas are

estimated by an OLS regression, based on

equation (3) and (7). a, b and l, then,

symbolise OLS estimates. The estimation

period starts in January 1990 and ends in the

month before the prediction date (which is

the beginning of January of each year). For

example, when returns are forecasted at the

beginning of 1995, the estimation period

covers the period from January 1990 up to

December 1994. This rolling forecasting

scheme uses only lagged information to

predict future returns. If the return series of a

specific fund starts later (because the fund has

been created after January 1990), a minimum

of 52 weeks are required for parameter

estimation. To obtain precise estimates,

weekly returns are used.

Stotz


Factor returnsExpected factor returns are estimated both

unconditionally and conditionally, whereby

we can investigate whether or not fund

managers are able to exploit the predictability

of factor returns. In both cases, the

estimation period starts at the beginning of

1980, and uses yearly returns because 1-year-

ahead forecasts are made. The unconditional

estimation approach (that is constant factor

returns) uses the average of the realised

factor returns over the estimation period

of length T, which is denoted by

E ~r ktþ1

� �¼ AVG rk

t

� �¼ 1

T�XT

t¼1

rkt : (8Þ

Conditional factor returns are assumed to be

linearly related to information variables It. The

prediction of each factor’s conditional expected

return is then based on the following model:

~rktþ1 ¼ f2k�1;t þ f2k;t � ~Ik

t þ ~et: (9Þ

The estimated OLS regression coefficients

fk,t are used to obtain conditional forecasts of

1-year ahead returns for each factor:

E ~rktþ1jIt

� �¼ f2k�1;t þ f2k;t � Ik

t : (10Þ

We use information variables that are

based on the empirical evidence of Kothari

and Shanken (1997), Pontiff and Schall

(1998), Lewellen (1999) and Cohen et al

(2003). They demonstrate that the book-to-

market ratio (or spread of the ratio) is able to

predict the return in the market, size return

and value factor. The return of the

momentum factor will be forecasted on the

lagged momentum return because

momentum relies on the notion of return

continuation. These assumptions result in the

following information variables:

IMARt ¼ logðBMMAR

t Þ;

ISMBt ¼ logðBMS

t Þ � logðBMBt Þ;

IHMLt ¼ logðBMH

t Þ � logðBMLt Þ and

I1YRt ¼ r1YR

t�1 :

where BMtMAR is the book-to-market ratio

of the market index at t, BMtS (BMt

B) is the

book-to-market ratio of stocks with a small

(large) market capitalisation, and BMtH

(BMtL) is the book-to market ratio of value

(growth) stocks.

Finally, the variance of the factor return is

estimated by the sample variance of realised

Table 1: Details of prediction models

Predictionmodel

Prediction offactor returns

Consideration ofmanager’sinvestmentdecisions

Expected return

1 Unconditional Management style,selection skill E½~ri;tþ 1� ¼ ai þ

P4k¼1

bki � AVG½rk

t �

2 Conditional Management style,selection skill E½~ri;tþ 1jIt � ¼ ai þ

P4k¼1

bki � ðfi;2k þ fi;2kþ 1 � Ik

t Þ

3 Conditional Management style,selection skill,timing skill

E½~ri;tþ 1jIt � ¼ ai þX4

k¼1

bki � ðfi;2k þ fi;2kþ 1 � Ik

t Þ

þX4

k¼1

lki � ððfi;2k þ fi;2kþ 1 � Ik

t Þ2 þ s2

kÞ

4 — Naıve E½~ri;tþ 1� ¼ ri;t

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.



factor returns, which is denoted by

s2k ¼ 1

T�1�PT

t¼1ðrkt � AVGðr k

t ÞÞ2.

Given these estimation details, Table 1

presents an overview of the resulting models

and their parameters.

EVALUATING PREDICTIONMODELSWe evaluate the forecast of each model on

the basis of forecast performance (that is

statistical perspective) and investment return

(that is investor’s perspective). The next

section presents the statistical perspective

and the section after this the investor’s

perspective.

Mean absolute error, meansquared error and hit ratioThe statistical performance of each

prediction model is evaluated by the

difference between the return forecast

and the realised return (that is forecasting

error). Hereby, we compute two common

statistical measures, the mean absolute

error (MAE) and the mean-squared error

(MSE). The MAE and the MSE are

defined as the average across individual

funds (Mt denotes the number of available

funds in t) and over time (T¼ 15 prediction

periods):

MSE ¼ 1

T�XT

t¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

Mt

�XMt

i¼1

ðE½~ri;tþ1� � ri;tþ1Þ2vuut

(11Þand

MAE ¼ 1

T�XT

t¼1

1

Mt

�XMt

i¼1

E½~ri;tþ1� � ri;tþ1

�� !:

(12ÞThe degree of accuracy of the respective

forecast does not necessarily translate into

large investment returns. To achieve large

investment returns, the direction of the

forecast (positive or negative) can be more

important (for example Leung et al, 2000).

Therefore, we also calculate the average hit

ratio (HR) as

HR ¼ 1

T�XT

t¼1

1

Mt

�XMt

i¼1

hri;tþ1

!; (13Þ

where

hri;tþ1 ¼1 if E ~ri;tþ1

� �� ri;tþ140

0; if E ~ri;tþ1

� �� ri;tþ1p0:

(

HR indicates in how many years the

prediction model will get the correct sign of

the return.

Table 2 summarises the forecast

performance results for each model. As

expected, the naıve prediction model 4

produces the highest prediction error. The

MSE and MAE criteria show an estimation

error of 27.47 per cent and 25.21 per cent,

respectively. This is even higher than the

average standard deviation of fund returns,

which is about 22 per cent. The use of

information on the fund manager’s

investment decisions (management style and

selection skill) increases the forecast

performance. Model 1 reduces the

prediction error by about 24 per cent. The

consideration of management style and

selection skill improves the prediction results

substantially.

If factor returns are predicted

conditionally (model 2) instead of

unconditionally (model 1), the prediction

error is reduced by additional 10 per cent.

Compared to model 4, the reduction is about

30 per cent. Therefore, the conditional

prediction of factor returns seems to improve

the forecast performance vis a vis the

unconditional prediction. However, fund

Table 2: Forecast performance of prediction models

Model MSE(%) MAE(%) HR(%)

1 21.15 19.04 66.892 19.85 17.89 67.313 20.80 18.68 64.494 27.47 25.21 57.17

Stotz


managers do not seem to be able to exploit

this predictability. Model 3 – which

models the timing of factor returns of fund

managers – does not improve forecast

performance compared to model 2. This

result resembles the empirical evidence of

other studies that show that fund managers

are not successful in timing (for example

Chan et al, 2002; Bollen and Busse, 2004).

Under the HR evaluation criteria, the

same conclusions can be drawn. The use of

information on the fund manager’s selection

skill and the fund’s style in general improves

the HR compared to the naıve model 4.

Furthermore, the conditional prediction of

factor returns enhances the HR. Model 2’s

HR of 67.31 per cent is slightly higher than

the HR of model 1. Accounting for factor

timing by the fund manager (model 3),

however, worsens the HR.

In summary, model 2 (conditional

prediction of factor returns and use of

information on management style and

selection skill) is the best forecast model, as

expected. The prediction error is almost 30

per cent lower compared to the naıve model 4.

In addition, model 2 produces an increase in

the HR of more than 10 percentage points.

The consideration of these observations

should result in a better investment

performance, which will be investigated in

the next section.

Decile portfoliosReturn forecast are mainly used to guide

investment decisions. Therefore, we further

evaluate the forecast models from the

perspective of an investor, and address the

issue of whether forecasts of models 1–3 can

be translated into investment decisions that

are superior to those of the naıve model 4.

This issue is investigated with decile

portfolios that are formed on the basis of

estimates of each model’s expected returns.

Therefore, for each prediction date, funds are

ranked into deciles on the basis of their

expected return. Funds with the highest

(lowest) expected returns are designated to

decile 1 (decile 10). The funds in each decile

portfolio are held constant for the prediction

period (1 year), and are rearranged at the

next prediction date according to their new

expected returns. In each decile portfolio,

funds are equally weighted. The yearly

return of each decile portfolio is averaged

over the 15 prediction periods. If a model

produces good forecasts, the average

return should decrease from decile 1 to

decile 10, with a large difference between

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 return1 9.68 9.64 10.25 9.79 8.91 9.68 7.63 8.40 8.00 6.58 3.102 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 3.214 9.56 9.53 9.54 9.87 8.81 9.20 8.85 8.26 8.35 6.97 2.59

ALL 8.88Panel B: Sharpe ratio=(mean realized return–risk-free rate)/standard deviation of realized return1 18.15 22.20 23.80 21.69 18.42 21.97 13.96 17.34 16.11 9.97 8.182 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 12.194 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.



Results for average returns of decile

portfolios are displayed in Panel A of Table 3.

Four main results can be observed from

Table 3. First, prediction model 2 shows the

best investment performance, and, therefore,

reinforces its superiority from the statistical

perspective. For example, decile 1 of

prediction model 2 produces a return, which

is the largest of all prediction models (11.00

per cent per year). This is about 200 basis

points higher than the average of all mutual

funds (symbolised by ‘ALL’), and almost 150

basis points better than model 4. In addition,

the difference between decile 1 and decile 10

is also the largest (6.22 per cent per year), and

significantly different from zero. The average

return decreases almost uniformly from

decile 1 to decile 10. Thus, the superior

forecast performance from the statistical

perspective, displayed in the last section, can

also be translated into a superior investment

performance. The use of information on the

fund manager’s selection skill, the fund’s style

and the conditional prediction of factor

returns also results in a good investment

performance.

Second, the conditional prediction of

factor returns results in a better investment

performance than the unconditional

prediction (model 2 is better than model 1).

The conditional prediction of factor returns

increases the performance by an additional

132 basis points per year (decile 1). The

predictability of factor returns translates,

therefore, into substantial investment gains,

and investors can benefit from the

conditional prediction of factor returns by

selecting funds that have a high style

coefficient (that is factor loading) for the

style that is expected to achieve a high

return.

Third, the results of model 3 show that

fund managers are not able to exploit the

predictability of factor returns. Model 3 –

which considers the factor timing of fund

managers – leads to inferior investment

results compared to model 2, and to almost

the same results as model 1. The

consideration of factor timing by the fund

manager, therefore, does not seem to

improve investment results. A likely reason

for this puzzling result seems, to us, to be

that either fund managers lack timing skills or

a timing strategy is not being followed by the

fund manager. This notion is consistent with

empirical research that finds that fund returns

are not enhanced through timing (for

example Chan et al, 2002; Bollen and Busse,

2004). This issue is explored in more detail

in the next section.

Fourth, the investment results for model 4

are not as bad as suggested by its statistical

performance. Panel A shows that the naıve

model 4 is able to select funds that perform

slightly better than the average fund. For

example, decile 1 achieves an average return

of 9.56 per cent per year, whereas the

average mutual fund delivers just 8.88 per

cent per year. The difference between the

returns of decile 1 and of decile 10 (displayed

in the last column) is 2.59 per cent per year,

which indicates that winner funds

outperform loser funds (although the

difference is not statistically greater than zero

at the 5 per cent level). This result indirectly

supports the findings of Elton et al (1996),

who provide evidence that the performance

of newly invested money (that is primarily in

funds with high past returns) marginally

outperforms money already invested. A likely

reason for this observation seems to be a

positive correlation between alpha and the

past year’s returns. Therefore, the past returns

seem to proxy partly the stock selection skill

(although not as well as alpha itself).

Panel B shows the corresponding realised

Sharpe ratios of each decile portfolio. The

results reinforce the forecast power of

model 2. For example, decile 1 of model 2

achieves the highest Sharpe ratio, which is

substantially larger than the Sharpe ratio of

the average fund and of model 4 (naıve

model). The Sharpe ratio of model 1

decreases uniformly from decile 1 to decile

10, indicating that this model can successfully

discriminate good funds from bad funds. On

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the basis of the test statistics of Jobson and

Korkie (1981), the difference in the Sharpe

ratio between decile 1 and decile 10 (last

column) is significantly greater than zero at

the 5 per cent level. Therefore, the superior

investment performance reported before

does not seem to be the result of a larger risk

(measured by the standard deviation of

returns), but instead of superior return

forecasts.

Why does modelling timing offund managers not improveforecasts?Results from the decile analysis summarised

in Table 3 suggest that the modelling of a

fund manager’s factor timing decision does

not improve investment performance. In this

section, we explain this result by

investigating timing coefficients in more

detail. We obtain two results: first, estimated

timing parameters are, on average, not

significantly different from zero. This

indicates that the average mutual fund

manager is not a good market timer. Second,

future timing parameters cannot reliably be

derived from past returns, as they display a

large degree of instability.

Table 4 summarises estimates of gamma

from equation (6) over the full sample

period. Parameters are averaged over all

individual funds. Estimated gammas are, on

average, not significantly different from zero,

which indicates that fund managers are not

successful market timers. Some average

timing parameters are even smaller than zero

(size, momentum), indicating that fund

managers are losing money with their timing

decisions. In addition, parameters are

estimated with a large estimation error, and

average t-values are small. Only 9 per cent of

all gammas are significantly greater than zero

at the 5 per cent level. In contrast, style

parameters’ betas are estimated with a lower

prediction error, resulting in 59 per cent

significant betas at the 5 per cent level (not

reported in Table 4).

We additionally investigate the stability of

estimated timing parameters. A positive

relation between past parameters and future

parameters is a necessary condition to infer

future timing skills from past return data (that

is persistency of skills). Therefore, past

parameter estimates are regressed on future

parameter estimates:

gi;t ¼ interceptþ slope � gi;t�1 þ ei;t

We regress past parameters (denoted by

gi,t�1) on future parameters (denoted by gi,t)

in a pooled regression approach. Past

parameters are estimated from 1990 to the

prediction date, and future parameters are

estimated over the year following the

prediction date. A positive slope then

indicates that timing skills persist. Table 5

shows that this is partly not the case. Future

gammas are not consistently and positively

related to their past estimates. For example,

the future timing parameter for the market

factor is positively related to its past value

(slope for gMAR equals 0.256, t-value¼4.514), whereas the relation between the

future and past parameter on the momentum

factor is negative (slope for g1YR equals

�0.512, t-value¼�3.794). These results

suggest that timing is not a persistent

management skill, which further explains the

Table 4: Results for timing parameter estimates

gMAR gSMB gHML gIYR

Average 0.31 �0.381 0.491 �0.242Average t-value 0.754 �0.565 0.815 �0.241

The table displays estimated timing parameters fromequation (6), which are based on the estimation periodfrom 1990 to 2005.

Table 5: Results for parameter stability from pooledregressions

gMAR gSMB gHML gIYR

Intercept 0.058 0.878 0.329 �1.561t-value 0.372 3.765 1.124 �10.182Slope 0.256 0.050 �0.104 �0.512t-value 4.514 0.876 �1.321 �3.794



bad investment performance of prediction

models that include timing parameters. In

contrast, stock selection parameters alpha and

style parameters beta display uniformly a

positive and significant relation between past

and future values with all t-values greater

than 4 (not reported in Table 5).

These results help to explain the findings

of the last sections. Skill and style can be

predicted from past returns (and therefore

persist), which leads to good forecast results.

Timing skills cannot be predicted from past

returns because parameters are (i) not

significantly different from zero and (ii) not

stable through time, resulting in no

improvement in investment returns. If mutual

fund investors want to exploit the predictability

of factor returns, they should, therefore, not

rely on fund managers’ timing abilities. Instead,

they should predict factor returns by

themselves, and select funds that have – given

the conditional return expectations – the

highest expected returns. For example, if the

conditional expected return for the factor

HML is exceptionally high, investors should

select value funds that have a high loading on

HML. Therefore, investors should follow an

active style-switching strategy (as in model 2)

that replaces the non-existent timing abilities of

fund managers.

CONCLUSIONIn this paper, a multifactor model for

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

momentum return. These risk factors have

been found to successfully explain the cross-

section of stock returns, and have been

extensively used for evaluating fund returns.

In terms of mutual fund management, three

sources from the multifactor model

contribute, then, to the expected mutual

fund return: the fund’s style, the manager’s

skills in stock selection and timing and the

predictability of factor returns.

We investigate various models from the

statistical perspective and the perspective of a

mutual fund investor. From both

perspectives, we found the most successful

model to be the one that considers the fund’s

style, the manager’s stock selection skills and

conditionally estimates the factor returns.

This model is able to select funds that

outperform the average mutual fund by more

than 200 basis points per year. Moreover, the

prediction error of this model is about 30 per

cent lower than that of a naıve model that

only uses information in the past return.

The skills in timing should not be

considered in the forecast model, as they

lower the forecast power of the respective

model. It seems that fund managers lack

timing skills. Therefore, fund investors have

to switch between funds with the appropriate

style characteristics if they want to exploit

the predictability of factor returns. The

empirical results in this study have shown

that such a strategy can be beneficial, as it

increases the return of an additional 130 basis

points per year. The gains from conditional

forecasts of factor returns are, in practice,

largely neglected. For example, fund-

tracking companies, like Morningstar, rank

funds according to measures of past

performance but not by expected returns,

thereby neglecting the benefits from factor

return predictability, even though these seem

to be an important issue, as shown by the

empirical results of this study.

NOTES1. BVI is the German mutual fund association.

2. Survivorship bias is an important issue in mutual fund

performance studies, as poorly performing funds disappear

more frequently from the mutual fund universe than good

performing funds do (for example Brown and Goetzmann,

1995). As a result, performance measures based on samples

of surviving funds may be upwardly biased (for example

Brown et al, 1992; Malkiel, 1995; Gruber, 1996; Carhart

et al, 2002).

3. MSCI¼Morgan Stanley Capital International

4. As the empirical analysis focuses on the German mutual

fund market, the portfolios include all German stocks that

are in the database of Datastream.

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