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Abstract
This paper analyzes a sample of monthly performances of 186 italian
equity and balanced funds from January 1995 to December 1999. We show
that a simple industry classiﬁcation based on the investments location is a
very good descriptor of mutual fund styles. This assessment is made considering the remarkable out of sample explanatory power of this classiﬁcation system when compared to other reasonable return based benchmark
categorization schemes. We ﬁnd that the classic growth versus value and
large versus small paradigm do not convey relevant information in terms of
performance prediction and that italian funds are progressively migrating
towards the large/growth segment of their reference market. According
to our return based style analysis, most italian funds historical performances could have been replicated by appropriate passive alternatives on
investable indices. Contrasting a strong empirical evidence from most US
fund studies and our a priori beliefs, italian funds do not seem to follow any recognizable dynamic trading strategy other than naive portfolio
rebalancing.
JEL codes: G20, G23, G11
Keywords: Italian mutual funds, Return based style analysis, Equity
styles
Management Styles of
Italian Equity Mutual Funds
Ignazio Basile
Department of Business Economics
University of Brescia
email: [email protected]
Nicola Doninelli
Department of Quantitative Methods
University of Brescia
email: [email protected]
Roberto Savona
Department of Business Economics
University of Brescia
email: [email protected]
1
Introduction1
In the U.S. pension fund industry, plan sponsors choose complementary managers, instead of portfolios of assets such as stocks, bonds or currencies (see,
e.g., Chan, Chen and Lakonishok (1999)). In fact, most fund managers consider
that the risk proﬁle of their overall portfolio depends on the investment styles
followed by the individual portfolio managers. As a consequence, their choices
are tipically consistent with a ”style diversiﬁcation” principle. While there is
no general agreement on the deﬁnition of this expression in Investments, we
use the term ”style” as the systematic portion of mutual fund returns which
include stock and bond characteristics as well as recognizable trading strategies
and behavioural patterns.
At an intuitive level, a fair degree of style diversiﬁcation is needed for several reasons. In some cases, the aggregate position of an investment company
could come out to be extremely unbalanced. This happens whenever the individual portfolio managers are exposed to the same asset classes or, in general,
implement trading strategies resulting in highly correlated returns.
In the mutual fund industry the situation is quite similar. Most mutual
fund investment companies tipically oer a variety of portfolios to match various
risk-return proﬁles. On the other side, the ﬁnal investors are interested in being
1 We thank all the partecipants of the AMASES 2000 conference and the seminars we held
at the University of Verona and the University of Brescia for their comments which greatly
improved this paper. A special thank goes to Stephen Brown for his helpful suggestions and
the numerous discussions, Marco Ratti (our discussant), Andrea Berardi, Paolo Mottura and
Riccardo Campanini of IAM SIM.
1
informed on how aggressively their money are managed as well as the main asset
classes chosen by the funds. As a result, the disclosure of these characteristics
have become so important that sometimes a fund is identiﬁed by its investment
style, which enters as a part of the fund name itself.
Since both plan sponsors and the public are paying attention on style matters, any information about this concern is likely to be rewarded accordingly.
Therefore, reliable informations regarding styles and trading strategies should
play a fundamental role in the process of mutual fund selection. In fact, many
US vendors provide data services including, for example, mutual fund classiﬁcations based on the growth/value and large/small categories as well as quality
ratings within styles and peer groups (see, e.g, Graham and Harvey (1996)).
In the European market, other companies and mutual fund associations provide similar services. These databases are not as detailed as their US counterparts in terms of historical performance and institutional/stylistic characteristics. In most cases, the coverage is limited to the biggest and oldest markets,
namely France and the UK.
In Italy, both the Central Bank and Assogestioni (the Italian mutual funds
association), started providing some categorizations only a few years ago. The
Bank of Italy partitions mutual funds by investment objective into three groups:
bond funds, balanced funds and equity funds, according to some basic indications derived from the prospectus. No other distinction is made.
2
The Assogestioni classiﬁcation is much more involved. At the end of 1999,
Assogestioni contemplates 10 dierent clusters for the equity and balanced categories: Equity Italy, Equity Europe, Equity Euro area, Equity Paciﬁc, Equity US, Equity Emerging markets, Equity International, Other specializations
and Balanced funds. It has been noted several times (see, e.g., Cesari and
Panetta (1998)) that the distinction between funds investing in Italian securities as opposed to international investment vehicles, which operates since the
liberalisation reform of capital ﬂows in 1990, is an important step. However, the
Assogestioni classiﬁcation suers of some limitations, at least in theory. First,
it gives no informations regarding objectives other than the geographical focus and the proportion of wealth invested in equities. Second, it is prone to
missclassiﬁcation, being based on self reported declarations (see e.g. Witkowski
(1994) and Kim, Shukla and Thomas (1995)).
In the italian mutual fund market, Morningstar like classiﬁcations or publicly available ratings based on historical performance analysis, individual fund
research and the small/large, value/growth paradigm do not exist. This means
that the portfolio managers and the fund researchers who believe in the explanatory power of these categorizations must refer to proprietary analyses.
Now, two questions: ﬁrst, is this interest in better classiﬁcation methods
really justiﬁed or, put in dierent terms, stylistic dierences do really explain
a signiﬁcant amount of the cross sectional expected returns variability (Brown
and Goetzmann (1997))? Second, what is the best method to classify Italian
3
funds?
As was recognized a long time ago in the ﬁnancial literature, style analysis
is related to another important issue, relative performance evaluation (see, e.g,
Jensen (1968) and Grinblatt and Titman (1995)). Plan sponsors need to ﬁx
meaningful benchmarks, reasonable return targets and the achievement of their
portfolio managers. To accomplish this, the systematic style component must
subtracted from the ex post total return to determine skill, that is the proportion
of return that is to be attributed solely to superior active management or above
average talent (Fama (1972)). Any investment company and, in general, any
rational investor is willing to pay higher fees only if this superior ability is in
some sense unanmbiguously evident. However, this unambiguous evidence is far
from being simple to ﬁgure out. To realize this, consider that the introduction of
style adjusted performance evaluation techniques in the context of asset pricing
theories dates back to the study of Sharpe (Sharpe (1966)).
Recently, Sharpe (1992) and Fung and Hsieh (1997) pointed out that most
mutual fund managers are rewarded relative to benchmarks, mimicking the behaviour of broad, naive combinations of investable assets. This benchmarking
practices could induce fund returns to remain closely related to their benchmarks, which reﬂect an investment mandate. Mutual funds returns are then
expected to be highly correlated to the performances of the main asset classes
in the market. Moreover, mutual fund managers are subject to institutional
restrictions: they can’t short sell and have very limited if no access to leverage.
4
Thus, we can expect the time series of fund returns to be approximately replicated by a passive, constantly rebalanced combination of market indexes. This
observation is the economic rationale behind the celebrated Sharpe return based
style analysis procedure (Sharpe (1992)). The Sharpe procedure is widely used
both by academics (see, e.g., Blake, Elton and Gruber (1993)) and practitioners,
thank to its simplicity and intuitive ﬁnancial interpretation. Nevertheless, the
Sharpe method suers of several problems.
While we may be content with the representation of fund returns as a passive
portfolio of index returns at an instant of time, Sharpe model asserts that we
can represent the fund not really as a purely passive portfolio or buy and hold
strategy (see, e.g., Ferson and Schadt (1996)), but rather, a portfolio constantly
rebalanced to weights given as linear coe!cients in a constrained regression
framework.
In principle, stylistic dierences are not limited to the location component2 .
In fact, it seems that most, if not all, actively managed funds dynamically change
their portfolio composition in response to changed economic conditions, so that
the eect of non-trivial dynamic portfolio rebalancing patterns must be somehow taken into account (Bansal and Harvey (1996)). In Sharpe original work
this fundamental concern was addressed through the use of rolling regression
procedures. As an alternative solution, one could carry out a family of simpli2 Fung and Hsieh (1997) decompose hedge funds returns into three components: location,
trading strategy and leverage. Mutual funds can’t make use of leverage and can’t short sell, so
that their returns are aected only by the location and the ”long” dynamic trading strategy
component. For an alternative approach, see, for example, Glosten and Jagannathan (1994).
5
ﬁed constrained regressions within short non-overlapping periods and still get a
picture of the portfolio weights evolution through time. Fung and Hsieh (1997)
address this issue using portfolios of funds chosen to be maximally correlated
to the ﬁrst principal components extracted from the cross product matrix of
standardized fund returns.
Neither approach is completely satisfactory from an econometric viewpoint.
For example, heteroskedasticity in funds returns could induce signiﬁcant biases
in the estimated principal components and weights of the factor mimicking
portfolios.
Another important limitation regards the original speciﬁcation of the Sharpe
procedure, which aimed at capturing the US mutual fund return exposure to
standard asset classes. Nothing guarantees that some asset classes may be
redundant, misspeciﬁed and others simply excluded. It can also be that the
Sharpe equation needs to be completely re-cast in order to work outside the US.
Any linear representation of the mutual fund styles will be misspeciﬁed if
there are omitted factors, or the manager systematically underperforms or overperforms a passive fund benchmark. A straightforward way most practitioners
use is to include a constant term in the regression and then impose the constraint
that the sum of the coe!cients be less than or equal to one. The constant term
reﬂects both the degree of under/over performance plus the average exposure to
omitted factors3 . A version of this ”workmanlike” solution has been applied in
3 Note
that the excess return over the style component will be under/over-estimated if the
6
Brown, Goetzmann, Hiraki, Otzuki and Shiraishi (1999) to illustrate that in the
Japan mutual fund industry the ”Other” classiﬁcation represents international
fund exposure not otherwise captured by the standard set of factors used in
US studies. This paper also points out that the constrained linear model systematically underrepresents fund returns due to a tax dilution factor (Japanese
funds, like Italian funds, are taxed at source even if the mechanics behind the
calculation of the oering price per share are substantially dierent).
This paper applies various style classiﬁcation methods to a sample of 186
italian equity and balanced fund returns from January 1995 to December 1999.
We show that a simple industry classiﬁcation, not including the small/large and
value/growth attributes works better than complicated return based classiﬁcations, both in sample and out of sample. In addition, only a few style factors
are shown to be enough to explain most of the cross sectional variation in the
returns panel and each time series could be better and better approximated by
semi-passive benchmarks.
The structure of the paper is as follows. Section 2 describes the methodology. Section 3 is about the main institutional features characterizing the italian
mutual funds market. Section 4 deals with after-tax returns calculations. We
have included a section on tax issues because italian mutual fund researchers are
forced to use after-tax returns. In general, after-tax returns might be preferred
to pre-tax returns. However, the quite cumbersome way used to compute the
systematic risk taken by the fund on the ﬁnancial indexes is signiﬁcantly dierent from one.
7
performances and the italian tax regulation could introduce potential biases in
our analysis. We will discuss qualitatively why this will not aect the results
in our case. Section 5 is about some necessary details regarding data. Section
6 derives a speciﬁcation of the Sharpe equation that is suitable for the italian
case. Section 7 is about style classiﬁcation and the existence of dynamic trading
strategies. Section 8 concludes.
2
Methodology
We assume that security returns in the economy evolve according to a multifactor stochastic speciﬁcation. The j-th asset return for the t-th month is then
given by:
Q
X
ji Fit + %jt
Rjt =
(1)
i=1
© ª
where Fit , i 5 {1, .., Q} is the return on the i-th factor, ji is a matrix of
real valued coe!cients or factor loadings, t < T < 4 and j 5 {1, .., N }; % is the
idiosyncratic returns. In general, under these assumptions, Q ranges from ﬁve
to ﬁfteen, much less than N , the total number of assets, usually in the order of
thousands. Consequently, relatively few factors explain much of the variation
in security returns. These factors could be exogenously determined as innovations to important macroeconomic variables as in Chen, Roll and Ross (1986)
and Berry, Burkmeister and McElroy (1988) or predetermined ﬁnancial indexes
8
(naive traded portfolios) as in Sharpe (1992). Other authors (e.g. Lehmann and
Modest (1988)) prefer to endogenously derive the Fit ’s using principal components analysis and factor maximum likelihood techniques. As Campbell (1996)
points out, all these speciﬁcation methodologies have their advantages and limitations. First, they are based on weak theoretical assumptions. Second, they
give little economic guidance in the factor picking process. Third, they are
silent about the determinants of factor risk prices. Nevertheless, they appear to
empirically ﬁt the cross section of asset returns.
Given that a mutual fund is a portfolio of assets for each t, the above multiP
F
= D wjt Rjt .
factor speciﬁcation must hold for the mutual fund returns RM
qt
j=1
In formulas:
F
=
RM
qt
Q
D X
X
wjt ji Fit +
j=1 i=1
D
X
wjt %jt
(2)
j=1
where D is the number of assets in q-th fund portfolio and q 5 {1, .., M }.
Sharpe (1992) exogenously identiﬁes the Fit ’s as investable indexes, mimicking the aggregate dynamics of some broad standard asset classes (US stocks,
international stocks, corporate bonds, government bonds and gold):
Q
X
MF
Rqt
=
i Fit + %qt
(3)
i=1
with i =
PQ
i=1
wjt ji . To estimate the factor loadings, the following regres-
9
sion is found to be appropriate:
MF
Rqt
= q +
Q
X
i Fit + %qt .
(4)
i=1
We may interpret %qt as the q-th fund absolute tracking error with respect
to the passive alternative
PQ
i=1
i Fit and the intecept term q as a relative
performance measure with respect to a style benchmark. This unconstrained
version of Sharpe (1992) could be thought as a multifactor generalization of
the Jensen performance measurement equation (Jensen (1968)). The dierence
relies in the functional form of the conditional expected return and the size of the
e5
conditioning set at time t. Imposing to the above equation the constraints e e
e
e
RK
+ ^{0} and • 1 = 1 ( is a K-dimensional vector and 1 is a conforming vector
of ones) and minimizing the tracking error variance (%jt ), we can interpret
e as a vector of portfolio weights4 . The R2 coe!cient (R2 , 1 (%jt )
(Rj ) )
of
this constrained regression measures the best proportion of variance explained
by all the linear portfolio combinations of market indexes. The nonnegativity
constraint reﬂects an important institutional limitation for mutual funds, which
cannot take short positions.
As we mentioned in the introduction, this method suers of some serious
problems. Despite this, it has become an accepted industry standard. There
4 The passive portfolio that is identiﬁed must deﬁne a feasible and low cost index fund
alternative. American index funds approximately cost 23 basis points a year (Gruber (1996)).
Italian index funds are much more expensive (even more than 1,5% per year). This fact is
almost ubiquitous in Europe. For example, the average cost for a French index fund is as high
as 1,20% (Otten and Schweitzer (1998)). This dierence might indicate that italian index
funds do not properly replicate indices or that there is limited competition in the industry.
This fact must be taken into account when evaluating extra performances with respect to a
multi-index portfolio.
10
are some obvious reasons for this success: the procedure is easy to implement, it
admits an intuitive ﬁnancial interpretation, requires minimal statistical knowledge and there is a need for a few data to run the estimation. Moreover, the
style benchmark that is produced is undoubtly objective, being based on historical data, it can be speciﬁed ex ante, is not easy to beat in principle and is
consistent across managers.
e doesn’t depend
It should be noted that the vector of portfolio weights on t. However, a convenient style descriptor should allow the fund portfolio
weights to change dynamically through time (Bansal and Harvey (1995)). Simple and computationally e!cient classiﬁcation procedures, which are also consistent with dynamic portfolio rebalancing already exist in the literature (see,
e.g, Elton and Gruber (1970)). One of these is the Generalized Style Classiﬁcation algorithm (GSC) introduced in Brown and Goetzmann (1997). The GSC
procedure makes minimal demand on available data. In fact, it uses only the
N × T panel of fund returns optimizing an intuitive criterion function based
on the squared deviations from the adjusted centroid means, as in the k-means
approach of cluster analysis (see, e.g. Everett (1974)). The GSC allows for
fund speciﬁc and time varying variance: at each step a generalized least squares
adjustment takes place, reducing the inﬂuence of outliers on the centroid estimates. Brown and Goetzmann (1997) observe that when returns admit a
multifactor representation, the GSC model is identical to a switching regression
technology5 .
5 The
connections between clustering algorithm and switching regime models has been
11
A justiﬁcation to this analogy can be made as follows. Start from a reduced
factor representation of the fund returns Rjt , t < T < 4, j 5 {1, .., N}:
Rjt = J +
K
X
Ji Fit + %jt
(5)
i=1
where Ji are real valued coe!cients. If the j-th fund belongs to the J-th
style with J 5 {1, ...K}, K ¿ M the above expression simpliﬁes to:
Rj,t = sJt + %j,t
(6)
where sJ t is the conditional expected return E ( RJ,t | F1,t , ...FQ,t ) and each
vector of coe!cients
©
ª
J , J1, ..., JQ is associated to a style. The analogy
between the two methods is easily seen since one of the outputs of the GSC
procedure is the vector [s1t , .., sKt ], obtained by a volatility adjusted distance
minimization criterion.
The GSC procedure and Sharpe model aren’t necessarily conﬂicting. To
use the language of econometrics, the GSC procedure is the ”reduced form”
and the Sharpe procedure is the ”structural form” of a linear asset pricing
model. Given a multifactor stochastic speciﬁcation, the sJt estimated via the
GSC procedure are linear in unknown factors, whereas the Sharpe procedure
attempts to explicitely specify this linear relationship.
recognized several times in the statistical literature.
12
The traditional k-means clustering algorithm (as well as other grouping procedures) can be applied to other spaces too, not only to the returns panel. For
example, the space of factor loadings or the space of Sharpe portfolio weights
can serve as a basis for a reduction of dimension procedure. The relative performance of these alternative methods must be tested out of sample (see, e.g.,
Blake and Morey (2000)) and compared in terms of predictive power to the
existing industry classiﬁcations, which can be based on the geograﬁcal or sector
preferences of the funds or the classical equity styles.
3
The Italian mutual funds industry
In Italy there are two types of mutual funds: open end funds and closed end
funds. Italian open end funds do not have a long history. They were introduced
in 1983 and started operating in 19846 . Since then, the industry has experienced
a steady growth, especially from 1996.
The net amount of assets under management increased by 53% in 1996, by
86% in 1997 and by 96% in 1998 7 . Pure equity funds8 showed even more
pronounced dynamics. The net amount of assets under management increased
by 124% in 1997 and by 83% in 1998. The total number of funds has sustantially
increased too. In 1990 there were only 183 registered funds which became 703
6 Starting from 1998 mutual funds must mandatorily declare a benchmark in the periodic
reporting statements. As far as we know, Italy is the only country where the benchmark has
been introduced by the law.
7 All the data come from Assogestioni.
8 For the sake of clarity, we distinguish between pure equity funds and equity funds. Pure
equity funds do not include balanced funds. In this study we refer to equity funds including
balanced funds, as it is customary in the US studies.
13
in 1998. In the year 2000 there are more than 1000 existing funds. It should be
noted, however, that equity funds still count for only one fourth of the overall
assets under management.
A recent study by Otten and Schweitzer (1999) shows that the preference for
bond funds is a common feature of the European mutual funds market. Using
1997 data, these authors observe that the European equity funds counted for
the 32% of the total mutual funds asset value, compared to the 50% in the
US. In Table 1 we report the evolution of the assets under management by the
European based mutual funds from 1990 to 1999. Note that the average increase
in the net asset under management (excluding Italy) is about 313%. In Italy the
same ratio is roughly four times greater. Figure one shows the distribution of
the investment vehicles between the pure equity, bond, liquidity and balanced
categories. The preference for bond and liquity funds is weaker that in the past,
but it is still important.
14
Figure 1: Europe an mutual funds by type
100
11
90
13
80
70
31,2
40
9,8
18
28,4
15
60
33
50
35,8
40
34,8
31,5
30
20
10
34
26
21
17,5
0
1992
1994
Equity Funds
1996
Bond Funds
1999
Liquidity Funds
Balanced
and
Others
Table 1 : Evolution of the assets under management by european
mutual funds, 1990-99 (million euros)
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
A us tria
1 0 .6 0 9
1 1 .2 7 6
1 2 .4 8 5
16.328
19.155
26.083
31.779
4 0 .8 2 1
5 4 .3 3 6
6 9 .7 4 5
B e lg iu m
3 .3 2 5
4 .5 3 4
7 .4 2 4
13.908
15.434
18.764
22.042
3 0 .6 0 3
4 8 .2 3 6
5 6 .0 5 0
D e n m a rk
Fr a n c e
G e rm any
2 .6 3 3
2 .7 8 9
2 .8 3 9
3.984
4.452
5.023
7 .5 0 0
1 1 .8 6 5
1 6 .6 0 5
2 1 .6 1 6
2 7 8 .3 6 7
3 3 1 .1 0 0
3 7 1 .4 8 0
4 3 3 .8 8 2
406.498
406.818
426.117
450.741
5 0 3 .1 0 4
6 5 5 .6 0 0
5 1 .9 5 7
5 9 .2 2 7
5 8 .1 0 1
70.460
92.065
104.733
110.097
133.661
1 6 6 .8 3 4
1 9 6 .3 9 7
G re e ce
688
733
844
3.106
4.551
8.705
12.612
2 3 .5 4 1
2 7 .4 2 5
3 5 .5 4 1
Ire la n d
5 .1 0 9
5 .5 3 6
4 .9 0 7
4.705
6.359
6.558
7 .3 5 0
2 3 .0 0 0
2 0 .2 4 1
2 0 .2 4 1
Ita l y
3 0 .6 4 7
3 6 .5 3 6
3 4 .1 6 2
57.687
65.425
62.443
103.859
182.610
3 7 1 .9 1 2
4 5 4 .4 9 0
L ux e m bu rg
6 2 .0 3 1
8 7 .4 8 8
1 5 1 .1 4 2
2 2 2 .2 2 1
231.376
253.333
283.035
349.726
3 5 3 .1 1 6
4 3 4 .9 1 4
N e the rland s
1 7 .8 2 5
1 5 .3 0 0
2 8 .8 0 0
40.821
39.043
48.637
53.959
6 4 .0 4 4
6 4 .6 8 3
7 5 .1 0 0
Po rtu gal
3 .7 0 6
4 .7 8 5
6 .5 9 1
8.356
10.521
10.393
12.562
1 6 .1 9 7
1 9 .8 4 5
2 0 .4 7 1
S p a in
8 .9 6 7
3 0 .2 3 5
4 5 .3 8 5
64.596
70.129
48.335
114.325
161.627
2 0 3 .7 7 9
2 0 5 .2 3 1
Sw e d en
1 5 .6 4 4
1 3 .1 3 0
1 4 .9 8 3
22.280
16.482
21.019
28.263
4 1 .6 9 9
4 7 .1 3 6
6 3 .4 4 2
S w it ze rl a n d
1 4 .2 8 7
1 5 .0 7 2
1 6 .2 0 0
30.647
31.770
34.974
38.404
4 8 .8 5 6
6 1 .2 8 8
7 0 .5 6 6
U nite d K ingd om
6 5 .2 5 0
7 7 .9 6 1
7 5 .6 2 5
1 2 0 .1 9 3
108.881
120.390
159.551
213.324
2 4 3 .6 0 7
3 0 6 .4 4 5
15
In Italy, the investment in bond funds became increasingly predominant
in the early 90’s. In 1990 the 41% of the total mutual funds asset value was
represented by bond funds and this percentage reached 71,5% in 1997. From
1997 to 1999 it stabilized around 72%. This extreme preference for low risk
investment vehicles, which typically focus on ﬁxed income government bonds
and money market instruments could be attributed to a variety of reasons. The
traditionally strong degree of risk aversion of the italian investor, who still holds
the largest portion of the huge domestic public debt and a dierent pension
mechanism, with a limited role for pension funds.
Unlike their US counterparts, most of the funds are owned by banking
groups. In 1995, Italian banks held as much as the 74% of the italian mutual funds industry asset value, which became 94% in 1998. Moreover, the 60%
of the total assets is currently managed by the ten biggest mutual fund companies and as much as the 42% by the ﬁrst three (who still hold only 10 funds
each on average). The estimated degree of concentration for the future years
is even greater if you consider that a signiﬁcant number of italian banks have
recently merged or are to merge (Simper (1999)). Combining these two facts,
the ﬁrst ten banking groups now hold more that the 75% of the total assets
under management. As a result, in 1998, the largest part of italian funds was
oered through banking channels (58%) compared to a 10% in the US, where
brokers and direct sales count for more than the 70%. This is in part a european
phenomenon. On average, the european banking system distributes as much as
the 52% of the total mutual funds and only a 20% is left to brokers and direct
16
sales (FEFSI).
These unambiguous ﬁgures suggest that there are at least two signiﬁcant
institutional dierences between the italian and the US mutual funds industry. First, the control of the italian banking system over the domestic mutual
funds market is tighter. This fact might result in similar investment policies
and scarcely innovative trading strategies. Second, given the increasing concentration of the italian banking industry, a substantial proportion of the mutual
funds are supervised, if not managed, by a few people. A few managers, i.e.
limited competition, results in a few investment styles i.e. poor variety. We
anticipate that the empirical analysis based on historical performance ﬁgures
will conﬁrm our ﬁrst guess, that, at this stage, is based on a rather elementary
discussion of some institutional aspects.
4
After tax returns
US Mutual funds studies always use pre-tax returns. After tax returns are better
in principle and should be preferred, but they are never used. The reason behind this choice is simple. In the US, the amount payed by ﬁrms and individuals
does vary greatly due to dierential tax rates. As a result, reasonable approximations to the after-tax performance are almost impossible to reconstruct (see,
e.g. Kent, Grinblatt, Titman and Wermers (1997)). Moreover, dierent conclusions regarding absolute and relative performance could be drawn depending on
the tax regime to which the investor is referenced. On the contrary, long and
17
accurate time series of pre-tax returns are widely available in the US9 .
In other countries, for example in Japan, it happens to be exactly the opposite. Mutual fund researchers are forced to use exact or proxy after-tax returns.
A recent study by Brown, Goetzmann, Hiraki, Otzuki and Shiraishi (2000) on
the Japanese fund case shows that sometimes the ﬁscal policy could be everything but neutral. In particular, it could substantially aect the return dynamics, i.e., the strategies originating the returns themselves are partially driven by
tax factors. Using proxies for after tax returns, Brown et al. illustrate that the
plain Sharpe procedure will systematically underrepresent the fund returns due
to a tax dilution factor. The way this phenomenon is analyzed relies on a two
step procedure. First a number of style centroid means (the GSC style or analogous style representation) is estimated and then related to standard factors and
tax dilution proxies.
In Italy the situation is apparently similar to Japan, since open end mutual
funds are taxed at source. Mutual fund returns are still subject to dierent tax
rates and all the capital gains are uniformly taxed (12,5%). More precisely, there
are some marginal tax exempt asset classes and income from short term government bonds is taxed at a dierent rate. In any case, considering a homogenous
12,5% tax rate is su!cient for our purposes. From July 1998 dividends have
been subject to dierent tax rates: 22,5% from July to December 1998 (12,5%
+ an additional 10%) and 12,5% from January 1999.
9 Most of the US academic studies regarding mutual funds appeared after 1968. Reliable
mutual fund data for a limited number of US investment companies were available even in the
ﬁfties (see, e.g, Jensen (1968)).
18
The net asset value per contract at time t, N AVt , is calculated every day on
a post-tax basis and it is precisely the price at which a new quote of the fund
can be purchased by the public. The pre-tax return for an accumulating fund,
that is the return normally used in the US studies, could be deﬁned as:
gt1,t =
N AVt qt + T AXt
1
N AVt1 qt1 + N AVt1 (qt qt1 )
(7)
where qt is the number of fund shares in t. T AXt stands for the sum of tax
amounts computed every day as a proportion of the increase in the asset value
and is the tax rate. After some algebra we get:
T AXt =
t
X
i
qi (N AVi N AVi1 )
1
(8)
The sum T AXt must be payed o once a year, in February. The daily aftertax return nt1,t is easily obtained by analogous formal algebraic manipulations
as a function of gt1,t , T AXt , N AVt1 , qt and :
µ
nt1,t =
¶
N AVt
1
N AVt1
µ
= gt1,t +
T AXt
N AVt1 qt
¶
(1 )
(9)
As we mentioned earlier, we are forced to use post tax returns, since we
didn’t record any information regarding the tax payments of the individual
funds. Unfortunately, the nt1,t ’s do not only depend on the appreciation of
the fund portfolio but also on the number of shares, qt , that is revealed ex post.
Can the inclusion of these tax factors produce a signiﬁcant impact on return
based style classiﬁcation procedures?
19
In principle, including the end of day number of shares in the returns calculation can produce a signiﬁcant impact on performance evaluation analysis,
because the benchmark return is not sensitive to positive or negative variations
in the net inﬂows. In particular, this bias is inversely proportional to the size
of the fund: the smaller the funds the higher the bias. In addition, given that
in Italy funds practically cannot fail, because of the strict regulation imposed
on the industry, an abnormal decrease in qt , that could be associated to poor
past performance, could result in artiﬁcially increased returns which are not to
be attributed to improved asset management.
Tax issues are much less important for style identiﬁcation purposes. In
return based style identiﬁcation we’re not concerned with the absolute eect of
qt on nt1,t , as in performance evaluation, but, rather, on the undesired cross
sectional dierences induced on the nt1,t ’s by substantial inﬂows/outﬂows of
funds across managers. In the italian case, these cross sectional dierences
can be neglected because the mutual funds industry experiences remarkable yet
homogenous periodic variations in the qt ’s, at least within the category of equity
funds. In practice, investors tend to go in and out of the market together and
normally do not switch massively between equity funds. Moreover, the average
size of the funds included in our sample is above the market average, so that
the eect of tax payments on the return dynamics is somehow mitigated.
For the sake of completeness, we mention that before 1998 mutual funds
didn’t pay taxes on a performance basis but relative to the portfolio compo-
20
sition at an instant of time. Industrial, non industrial stocks and bonds were
treated dierently for tax. Capital gains and income from mutual funds were
tax exempt for households and the mutual funds were paying dierent tax rates
on their total asset value: 0,05% on cash, government bonds and bank deposits,
0,10% on stocks issued by italian manufactoring ﬁrms and 0,25% on the residual
category10 .
5
The data
In this paper we start from a complete dataset of monthly returns of all the
Italian equity funds classiﬁed by Assogestioni (December 1999) from January
1995 to December 199911 .
First of all, we eliminate funds having less than 60 months of valid observations. After this, we eliminate funds of funds, funds whose target currency is
dierent from Italian lira, sector funds and a few ”country” funds which declare
to exclusively or mainly invest in a single country other than Italy, the UK,
Switzerland, France, Germany, Japan and the US. As Wermers (2000) correctly
notices, mutual funds sometimes oer the same portfolio to their clients, but
charging diering expense ratios and fees to dierent investors. For example,
1 0 Dierent tax rates were to favour private investment in manufactoring ﬁrms. This could
have been an additional temptation for window dressing practices. As far as we know, there
is no study regarding the eects of these incentives on mutual funds investing in asset classes
subject to non-homogenous tax rates.
1 1 The data were provided by Independent Asset Managers SIM (IAM SIM) and Compage
SGR. IAM SIM is an investment ﬁrm specialized in selecting fund managers and Compage
is an asset management company belonging to the Mediobanca group. Both institutions are
based in Milan.
21
long term investors prefer low expense ratios and high fees while high expense
ratios and low fees are usually chosen by short term investors. Italian funds
recently started oering structured portfolios formed within their existing funds
to allow a higher degree of diversiﬁcation at a lower cost. Sometimes the pool
of assets under management is the same, and the target currency is dierent.
In all these cases it is su!cient to take a representative element for the entire
class of clones oered by the same company. A similar justiﬁcation is valid for
fund packages, to be treated as redundant assets.
We drop country funds and sector funds because they do not present any
evident problem of classiﬁcation and funds whose target currency is dierent
from Italian lira to reduce the number of indexes in the constrained linear model.
We also slightly modify the Assogestioni classiﬁcation12 , merging the balanced
and the ﬂexible category as well as the Euro and the European group. All the
funds belonging to the ”Other specializations” category are excluded from the
sample (all of them are either country funds or sector funds).
We refer to this simpliﬁed 7-categories clustering as the industry classiﬁcation. The 186 funds comprised in the sample fall into the market location
and investment mix categories as follows: Balanced (47 funds), Emerging Markets equities (6 funds), European equities (25 funds), International equities (38
1 2 The Assogestioni categorization has changed during the course of this research. For example, at the end of 2000 you have three dierent categories for balanced funds (by the
way, our analysis shows that this distinction may be unnecessary for style analysis purposes).
The number of groups is obtained exogenously by the standard determinant ratio procedure
discussed in Everett (1974). We think that this intuitive method is more robust than the commonly employed likelihood ratio statistics, that are sensitive to departures from the normality
assumption.
22
funds), Italian equities (41 funds), Paciﬁc equities (13 funds) and US equities
(16 funds). The average annualized returns vary from 2,7% (an Emerging Markets fund) to 31,3% (an International fund). The highest annualized volatility
is found with vehicles primarily investing in Italy: 13 out of the 14 funds having
an annualized volatility higher than 30% (34,54% is the highest) belong to the
Italian Equities category. The average equally weighted market return is 17%
and the average unconditional volatily per annum is 20,6%. The same statistics by industry category indicate that the absolute dierence in average annual
returns across groups is rather sharp. The lowest mean return is found within
the Paciﬁc Equities category (8,8%) and the highest within the American Equities style (24,9%) and the Italian category (23,4%). Similar dierences arise
between the average annual unconditional volatilities. The Emerging Markets
funds show the highest standard deviation per annum (25,65%). As expected,
the lowest value is found within the balanced category (11,7%). More intrinstingly, the standard deviations for the Emerging Markets, the Italian and the
American Equity funds are very close (25,65%, 22,3% and 21,6% respectively).
Consequently, the dierence in the average Sharpe ratios is little, from 1,2 (International equities funds) to 1,0 (Italian Equities funds), with two exceptions
behaving similarly (Emerging markets and Paciﬁc funds, both with a Sharpe
ratio of 0,4).
23
Table 2a : Standard Deviations within GSC Groups
1995-I
1995-II
1996-I
1996-II
1997-I
1997-II
1998-I
1998-II
1999-I
1999-II
mean
G1
0, 0095
0, 0069
0, 0099
0, 0089
0, 0093
0, 0111
0, 0163
0, 0112
0, 0082
0, 0125
0, 0104
G2
0, 0228
0, 0155
0, 0159
0, 0169
0, 0200
0, 0306
0, 0326
0, 0273
0, 0259
0, 0285
0, 0236
G3
0, 0123
0, 0114
0, 0120
0, 0093
0, 0103
0, 0135
0, 0130
0, 0121
0, 0115
0, 0146
0, 0120
G4
0, 0145
0, 0079
0, 0081
0, 0088
0, 0123
0, 0108
0, 0148
0, 0132
0, 0117
0, 0141
0, 0116
G5
0, 0107
0, 0090
0, 0130
0, 0138
0, 0194
0, 0219
0, 0178
0, 0253
0, 0199
0, 0151
0, 0166
G6
0, 0109
0, 0111
0, 0117
0, 0091
0, 0101
0, 0113
0, 0135
0, 0107
0, 0144
0, 0219
0, 0125
G7
0, 0080
0, 0069
0, 0093
0, 0083
0, 0089
0, 0111
0, 0109
0, 0100
0, 0102
0, 0186
0, 0102
mean
0, 0127
0, 0098
0, 0114
0, 0107
0, 0129
0, 0158
0, 0170
0, 0157
0, 0145
0, 0179
0, 0138
Table 2b: Standard Deviations within Assogestioni Groups
1995-I
1995-II
1996-I
1996-II
1997-I
1997-II
1998-I
1998-II
1999-I
1999-II
mean
Bal/Flex
0, 0170
0, 0106
0, 0116
0, 0095
0, 0140
0, 0135
0, 0204
0, 0155
0, 0106
0, 0148
0, 0137
Emerg
0, 0259
0, 0128
0, 0152
0, 0121
0, 0195
0, 0258
0, 0240
0, 0321
0, 0294
0, 0171
0, 0214
Europe
0, 0223
0, 0175
0, 0205
0, 0148
0, 0217
0, 0185
0, 0276
0, 0179
0, 0124
0, 0171
0, 0190
Int
0, 0208
0, 0166
0, 0148
0, 0113
0, 0161
0, 0158
0, 0225
0, 0183
0, 0150
0, 0182
0, 0169
Italy
0, 0115
0, 0096
0, 0129
0, 0098
0, 0115
0, 0125
0, 0132
0, 0099
0, 0080
0, 0161
0, 0115
Paciﬁc
0, 0235
0, 0143
0, 0134
0, 0184
0, 0208
0, 0220
0, 0296
0, 0195
0, 0202
0, 0280
0, 0210
US
0, 0184
0, 0154
0, 0146
0, 0146
0, 0165
0, 0167
0, 0246
0, 0127
0, 0134
0, 0135
0, 0160
This table reports the return monthly standard deviation within each GSC and
industry group. Each line corresponds to a semester, for example 1995-I corresponds
to the ﬁrst semester of 1995. The last column reports the mean values of the standard
deviations for each subperiod and the last row the mean values of the standard deviations for each group. We pack together the results to give a feeling of the variability
24
mean
0, 0199
0, 0138
0, 0147
0, 0129
0, 0172
0, 0178
0, 0231
0, 0180
0, 0156
0, 0178
0, 0171
reduction of the clustering tecnique obtainable starting from an industry allocation.
All the GSC groups are obtained starting from random allocations.
Table 3: GSC groups composition
Bal./Flex
Emerg
Europe
International
Italy
Paciﬁc
U.S.
Total
G1
32
0
1
0
1
0
0
34
G2
1
6
2
29
0
13
14
65
G3
0
0
17
3
0
0
0
20
G4
12
0
0
1
0
0
1
14
G5
1
0
0
2
0
0
0
3
G6
1
0
3
3
16
0
1
24
G7
0
0
2
0
24
0
0
26
Total
47
6
25
38
41
13
16
186
This table reports the number of funds within each GSC group as classiﬁed by
the modiﬁed industry categorization. Each GSC grouping is obtained minimizing the
euclidean distance of each fund return series from a centroid mean estimated according
to the following model:
Rj,t = sJt +%j,t
where sJt is the fund expected return conditional on knowing the realizations of
the market factors and the residual fund speciﬁc variance is allowed to vary through
time. The method is a generalized least squares variation of the traditional k-means
algorithm of cluster analysis (see, e.g, Everett (1974)). Given that the method is nongerarchic, the number of groups must be speciﬁed exogenously, in other words, it is not
necessarily optimal. We do not employ the classical regression based likelihood ratio
25
test, that is very sensitive to departures from the normality assumption. Although
there are no completely satisfactory methods for determining the number of population
clusters for any type of cluster analysis (see, e.g., Hartigan 1985; Bock 1985) we use
a version of Arnold’s (see, e.g., Arnold (1979)) method that is based on the the ratio
between the determinants of the within-cluster sum of squares and the overall sum
of squares matrix. The correct number of clusters is reached when this ratio comes
to a ﬁxed point (other approaches suggest to use the trace of the within-cluster sum
of squares matrix instead of the determinant, see, e.g., Marriott (1971, 1975)). We
have repeated the same analysis (unreported) for other clustering methods, such as
the style classiﬁcation algorithm applied to the space of the Sharpe coe!cients and the
Lehman-Modest factor loadings obtaining rather puzzling results. These results do not
need to be reported because the explanatory power of such models, in particular the
second, is extremely low. Instead, we obtain analogous groupings for the SC algorithm
applied to space of fund returns
In table 2 we report the monthly standard deviation of fund returns within
the industry categories and the endogenously groups estimated with the GSC
methodology. The results of this procedure are in table 3, which reports the
cross-tabulation as classiﬁed by Assogestioni and GSC. As a ﬁrst approximation,
the low values of the intra group standard deviation might indicate that the style
component not to be attributed to the industry classiﬁcation is small.
We have also investigated some summary measures of predictability in the
spirit of Harvey (1989) and Breen, Glosten and Jagannathan (1989). The ﬁrst
26
order autocorrelation coe!cient is greater than 0,1 in 49 out of 186 cases. The
unconstrained regression adjusted R2 of the fund returns versus a set of instrumental variables (a constant, the Italian Treasury bill return taken as a proxy
for the risk free rate, the lagged MSCI equity Italy and the lagged excess return
with respect to the risk free rate) exceeds 5% for 23 out of 186 funds and exceeds
10% in 14 cases.
When a fund changed name during the sampling period, we directly linked its
return series to the old one. This could be in part a problem, since italian funds
could have changed name and objective instead of dissolving. On the other hand,
our database is not directly subject to survivorship bias (Brown, Goetzmann,
Ingersoll and Ross (1992)). This issue is very important in performance studies
but yields limited eects in return based style analysis. The most interesting
case happens whenever most of the defunct funds are concentrated within a
desappeared style (Fung and Hsieh (1997)), which means that terminated funds
behaved so dierently from the rest of the population to force an extension of
the categorizations.
6
The Sharpe equation
Our speciﬁcation of the Sharpe procedure uses monthly observations of 14 independent variables (market indexes) from January 1995 to December 1999. All
the indexes come from the Ibbotson and Associates database.
27
A ﬁrst problem in applying the Sharpe methodology outside the US is that,
in many cases, the currency of the indexes and the target currency of the funds
aren’t the same. Therefore, a decision must be made on how to convert returns
and hedge currency risk (see, e.g., Detzler (1999)). We converted all the monthly
total return series into Italian Lira applying the monthly JPM spot rate from the
Ibbotson and Associates database. We followed this direct conversion procedure
for the MSCI emerging markets Europe index, the MSCI emerging markets
Latin America Free index, the MSCI Japan index, the MSCI Germany index,
the MSCI Switzerland index, the MSCI France index, the MSCI Nordic index,
the MSCI U.S. index, the MSCI U.K. index, the MSCI AC Asia Paciﬁc ex
Japan index. The FTSE Italy Med-Small Cap, the FTSE Italy Large Cap, the
IMF Italy Tbill and the JPM Italy 1+ Yr Gvt bond indexes do not need to be
converted.
Our choice of the independent variables deserves some words of comment13 .
We subdivide the european market (ex Italy) into su!ciently orthogonal components: Nothern Europe, European emerging markets, the U.K., Switzerland,
France and Germany. The rest of the world is represented by a few, whenever
possible free14 market indexes. The italian market is proxied by a small-mid cap
and a large cap equity index. The exposition versus the short and the mediumlong term interest rates is captured by two government bond indexes. We do not
include any corporate and municipal bond index given the the marginal size and
1 3 The right choice of the explanatory variables is always a problem. In particular, the
number of regressors may even exceed 60, as in the BARRA software proprietary model.
1 4 In order to maximize the correlation with a representative investable entity we recommend
the use of equity market proxies not including assets restricted to foreign investments.
28
scarce liquidity of the domestic corporate and municipal bond markets and gold
because its explanatory power as a substitute for investments in commodities,
is not meaningful in the italian case15 .
Our approach is then eurocentric, as opposed to the US focus of Sharpe
(1992), as most funds in our DB are classiﬁed in the Equity Italy, Equity Europe
or Equity Euro Area categories.
Table 4: Change in the implied portfolio weights
CH
F
IT1
N
J
US
IT2
UK
EML
APJ
EME
B1+
D
L
G1
0,0%
3,2%
-7,7%
-0,2%
-0,5%
-2,4%
8 ,7 %
- 4 ,3 %
- 0 ,6 %
2 ,3 %
- 0 ,2 %
- 1 0 ,4 %
1 ,6 %
10,6%
G2
0,0%
-1,2%
0,0%
6,9%
-4,9%
8,7%
0 ,7 %
0 ,0 %
- 4 ,7 %
- 2 ,3 %
1 ,5 %
1 ,1 %
- 5 ,9 %
0 ,0 %
G3
4,7%
4,3%
1,0%
1,6%
-0,9%
-4,3%
3 ,4 %
1 ,3 %
- 3 ,0 %
1 ,5 %
1 ,5 %
- 3 ,5 %
- 3 ,6 %
- 3 ,9 %
G4
-3,7%
3,9%
0,5%
0,0%
-0,2%
3,5%
0 ,4 %
- 2 ,3 %
- 2 ,5 %
1 ,3 %
0 ,0 %
- 0 ,2 %
- 5 ,6 %
4 ,9 %
G5
4,1%
0,0%
-40,5%
1,6%
4,7%
9,8%
0 ,0 %
1 3 ,3 %
1 ,0 %
9 ,2 %
0 ,1 %
- 1 0 ,4 %
- 2 ,0 %
8 ,9 %
G6
0,0%
2,0%
-0,7%
1,9%
0,0%
-3,2%
1 3 ,5 %
- 0 ,9 %
- 0 ,6 %
1 ,6 %
- 0 ,5 %
- 1 4 ,4 %
0 ,7 %
0 ,6 %
G7
0,0%
-1,5%
-6,7%
3,8%
0,0%
0,0%
1 9 ,4 %
0 ,0 %
- 0 ,4 %
- 0 ,7 %
0 ,0 %
- 2 2 ,4 %
4 ,1 %
4 ,4 %
This table reports the dierence between the implied portfolio weights estimated
in the period July 1997-December 1999 and January 1995-June 1997 for each GSC
group. IT1 and IT2 are the FTSE Italy Med-Small Cap and the FTSE Italy Large
Cap indexes, EME is the MSCI emerging markets Europe index, EML is the MSCI
emerging markets Latin America Free index, J is the MSCI Japan index, D is the MSCI
Germany index, CH is the MSCI Switzerland index, F is the MSCI France index, N is
the MSCI Nordic index, US the MSCI U.S. index, UK is the MSCI U.K. index, APJ
is the MSCI AC Asia Paciﬁc ex Japan index, L is the IMF Italy Tbill, used as a proxy
for cash and B1+ is the JPM Italy 1+ Yr Gvt bond index, to represent the eventual
1 5 Italian
mutual funds can’t invest in commodities and real estate.
29
bond fund component.
Some results regarding the Sharpe implied portfolio weights are given in
table 4 and ﬁgures 2 and 3, which report the average exposures to the 14 exogenously prespeciﬁed asset classes. As one could expect, the preferences of the
italian equity portfolio managers are directed towards italian stocks and government bonds instruments. In particular, investments in short and long term
government bonds count for approximately the 25% of the industry portfolio.
Such a high estimated exposure to the returns on cash and bonds could
be attributed to the selection of a wrong set of benchmarks16 , given that the
constant and the return on cash are collinear. This potential distorsion is always
latent in the application of the Sharpe procedure. However, at the exploratory
stage, we obtained similar estimates of the bond and cash component of the
equity portfolios using dierent sets of benchmarks.
In any case, this result must be interpreted much more as an indication of
an order of magnitude and on a comparative basis, rather than a completely
reliable approximation. Here we’re not giving much importance to the fact
that the estimate could be upward biased since we’re interested in pointing
out the dierence from the implicit weight calculated in the US studies. For
example, Brown and Goetzmann (1997) report an average exposure as low as
1 6 Using the methods developed by Gibbons Ross and Shanken (1989) and Green (1986),
Basile, Doninelli and Savona (2000) show that the equity indexes used by the italian fund
managers are e!cient in the mean variance sense and the maximal benchmark error is bounded
by a small constant.
30
0%
31
Italy Tbill
Bond Italy 1+
Asia Pacific
ex Japan
U.K.
U.S.A.
Nordic
France
Switzerland
Italy Large
Cap
Germany
Japan
EM Latin
America
Italy MedSmall Cap
Italy Tbill
Bond Italy 1+
Asia Pacific
ex Japan
U.K.
U.S.A.
Nordic
France
Switzerland
Italy Large
Cap
Germany
Japan
EM Latin
America
Italy MedSmall Cap
EM Europe
0%
EM Europe
Figure 2: Sharpe implied portfolio weights by asset class
18%
16%
14%
12%
10%
8%
6%
4%
2%
Figure 3 : Changes in portfolio weights
first subperiod second subperiod
25%
20%
15%
10%
5%
2, 4% versus the Tbill and 1% versus long term government bonds17 . This
means that american equity funds consider cash and long term bonds as residual
instruments and this evidence is supported by the estimated coe!cients of the
Sharpe style analysis. Some investment in cash is needed for liquidity purposes,
the second is of negligible importance. On the contrary, italian equity funds
reserve a much more substantial amount of their asset allocation to non equity
instruments.
In ﬁgure 4 and 5 we group our sample by the overall Sharpe regression unadjusted R2 . The performance of the linear model is quite satisfactory, indicating
that a multifactor linear approximation explains the returns dynamics quite
well. The R2 of the Sharpe regression over the whole 1995-1999 period exceeds
0, 95 for roughly the 75% of the funds with a lowest value around 0, 70. Subdividing the sample into two non-overlapping subperiods of 30 observations each
we observe a signiﬁcant improvement in the performance of the linear model in
the second subperiod. From January 1995 to June 1997 only the 35% of the
funds style regression exceeds 0.95 compared to more than the 60% in the second period. This phenomenon characterizes the whole industry: as can be seen
from ﬁgure 6 there aren’t any appreciable dierences across dierent categories.
Most of the funds progressively increased their exposure towards large cap
stocks and cash or money market instruments, that is, safer assets. This could
be a consequence of the recent introduction of ”public benchmarks” in evalu1 7 We recalculated these exposures from the GSC group compositions and the GSC implied
portfolio weights means in Brown and Goetzmann (1997), table 1 and 2 respectively.
32
Figure 4 : In sample explanatory power of Sharpe regressions
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
70%
75%
80%
85%
90%
95%
99%
2
R of Sharpe regression
Figure 5 : Changes in the explanatory power of Sharpe regressions
first subperiod second subperiod
70%
60%
50%
40%
30%
20%
10%
0%
20%
30%
40%
50%
60%
65%
2
70%
75%
R of Sharpe regression
33
80%
85%
90%
95%
99%
Figure 6 : In sample explanatory power of Sharpe regressions by industry class
overall period first subperiod second subperiod
100,00%
R of Sharpe regression
95,00%
2
90,00%
85,00%
80,00%
75,00%
70,00%
U.S.
Bal./Flex
Emerg
Europe
34
International
Italy
Pacific
ating mutual funds performance. Starting from 1998, italian funds are forced
to declare a benchmark in order to fulﬁll a Consob (the italian Securities and
Exchange Commission) regulation. This regulation is still eective and states
that ”an objective parameter (benchmark), built by third parties and of common utilization, coherent with the risks assumed...” must be provided as a part
of the periodic statements.
As a result, most of the benchmarks are broad spectrum indexes or combinations of dierent market portfolios proxies such as the MSCI indexes. Mutual
fund managers are then really invited to track their whole reference market,
instead of concentrating on potentially proﬁtable, but risky practices such as
market timing and security selection.
7
Equity styles and dynamic trading strategies
Many ﬁnancial analysts classify mutual funds with respect to investment styles
derived from classic descriptors including the small cap, mid cap, large cap,
aggressive growth, income and capital appreciation indicators. As a result,
most US investors believe that these styles attributes are informative and think
of them as stable fund characteristics. Our ﬁrst question is: are these categories
informative in the italian case?18 . To answer this, we classify the sample starting
from the implied portfolio weights on the IIA style indexes (from the Ibbotson
1 8 The
question can be phrased dierently: do the terms growth fund or value fund, for
example, mean something when applied to the italian equity funds case? You could think of
it as a particular case of a more general question: do the US textbook equity styles explain
something outside the US?
35
and Associates DB) explaining most of the fund return hystorical variation.
Using the coe!cient estimates coming from the Sharpe return based style
analysis reported in the preceding section we deﬁne the reference market as
the maximally weighted index in the passive alternative. For example, if the
maximum implied portfolio weight is represented by the MSCI Japan coe!cient,
we have choose the Japan IIA stylistic indexes. This elimination procedure
leaves us with the the IIA Italy, IIA Europe, IIA Paciﬁc, IIA Paciﬁc ex Japan
and IIA U.S.large growth, small growth, large value and small value indexes.
Then, for each fund return series, we run separate portfolio constrained
ref
ref
regressions on the reference market IIA indexes IIAref
LG , IIASG , IIALV and
IIAref
SV as follows:
Rj,t
i
ref
ref
ref
= + 1 IIAref
LG + 2 IIASG + 3 IIALV + 4 IIASV + %j,t (10)
0, ;i and
4
X
i = 1
i=1
A fund is assigned to one of the four categories, small value, small growth
large value, large growth according to the Morningstar-like procedure.
36
Table 5: Industry classification and equity styles
Bal./Flex
Emerg
Europe
International
Italy
Paciﬁc
U.S.
Total
Large/Growth
43
1
11
17
22
4
6
104
Large/Value
0
0
5
5
0
0
4
14
Small/Growth
4
5
5
13
18
9
5
59
Small/Value
0
0
4
3
1
0
1
9
We classify the funds performing Sharpe regressions on the reference IIA indexes
ref
ref
ref
IIAref
LG , IIASG , IIALV and IIASV as follows:
Rj,t
i
ref
ref
ref
= + 1 IIAref
LG + 2 IIASG + 3 IIALV + 4 IIASV +%j,t
0, ;i and
4
X
i = 1
i=1
A fund is assigned to one of the four categories, small value, small growth large
value, large growth according to the maximally weighted coe!cient in the regression.
The IIA International Style Indices are developed by MSCI and IIIA, a Boston based
money management ﬁrm. IIA divides the corresponding MSCI into two sub-indices
basically using the price to book ratio. All the securities in a given market are sorted
in ascending order by their previous month-end ratio as it was published in MSCI
Perspective; the cut-o is set at the 50-th percentile. As far as the Large vs Small
is concerned, in each market, stocks are ranked by their market capitalization. The
large index encompasses the top 70% of the market capitalization, while the small
index encompasses the bottom 30% of the market capitalization.
37
Figure 7 : Mutual funds and equity styles
100%
Large
Small
80%
60%
40%
20%
0%
1995-96
1996-97
1997-98
100%
80%
1998-99
80%
Large/Growth
Large/Value
60%
Small/Growth
Small/Value
60%
40%
40%
20%
20%
0%
0%
1995-96 1996-97 1997-98 1998-99
1995-96 1996-97 1997-98 1998-99
38
Both the overall period and 24 months rolling regressions support a strong
empirical evidence for an increasing style drift towards the ”large-growth” category (see table 5 and ﬁgure 7). Italian funds didn’t choose for size or income
characteristics once and for all. Instead, they dynamically adjusted their preferences and progressively concentrated their allocation on large cap stocks (large
cap index tracking) during the sampling period. These results also conﬁrm that,
in the italian case, the explanatory power of these ”classic” stylistic categories
is scarce. Additional evidence can be found considering that only a few funds
use value (reddito), growth (crescita) or aggressive growth (aggressivo) as part
of their names. In general, the location component is much more importan than
the category of assets chosen by the funds as deﬁned according to the widely
used small/large value/growth paradigm.
Now we introduce another question. Is it true that italian mutual funds
follow dynamic trading strategies, at least to some extent? The performance of
the linear model is, by itself, a negative reply to this question, but we want to
consider this issue in more detail.
In the U.S. mutual fund literature there are several important studies supporting the belief that almost all fund managers follow some kind of dynamic
trading strategies adjusting their portfolio weights quite often, so that the overperformance with respect to passive benchmark deseappears when the appropriate instruments are considered (see e.g. Graham, Harvey (1996)). We can’t
simply transfer this conclusion to the italian case as if it was necessarily true.
39
The way to test if funds follow dynamic strategies is rather straighforward:
ﬁrst estimate the style benchmarks and then see if the style really evolves nonlinearly in the main asset classes. To accomplish this task, we combine the GSC
and Fung and Hsieh (1997) non parametric methodology (FH) and use the
relative advantages of both. The GSC provides a better estimation technique
for the style factors and the FH non parametric approach is to be preferred for
its simplicity and graphical appeal. In our case, we let the reference market
vary while the majority of US studies concentrate on the U.S stock market: in
ﬁgure 8 we plot the GSC equally weighted portfolios versus 5 states of nature
(return quintiles for the reference market index).
Figure 8 shows that all the payo functions behave linearly conditional on
a 5 states of nature structure. Carrying out similar experiments using deciles
instead of quintiles we get payo proﬁles apparently similar to bullish vertical spreads. This suggests that some kind of insurance strategies19 protecting
from extreme market moves could have been used, but nothing really signiﬁcant
supports the evidence of recognizable nonlinear patterns.
1 9 Successful market strategies provide cheap options to the investor (see Merton (1981)).
However, analogue positive results could be obtained using derivatives (inherently non-linear
instruments), which can be employed for hedging purposes.
40
Figure 8 : Sensitivity of the GSC estimators
GSC 1
GSC 2
15%
GSC
10%
Italy
GSC
10%
U.S.
5%
return
return
5%
0%
0%
-5%
-5%
-10%
1
2
3
4
-10%
5
1
2
quintiles
3
4
5
quintiles
GSC 3
GSC 4
10%
GSC
10%
Europe
GSC
Europe
return
5%
return
5%
0%
0%
-5%
1
2
3
4
-5%
5
1
2
quintiles
3
4
5
quintiles
GSC 5
GSC 6
15%
15%
Italy
GSC
Italy
10%
10%
5%
5%
return
return
GSC
0%
0%
-5%
-5%
-10%
2
3
4
-10%
5
1
2
quintiles
3
quintiles
GSC 7
15%
GSC
Italy
10%
5%
return
1
0%
-5%
-10%
1
2
3
quintiles
41
4
5
4
5
Table 6: Sharpe implied portfolio weights and dynamic trading strategies
Italy
World ex Europe
R2
T-bill
mean
s.d.
corr
mean
s.d.
corr
mean
s.d.
corr
mean
s.d.
G1
0,1902
0,1828
0,2003
0,3600
0,1274
-2333
0,4498
0,1953
0,2433
0,8388
0,1382
G2
0,3717
0,1122
0,0765
0,1041
0,0919
-0,7863
0,5242
0,0911
-0,1244
0,9606
0,0218
G3
0,1660
0,1617
0,2003
0,6474
0,2733
-0,6306
0,1865
0,1767
-0,0264
0,8297
0,1241
G4
0,0912
0,0766
0,2003
0,6087
0,1077
0,1599
0,3000
0,11221
-0,2211
0,9333
0,0677
G5
0,6971
0,1947
0,0765
0,0505
0,0742
-0,5808
0,2524
0,1550
-0,0935
0,9635
0,0227
G6
0,5960
0,2577
0,0765
0,1601
0,2412
-0,2542
0,2440
0,1259
-0,0935
0,9590
0,0310
G7
0,8014
0,1804
-0,1215
0,0399
0,0699
-0,4570
0,1587
0,1405
-0,0935
0,9664
0,0180
For each index, in the ﬁrst column we compute the mean and the standard deviation of the Sharpe implied portfolio weights estimated within 6 months non-overlapping
period. In the third column we report two informations. One is correlation between
changes in the Sharpe portfolio weights on a reduced set of independent variables and
the lagged return series on the same independent variables (the Morgan Stanley Capital International Italy, the Morgan Stanley Capital International ex Europe and the
Italian IMF Treasury bill indexes) over non-overlapping periods of six months each.
A trend chasing attidude corresponds to positive values of the correlation coe!cients.
Negative values of the correlation coe!cients indicate that a contrarian staregy may
explain part of the fund return dynamics. Note that some of the correlations are
identical across groups because the change in portfolio weights, which is a categorical
variable, is likely to assume the same values for dierent groups, which implies the
same correlation with the returns on the lagged indexes.
In Table 6 we report, for each GSC group, the correlation between changes
in the positive constrained portfolio weights on a reduced set of independent
variables, represented by a +1 for an increase, a -1 for a decrease and a zero in
42
case of no rebalancing, and the lagged return series for the same indexes (MSCI
Italy, MSCI world ex Europe and the italian Tbill returns) over 6 months nonoverlapping periods. This method has been used (see Brown and Goetzmann
(1997)) in detecting the trend chasing or contrarian attidude of the fund managers, but must be associated with other procedures when the time series of
returns is not very long (due to the non-overlapping nature of the regressions),
as it is in our case.
If a fund systematically follows a naive rebalancing strategy we should expect
very low values for these correlation coe!cients. This because the portfolio
weights are stationary with respect to time. This is indeed the case for the
Italian MSCI and the short rate index, but we obtain some signiﬁcant values
for the MSCI World ex Europe. The GSC procedure splits the Italian Equities
category in two groups (6 and 7) which might rebalance their portfolios of
italian stocks according to dierent trading rules. The sixth group tends to buy
italian stocks when the previous period returns are high (7,65% correlation),
the seventh when they are low (-12,5% correlation). All the other groups tend
to be weak trend chasers. As we expected, the ﬁrst GSC group, comprised of
balanced funds, has a positive correlation (24,33%) with the lagged return on
the Tbill, while for the other categories we found negative values.
The degree of correlation with the MSCI World ex Europe needs to be explained a little bit more carefully. In three cases (corresponding to the second,
third and ﬁfth GSC group) the correlation is high in absolute value (greater
43
than 0,5) and for all the GSC categories except the fourth (balanced funds)
the value is negative. The highest negative correlation, -78.63%, is found with
the second GSC group which is by far the biggest (it includes most International and US funds and all Paciﬁc and Emerging markets funds, a total of 65
cases). Therefore, the results obtained using the non-parametric methodology
and the correlation analysis leaves us with two apparenly contrasting pictures.
On the one side, the returns attributable to style respond linearly to the reference market but, on the other, some fund managers appear to behave as strong
contrarians. This result suggests that we need to take a further step in order
to assess the out of sample explanatory power of the GSC and other return
based categorizations and not necessarily assume that they work better than
the industry classiﬁcation.
8
The explanatory power of dierent categorizations
A model of mutual fund returns is useful if it can explain out of sample facts.
For this reason, we discuss the out of sample explanatory power of alternative
classiﬁcation systems in the spirit of Brown and Goetzmann (1997) and Blake,
Morey (2000). In this section we try to answer two basic questions. First, is it
true that a classiﬁcation system ”per se” provides some valuable information in
explaining the cross-sectional variability of mutual fund returns? Second, what
is the best fund classiﬁcation system? As we discussed in the previous section,
44
we can interpret the return dynamics of the italian equity funds by means of
various groupings, some of them derived from the existing asset pricing literature
and even ﬁnd apparently interesting common patterns. Interesting ad puzzlying
as they may seem, such common patterns arising from complicated clusterings
could be the result of a statistical artifact.
We divide the 186 by 48 return panel into three, partially overlapping 24
months data matrices, from January 1995 to the end of 1998. The empirical
statistic we construct for each subperiod should contain informations regarding the cross sectional dispersion of the next year annual compound returns
RNY,t . In other words, the categorization matrix D 5 M (N × K) estimated
by means of the previous 24 months returns data should convey statistically
signiﬁcant explanatory power. This hypothesis can be tested using cross sectional regressions which can be though as exact analogues to the cross sectional procedures common in the empirical asset pricing literature. We linearly project the 1 × N vector of annual returns RNY,t on the dummy matrix
D , {djJ = 1 if j 5 J and zero otherwise} estimated over a [t 1, t] time window:
RNY,t = t + t D[t1,t] + %t
(11)
and obtain a time series of coe!cient estimates {t , t }. Note that, if t is
statistically indistinguishable from the zero vector then the expected next year’s
return RN Y,t is constant for each t, that is all funds belong to the same style.
In this case the time varying mean model RiN Y,t = t + %i,t could be employed
45
as a universal ”fund pricing tool”.
Table 7: Explanatory power of classification methods
R2 1997
R2 1998
R2 1999
Assogestioni
0,8010
0,7953
0,6821
GSC
0,6620
0,6548
0,2771
Sharpe procedure
0,7064
0,5532
0,2866
L-M
0,3415
0,5501
0,5418
SC
0,6329
0,6406
0,6265
The table shows the cross-sectional return variance explained by the Assogestioni
categorization and the classiﬁcations derived using the GSC, Sharpe, Lehmann-Modest
and SC procedures. We employ partially overlapping 24 month estimation periods
from 1995 to the end of 1998 and linearly project the 1 × N vector of annual returns
RNY,t on the dummy matrix D , {djJ = 1if j 5 J and zero otherwise} estimated
over a [t 1, t] time period: RNY,t = t + t D[t1,t] + %t .
46
In Table 7 we report a summary of the results we obtain estimating the k+1dimensional vector [t | t ] by regressing RNY,t on dierent D’s. Each dummy
matrix D corresponds to a classiﬁcation method, which could make use of the
total returns history (GSC or SC), the loadings on endogenously determined or
prespeciﬁed factors or existing industry classiﬁcations based on recommended
allocations. The usefulness of the return based clustering approaches is considered when applied to dierent spaces: the Q-dimensional space of Sharpe
coe!cients (estimated via quadratic constrained optimization routines) and the
loadings coming from a PC analysis on the N × T returns matrix estimated as
in Lehmann and Modest (1988).
Both the GSC and the plain k-means method provide a necessary reduction
of dimension needed to derive stylistic approaches from a bunch of estimated coe!cients. In this sense, such techniques constitute a generalization of the classic
unidimensional Black-Scholes-Jensen beta sorting procedure. A comparison between the performance of the SC and GSC algorithms on the returns matrix is
also needed to test whether heteroskedasticity adjustments on the basic theme
adds predictive content to the estimates.
The results we obtain are rather surprising, since they indicate that the
same classiﬁcation methods work much worse in Italy than in the US. They also
conﬁrm that there is no value added complicating simple things, that is applying
a sophysticated computational machinery to naively generated returns.
The modiﬁed 7-categories classiﬁcation dominates all the others and explains
47
a really remarkable portion of the out of sample cross-sectional return variability.
The usual caveat that the original industry categorization changed from time
to time also applies to this case.We do not take classiﬁcation changes into account and proceed as if the 1999 classiﬁcation remained constant over the whole
1995-1999 period. Put in dierent terms, we test the power of the industry
categorization ”backwards in time”. Moreover, we couldn’t obtain any reliable
information regarding fund objective changes and eventual switches between
categories.
Table 7 contrasts some robust empirical ﬁndings regarding US based mutual funds. In the US case, cross sectional variability predictions based on
widely known industry classiﬁcations, such as Morningstar and similar, do rather
poorly. Such poor performance of the Morningstar classiﬁcation is certainly attributable to misspeciﬁcation. However, a lack of explanatory power doesn’t
imply that mutual fund styles are a coarsening of complex dynamic trading
strategies. It can also be that a simpler classiﬁcation based on the average asset
allocation of the funds (that doesn’t exist in the US, as far as we know) works
ﬁner than many unnecessary complications.
To further motivate this point of view, consider that Morningstar groups
funds in somehow vague categories, which sometimes refer to conceptually different criteria. The growth and the small group, for example, include very
diverse funds, even in terms of asset allocation policy. In addition, not all the
growth funds but only the US growth funds lie within the growth cluster. On
48
the contrary, the italian industry categorization, which is based on a recommended asset allocation, never makes use of the more intriguing but potentially
misleading concepts of growth and small.
Summarizing, we can conclude that:
1. classifying mutual funds is a simple task in a static, indexed market. Additional features complicate things and do not contribute with any information in order to assess the out of sample explanatory power.
2. Computationally intensive return based classiﬁcations are probably useful
in a dynamic enviroment, such as the US market, but need to be compared
to simpler, more robust naive benchmark groupings in the future.
Note that, even in a static market, neither clustering the Sharpe coe!cients
nor the portfolio factor loadings turns out to be a good choice. This has also
been noted in Brown and Goetzman (1997) for the US case. These coincident
negative results raise doubts on the general applicability of such methodologies,
independently of the confounding eect of dynamic trading strategies on the
return generating process.
9
Concluding remarks
Based on a large sample of Italian mutual funds, our paper shows that a modiﬁed industry classiﬁcation considering only the recommended asset allocation
49
(portfolio weights) is the best predictor of the cross-sectional variability of the
fund historical returns. The original Assogestioni classiﬁcation and our modiﬁed version do not make use of the classic growth versus value and large versus
small categories, which are shown to be volatile attributes. This empirical ﬁnding could also serve to improve some widely used US mutual fund industry
classiﬁcations, which perform extremely poorly in terms of predictive power,
possibly even when mutual funds follow linear strategies.
The US industry categorizations are quite involved but probably privilege
the wrong characteristics. In fact, the small and growth categories could be
better replaced by a broader range of asset class exposures as well as shared
dynamic strategies only if necessary, given that the reduced explanatory power
of the Morningstar-like categorizations could be improved not only by reﬁning
it towards more complicated but also simpler versions.
Our data seem to be rather easy to interpret in a linear asset pricing framework. A few style portfolios (that is, an asset pricing model in reduced form)
describe well the cross section of equity funds, which could have been replicated
by passive alternatives constructed combining investable entities. Our results
suggest that most of the italian fund managers do not think it is worth following dynamic strategies other than index tracking20 , reducing or increasing the
exposure versus dierent markets as a response to opposite changes in relative
prices.
2 0 Naive portfolio rebalancing is consistent with the Sharpe model and the linear unconstrained model. Obviously, relative value rebalancing and the buy and hold rule aren’t the
same thing.
50
As some ﬁnancial press already pointed out, Italian based funds are statistically indistinguishable from index funds. This extremely conservative attidude,
which continued to increase, is a mixture of poor asset management and the
rational response to some recent regulations from the Italian authorities, which
impose to mention the composition of the benchmark (restricted to the portfolio
combinations of publicly available indexes), as well as the relative performance
in the periodic statements. This choice of the italian regulators, aimed at improving the transparency of performance ﬁgures (the average investor must still
adjust for taxes by himself), basically forces the portfolio manager to act passively21 .
The structurally reduced competition and limited degrees of freedom of the
average italian portfolio manager explain only in part why italian funds still
cost so much. A few funds are signiﬁcantly dierent from naive portfolios and
innovative trading is virtually non existent, so that the tipical Italian investor
is paying more than a fair price for products that he could manage by himself.
Despite this, the italian mutual fund industry continues to grow. We leave the
solution of this empirical puzzle to future research.
2 1 Some recent theoretical ﬁnance literature (see, e.g., Admati and Pﬂeiderer (1997)) support
the total return incentive system. The italian case could indicate that implicitely imposing
a straight relative compensation scheme might reduce the allocative e!ciency and the style
diversity of the entire mutual fund industry.
51
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DIPARTIMENTO DI ECONOMIA AZIENDALE
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Daniela M. SALVIONI, Controllo di gestione e comunicazione nell’azienda pubblica,
aprile 1999.
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Arnaldo CANZIANI, Giovanni Demaria nei ricordi di un allievo, luglio 1999.
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Giuseppe BERTOLI, Salvatore VICARI, L'impresa diversificata come organizzazione
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2000.
7.
Virna FREDDI, L'approccio Resource-based alla teoria dell'impresa: fattori interni e
competitività aziendale, febbraio 2000.
8.
Maria MARTELLINI, Sviluppo, imprese e società, maggio 2000.
9.
Arnaldo CANZIANI, Per la critica della teoresi zappiana, e delle sue forme di
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Italia. Dalle origini agli anni settanta, dicembre 2000.
11. Giuseppe BERTOLI, Profili di efficienza delle procedure concorsuali. Il concordato
preventivo nell’esperienza del tribunale di Brescia, dicembre 2000.
12. Daniele RONER, Domanda e offerta di beni economici. Rassegna critica
dall’irrealismo neoclassico alla differenziazione dei prodotti, marzo 2001.
13. Elisabetta CORVI, Le valenze comunicative del bilancio annuale. I risultati di
un'indagine empirica, luglio 2001.
Serie depositata a norma di legge