DOI: 10.5817/FAI2017-1-2 No. 1/2017
19
The Return Variability and Dispersion: Evidence
from Mutual Funds in Post-Transition Countries
Dariusz Filip
Cardinal Stefan Wyszynski University in Warsaw (UKSW), Poland
Faculty of History and Social Sciences
Ul. Wóycickiego 1/3, 01-938 Warszawa
E-mail: d.filip@uksw.edu.pl
Abstract: The purpose of the paper is to evaluate the performance of mutual
funds operated in selected post-transition countries and to analyse their return
variability and dispersion. The study sample consists of 294 equity funds
(domestic and foreign ones) from the Czech Republic, Hungary and Poland. By
using classic measures of return as well as popular measures of risk, it was
possible to examine if equity funds from the CEE countries possess the ability
to outperform. It was observed that funds generally obtained mean returns,
which were below the corresponding benchmark. In most cases, however, the
results were statistically insignificant. Fund returns compared to equity indices
were characterised by lower ups and downs, especially during significant
market changes. The analysis of performance variability and dispersion
showed that there are entities which achieve marginally better return than
their competitors at a relatively low risk level. The test for equality of
variances applied in the study revealed evidence for the heterogeneity of
return variabilities, which could be caused by sample selection bias.
Keywords: mutual funds, performance, risk, return evaluation, CEE countries
JEL classification: G11, G23, G29
Introduction
The mutual fund industries in post-transition countries, particularly the ones
located in Central-Eastern Europe (CEE), are characterized by moderate
dynamics, which allows for sustainable development of the financial sector.
However, this growth is generally determined by economic situation. The asset
management industries in the European emerging markets grew significantly
over the last decade. According to the European Fund and Asset Management
Association (EFAMA, 2016), the value of assets of the Czech investment fund
industry at the end of the time horizon of the study amounted to EUR 7,818
million, which in comparison to 2005 (EUR 4,661 million) means an increase
by 67%. The value of Hungarian UCITS and non-UCITS funds increased from
7,757 million in 2005 to 18,105 million in 2015 (a 133% growth). The assets
under management of the Polish investment fund industry were valued at EUR
61,539 million in 2015 and at EUR 15,876 million in 2000, which means a
288% increase.
There has been a growing interest in these financial intermediaries in the
recent years, which resulted in an increased demand on various rankings,
analyses and reports concerning mutual funds. All these studies use a wide
20
variety of tools for the appraisal of effectiveness and risk. Apart from the
traditional approaches of comparing unit prices in subsequent periods, of
including risk and market factors or of employing contemporary methods for
measuring the level of managerial skills, the portfolio analysis makes also use
of graphic evaluation tools. One of them is risk-performance mapping, which
derives from the modern portfolio theory pioneered by Markowitz (1952) and
allows for collating the expected return with a given risk level.
During their operation period, mutual funds are evaluated in terms of
effectiveness (e.g. by comparing their performance with the benchmark) and
in terms of investment risk level. In general, examining the effects of asset
management is particularly significant while verifying the efficient-market
hypothesis; this, in turn, allows for explaining possible outperformance.
Hence, it might be assumed that perhaps it is possible for funds to outperform
in the seemingly less efficient markets of small size, the CEE markets being an
example. In view of the observations mentioned above, a research into the
discussed CEE markets offers a significant contribution to the existing
literature, especially as there is a serious lack of studies relating to emerging
European markets. Moreover, the addressed issue seems to be important not
only from the cognitive but also practical point of view. The returns achieved
by individual mutual funds might have an impact on investment decisions by
participants and suggest the possible potential for efficient asset management.
The financial institutions, in turn, may use the fact of possessing appropriate
effectiveness attributes in market play and media coverage.
The purpose of this article is to evaluate the effectiveness of mutual funds by
collating the achieved rates of return with the risk levels in funds.
Furthermore, the return dispersion analysis with particular emphasis on
differences in return variability will be essential. The study is an introduction to
the effectiveness evaluation of funds operated in the CEE countries and
provides a basis for further surveys and analyses in this area.
The rest of the paper proceeds as follows. Firstly, the selected empirical
literature on the effects of asset management by mutual funds, with a special
focus on local markets, will be reviewed in section 1. The methodological part
of the paper (section 2) presents the applied data, describes the measures of
return and risk level and research approaches used in the study. In Section 3,
we discuss and interpret the empirical results. The final section 4 summarizes
the major findings.
1 Conceptual Issues and a Brief Literature Review
One of the subjects regularly addressed by the financial literature on mutual
fund industries is the evaluation of asset management effects achieved by
financial intermediaries. The authors of major studies of the issue (e.g.
Treynor, 1962; Sharpe, 1964; Lintner, 1965; Mossin, 1966) formulated the
capital asset pricing model (CAPM), which is used to explain the crosssectional
differences in returns, and determined the ways of measuring risk on
securities (e.g. Merton, 1972; Friend and Blume, 1975). These findings
allowed for establishing tools for measuring mutual fund performance. The
21
early studies by Carlson (1970) and by Kon and Jen (1979) suggested that
mutual funds may be unable to generate abnormal returns, among others due
to management fees and other expenses. However, further studies (e.g.
Ippolito, 1989; Goetzmann and Ibbotson, 1994) indicate the ability of funds to
systematically generate positive results that underwrite the costs or even
exceed them. These conclusions seem to be in the minority, though. Due to
constraints (e.g. a survivorship bias documented by Brown et al., 1992; Elton
et al., 1996) in reporting outperformance, the subsequent studies tried to
explain returns by fund attributes or managerial characteristics.
More recent papers provide new tools for measuring return (e.g. Ferson and
Schadt, 1996; Modigliani and Modigliani, 1997) or new empirical approaches
(e.g. Huij and Verbeek, 2007; Kosowski et al., 2007). Consequently, within the
financial literature concerning the effectiveness of performance, some studies
take into account the specialist skills possessed by fund managers, which allow
them to beat the market (e.g. Switzer and Huang, 2007; Naidenova et al.,
2015). There are also papers devoted to return dispersion of mutual funds and
its measures (e.g. de Silva et al., 2001; Ankrim and Ding, 2002]. In general,
the ambiguity of findings results from the incomparability of time horizons
under study, the contents of samples, the measures of return used and the
empirical approaches adopted.
Most of the findings mentioned above relate to the US market; in the regional
literature, the investment fund industry is not a popular topic. One of the first
papers concerning mutual funds from developing countries has been written by
Kaminsky et al. (2001). Having analysed the investments in emerging markets
by financial intermediaries, e.g. in transition economies of the 1990s, they
found that mutual funds invested in Europe were mostly the funds invested in
the Czech Republic, Hungary and Poland. However, during the crisis within the
mentioned period, the outflows of fund assets were large in the majority of the
emerging markets. Another important study on this subject, written by
Khorana et al. (2005), examined the size of 56 mutual fund industries from
around the world and revealed the spread of development tendencies from the
US to non-US industries. Especially the increase in the market share of assets
under management was remarkable. Apart from the industry size, they also
analysed its age, legal and regulatory factors, the experience of investors, and
so forth. They also found out that the size of mutual fund industries had strong
implications for post-transition economies.
The better-known studies addressing the issue of individual mutual funds
relate to the Polish market (Swinkels and Rzezniczak, 2009; Białkowski and
Otten, 2011). In the first one, the performance of equity, balanced, and bond
funds was evaluated in relation to selectivity and market-timing skills of their
managers. The time horizon of the study was the 2000-2007 period, i.e. the
period directly preceding the onset of the global financial crisis. The results
obtained by Swinkels and Rzezniczak confirmed the existence of positive but
insignificant selectivity skills in the limited sample (38 funds). As for markettiming,
there have been no similar findings. The second of the mentioned
studies, the one by Białkowski and Otten (2011), used a considerably larger
sample of 140 mutual funds. By means of Carhart’s measure, they found that
22
Polish equity, bond and mixed funds might not have been able to achieve
abnormal returns in the 2000-2008 period. However, the domestic funds
outperformed their foreign peers. Moreover, the study revealed performance
persistence, which is a particularly valuable finding, especially with regard to
winning funds. A less-known paper worth mentioning is the one by Olbryś
(2009), in which she compares the market-timing and selectivity abilities of 15
Polish equity funds in the 2003-2009 period. The study, which used the
unconditional Treynor-Mazuy model to evaluate market-timing skills, reported
no significant evidence for outguessing the market. Moreover, the other of the
adopted approaches, the conditional Ferson-Schadt model, turned out to be
not very useful for evaluating the performance of Polish funds.
The mutual funds functioning in Hungary are described relatively rarely. Erdős
and Ormos (2009) performed the evaluation of asset management effects by
means of an original measure of return, the so-called daily recalculated
monthly returns. In their study of 20 Hungarian open-ended mutual funds
operated in the 2000-2007 period, they adopted a single index model within a
global approach to performance analysis. Filip (2014), in turn, tried to
establish whether the returns of Hungarian mutual funds – including equity,
mixed, bond and money market funds – are influenced by survivorship bias.
On the basis of discrete returns and Jensen’s alphas calculated for the 2000-
2012, he noted an insignificant influence of survivorship bias on the returns of
surviving funds. Bóta and Ormos (2013), in turn, analysed a sample of 30
mutual funds invested in Hungary, Central and Eastern Europe or more
developed markets. In order to measure performance, they used the
intercepts from the Carhart four-factor model. The study period from 2001 to
2013 was divided into bearish and bullish periods. They found no significant
excess returns. In the countries where the industry is still emerging and the
number of funds is low, the empirical research in this area is undertaken very
rarely. The performance of Czech mutual funds was analysed by Fajtová
(2004) and Filip (2011). The first of the mentioned studies examined the
performance of 24 closed-end funds from the perspective of market fluctuation
and legislative changes in the 1996-2001 period. By means of rates of returns,
market-adjusted returns and alphas from the one-factor CAPM model, she
found the evidence for informational efficiency in the Czech mutual fund
market. Filip (2011), in turn, tried to evaluate the performance of 14 openended
funds, classified as equity funds, in the 2004-2010 period. By means of
logarithmic rates of return, Jensen alphas and Carhart’s measures, he
obtained slightly abnormal but insignificant returns. He also noted that the
possible outperformance is related to the limited performance persistence in
consecutive periods and to market factors.
Within the financial literature on other post-transition economies, there are
several popular papers. One of them is the study by Podobnik et al. (2007),
who examined the efficiency of fund managers in the South-East European
countries. Following the performance analysis of 14 Croatian, 14 Slovenian
and 9 Bosnian mutual and investment funds using Sharpe ratio, Treynor ratio,
information ratio, appraisal ratio, Jensen’s alpha and Treynor-Mazuy
coefficient, they were able to rank the funds. However, the results did not
23
indicate that the funds possessed market-timing and selection abilities. Jargic
et al. (2007), in turn, evaluated the performance of 9 Slovenian mutual funds.
By means of Sharpe ratio, Treynor ratio, Jensen alpha, appraisal ratio, Beta
coefficient and R2
coefficient estimated for the 2000-2003 period, they found
that the analysed funds outperformed the market because they were well
diversified and possessed efficiency characteristics. Also Markovic-Hribernik
and Vek (2013) conducted the performance analysis for Slovenian mutual
funds for the 2005-2009 period. The study used risk-adjusted measures
(Modigliani-Modigliani ratio, Treynor ratio, Sortino ratio and information ratio)
as well as models for measuring managerial abilities (Jensen’s alpha and
Treynor-Mazuy coefficient) and examined 9 funds with the “energy”
investment policy. The authors, however, did not find stock selection and
market-timing abilities of managers operating mutual funds in Slovenia.
The last of the reviewed studies concerns, among others, a few countries from
the CEE region. On the basis of a vast number of performance measures such
as Sharpe ratio, Treynor ratio, Jensen’s alpha, Modigliani-Modigliani ratio,
Fama-French measure and Carhart’s measure, Lemeshko and Rejnuš (2015)
were able to analyse open-end equity mutual funds on the sample of 27
emerging economies of the world; the time horizon of the study was the 2000-
2014 period. They found that the examined mutual funds, including the ones
from the CEE countries, are usually characterized by constant
underperformance (the observation was made for the bearish as well bullish
periods). The equity funds from the CEE emerging economies turned out to be
among the most sensitive and prompt responding to macroeconomic changes.
Apart form the papers mentioned above, there are scarcely any well-known
papers concerning mutual fund industries in post-transition countries. Future
studies should include longer time spans and use multifaceted approaches or
new measures of returns. However, the financial markets in new European
Union (EU) member states, particularly in the CEE ones, are still perceived as
less efficient. Even though the studies discussed above concluded, in general,
that the analysed funds achieve returns below the benchmark, there is a need
of further investigations in this area.
2 Data and Methodology
The choice of tools for measuring the effects of mutual fund asset
management was made based on the review of empirical literature. The tools
comprise a set of ratios for return appraisal as well as measures of risk levels
in portfolios. Furthermore, Section 3 presents the scope of data and describes
empirical methods used in this study.
2.1 The Scope and Sources of Data
The study analyses open-ended mutual funds operating in the Czech Republic,
Hungary and Poland. The database constructed for the purposes of a broader
project consists of the monthly values of assets under management per unit
share. The measurement of return and risk level were conducted in yearly
periods. The data come from the organizations collecting information about
24
mutual funds in the Czech Republic (AKAT ČR), Hungary (BAMOSZ) and Poland
(Analizy Online). The number of equity funds under study is presented in table
1.
Table 1 The number of equity funds included in the study
Years
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Number
of funds
Czech
Republic
9 18 22 17 15 14 14 18 22 26 26 27 25 25 28 32
Hungary 25 26 32 33 32 32 34 38 47 61 77 93 136 129 132 109
Poland 10 12 13 16 17 20 26 38 58 79 89 107 118 135 143 153
Source: Own compilation
Due to the length limitations of this paper, the performance analysis was done
for the funds that invest their assets in domestic as well as foreign stock
markets. It should be noted that the number of entities in the selected
segment of funds is still relatively low, particularly in the Czech Republic.
Hence, we decided not to divide equity funds into uniform groups. The next
potential bias in the data collection may be the lack of distinction between the
investment strategies (passive or active) adopted by funds. The time horizon
of the study is the 2000-2015 period. Its beginning is related to the fact of
possessing a sufficient amount of data concerning the analyzed industries; its
end is the moment when the database was completed. In order to examine
performance over various market periods, we divided the time horizon into
subperiods referring to smaller stock market cycles.
2.2 Characteristics of Performance Evaluation’s Measures
The measures for performance evaluation of mutual funds include return ratios
and the measures of risk. The measurement employed in this study use the
asset unit values. Due to the shortage of relevant databases in the CEE
countries that would contain information about management fees, for
example, the applied performance calculation totally omits the expense ratio in
fund returns. Hence, all of the measures used are fee-unadjusted. Firstly,
probably one of the simplest ratios is discrete return. It shows the rate of
return on a unit of initial investment and can be expressed with the following
formula:
1,
1,,
,



ti
titi
ti
UP
UPUP
r (1)
where tir, is the discrete return of fund i in period t, tiUP, and 1, tiUP are the
unit prices of fund i at the end (t) and at the beginning (t-1) of the analysed
period.
25
The rate of return calculated this way is then deducted form benchmark
return, which is a stock exchange index. The market-adjusted return allows for
finding the rate of income exceeding the benchmark. The presented measure
of returns is defined as follows (Lee et al., 2008):
tmtiti rrrm ,,,  (2)
where tirm , is the market-adjusted return of fund i in period t; tmr , is the
return on the local equity market benchmark in period t.
The measures mentioned above ignore the differences in the risk level in
funds. These differences are shown by reward-to-volatility ratio in the form of
unsystematic risk (measured by standard deviation). The popular Sharpe’s
measure is calculated as follows (Sharpe, 1966):
)( ,
,,
,
ti
tfti
ti
r
rr
SR


 (3)
where tiSR , is the Sharpe ratio on fund i in period t; tir, is the mean rate of
return achieved over period t by fund i; tfr , is the mean risk-free return over
the analogous period; )( ,tir is the standard deviation of the rate of return on
fund i in period t. The mean rates of return and standard deviation are
calculated on the basis of monthly observations.
The modern portfolio theory uses the CAPM model to estimate the expected
return, which is a linear function of systematic risk and managerial skills. One
of the measures showing abnormal returns is an intercept of regression
models including the achieved returns and market risks. Thus, for each mutual
fund included in the database, we estimated a model from the following
formula (Jensen, 1968):
titftmitfti rrrr   )( ,,., (4)
where i is abnormal return of fund i (the so-called Jensen’s alpha); i is a
systematic risk value of fund i and t means a random error in period t. The
estimations of i coefficient were conducted on the basis of monthly
observations. The list of benchmarks used in the study is presented in table 2.
The data concerning return on investment without risk come from the
International Financial Statistics quarterly reports published by International
Monetary Fund. The values of main local market indices – PX, BUX and WIG –
were taken form Prague Stock Exchange, Budapest Stock Exchange and
Warsaw Stock Exchange respectively.
26
Table 2 The list of benchmarks for estimating the intercepts of CAPM models
Country Benchmark Risk-free rates
Czech Republic PX
Average rate weighted by volume,
on the three-month T-bills sold at auctions
Hungary BUX
Weighted average yield on 90-day T-bills
sold at auctions
Poland WIG
Weighted average yield on 13-week T-bills
sold at auctions
Source: Own compilation
The ratios representing risk level in funds constitute a counterbalance to the
ways of measuring returns. One of the measures most frequently referred to
in the financial literature is standard deviation, also known as the measure of
unsystematic risk. The measure of volatility is calculated on the basis of the
well-known formula (e.g. Isotalo, 2014):
1
)( 2
1
,
,




n
rr
SD
n
i
iti
ti , (5)
where tiSD , means standard deviation of fund i, and n is the number of
included periods. The measure allows for evaluating the historical variability of
investment. It also shows the deviations of fund return from the mean value of
return in a given period.
The performance of funds included in the sample was examined in yearly
perspective. In the case of dispersion analysis, we compared the average
annual returns on individual funds over the total period of their operating.
2.3 Description of Empirical Methods
In order to evaluate the effects of asset management and analyze the
variability of returns, we will use two methodological approaches. Firstly, we
will examine the differences between two populations of means in order to
compare returns of mutual funds with the benchmark. This will be possible by
the application of the Welch’s t-test, according to the following formula
[Welch, 1947]:
m
m
fund
fund
mfund
n
SD
n
SD
rr
t


 (6)
where fundr and mr are means of returns in the samples of funds and
benchmark, respectively, fundSD and mSD are standard deviations of returns
27
also in groups of funds and benchmark, and fundn as well as mn are sizes of
samples.
The t-statistic distribution depends on the mentioned sample size and variance
ratio within the sample. The null hypothesis about mean returns of funds from
the sample equal to the benchmark could be rejected when the absolute value
of the t-statistic, computed on the basis of the sample is higher than the
critical value for the adequate significance level and degrees of freedom
calculated as follows:
)1()1(
)(
2
2
2
2
2





mm
m
fundfund
fund
mfund
nn
SD
nn
SD
SDSD
v (7)
where v stands for the number of degrees of freedom. In other words, the
rejection of the hull hypothesis suggests that the differences between mean
returns in the examined samples are statistically significant in the study
period. The positive values of t-statistic defined by the formula (8) are
favourable to the alternative hypothesis about funds outperforming the
benchmark. However, the negative values mean underperformance. If there
are no grounds to reject the null hypothesis, we may assume that the
differences between the means in the analyzed samples are of random
character [see Schulz, 2003].
The significance level of returns’ variability in individual funds can be examined
using one of the tests for variances. In order to include a higher number of
samples with unequal size (ni>5) in the testing procedure for the analyzed
entities, we will use an amplification for the F-Snedecor test, i.e. the Bartlett’s
test of homogeneity of variances, based on the Chi-square statistic [Bartlett,
1937]:
)
1
)
1
1
((
)1(3
1
1
)ln()1()ln()(
1
1
22
2
kNnk
SnSkN
i
k
i
k
i iip










 (8)
where N means the total size of all samples, k is the number of samples, ni is
the size of the sample i, and
2
iS means variance in the sample i. The above
equation contains also
2
pS , which means the pooled estimate for the variance
and is calculated as:
 


i
iip Sn
kN
S 22
)1(
1
(9)
28
In the Bartlett’s test it is assumed that the samples come from populations
with normal distributions, for which the hypothesis about homogeneity of
variances in all sub-populations (individual funds) is tested. The χ2
-statistic
follows the asymptotic chi-square distribution with k-1 degree of freedom. The
calculated value of χ2
is compared with the critical value from tables of chisquare
distribution at the α level of significance [see Diamond and Jefferies,
2001]. The null hypothesis can be rejected at the minimal probability level of
0.05.
Moreover, in order to present mean returns achieved by individual funds
together with the corresponding risk levels in an illustrative way, we will use a
graphic tool, namely the so-called risk-performance mapping. The expected
return is plotted on the vertical axis and standard deviation, a measure of risk,
on the horizontal one. Finally, the measure of dispersion could be a coefficient
of variation calculated as a ratio of standard deviation to mean return.
3 Results and Discussion
As mentioned before, the study uses the data of Czech, Hungarian and Polish
mutual funds. The results will be presented in the form of average annual
returns generated by the analysed funds over individual periods as well as
sub-periods related to particular cycles in the stock markets. The results of the
dispersion analysis will include the values of yearly return and risk. The
findings will be presented separately for all of the selected CEE markets.
3.1 Czech Mutual Funds
A part of the Czech mutual fund industry is the first market of collective
investment investigated in this paper. The number of equity funds within the
analysed segment at the end of the study period was 32, whereas the total
number of observations is 338. We measured returns using discrete return,
market-adjusted return, Sharpe ratio and Jensen’s alpha. The results are
presented in table 3. Moreover, the values of the Welch’s t-test are included in
the lower part of the table.
The analysis revealed that Czech equity funds were on average able to attain
positive performance in ten out of sixteen yearly periods; however, the funds
from the sample outperformed the benchmark for the segment (see marketadjusted
returns in table 3) only in several periods (2008-2011 and 2013-
2014). These abnormal returns were observed partly in periods following sharp
declines in the local and global securities markets. After including
unsystematic risk in Sharpe ratio calculations the positive values were noted
for similar periods (2009 and 2013-2015). This was also confirmed by the
results for the subperiods referring to market cycles. The two measures
mentioned above produced negative results for the total time horizon. The
fourth measure – Jensen’s alpha1
– brought positive results exactly for the half
1
The results obtained by using Jensen’s alpha should be treated carefully. Out of 338
estimated parameters only 44 (approx. 13%) were statistically significant for Czech
equity funds.
29
of the yearly periods included in the study. The average annual alphas were
slightly positive for the entire time horizon. These overall findings do not
provide strong evidence for confirming the thesis about the existence of
returns exceeding the benchmark. The measurement of risk level, in turn,
done by using standard deviation, produced results showing return volatility
relatively lower than benchmark volatility. The values of standard deviation
were between 0.02 and 0.07 of the interval, and the mean value obtained for
the entire time horizon (0.0404) was the lowest among the three analysed
CEE fund markets; by comparison, the standard deviations for benchmark in
the total period equalled 0.0573.
Table 3 Return and risk evaluation for Czech equity funds in given periods
and the value of t-statistic testing the difference between the returns
of mutual funds and benchmark means in the total period under study
Period r Rm SR Alfa SD
Benchmark*
Return Risk
2000 -0.0561 -0.0332 -0.2729 -0.0087 0.0282 -0.0229 0.1002
2001 -0.1991 -0.0238 -0.1568 -0.0092 0.0552 -0.1753 0.0675
2002 -0.2292 -0.3967 -0.0871 0.1243 0.0562 0.1675 0.0617
2003 0.0973 -0.3334 -0.0512 -0.0022 0.0340 0.4306 0.0421
2004 0.0809 -0.4849 -0.0855 -0.0025 0.0262 0.5658 0.0466
2005 0.1376 -0.2898 -0.1143 0.0021 0.0278 0.4273 0.0455
2006 0.0497 -0.0290 -0.1709 -0.0003 0.0262 0.0787 0.0396
2007 0.0070 -0.1354 -0.1408 -0.0036 0.0331 0.1424 0.0483
2008 -0.4731 0.0540 -0.0940 -0.0135 0.0760 -0.5272 0.0974
2009 0.4184 0.1165 0.0077 0.0191 0.0592 0.3019 0.1151
2010 0.0998 0.0036 -0.0121 0.0033 0.0424 0.0962 0.0557
2011 -0.1560 0.1001 -0.0305 -0.0001 0.0463 -0.2561 0.0494
2012 0.1233 -0.0168 -0.0102 0.0037 0.0326 0.1401 0.0476
2013 0.1179 0.1657 0.0055 0.0115 0.0281 -0.0478 0.0394
2014 0.0589 0.1017 0.0016 0.0058 0.0230 -0.0428 0.0266
2015 -0.0118 -0.0220 0.0013 0.0015 0.0414 0.0102 0.0346
2000-2003 -0.1133 -0.2291 -0.1222 0.0372 0.0439 0.1000 0.0679
2004-2007 0.0644 -0.2254 -0.1295 -0.0012 0.0288 0.3035 0.0450
2008-2011 -0.0114 0.0694 -0.0297 0.0028 0.0555 -0.0963 0.0794
2012-2015 0.0664 0.0533 -0.0003 0.0054 0.0315 0.0149 0.0371
2000-2015 0.0074 -0.0460 -0.0558 0.0097 0.0404 0.0805 0.0573
The value of
the Welch’s
t-statistic
-1.2025
The number
of degree of
freedom
16
The minimal critical
value /t/ to obtain the
significance level of 10%
1.7459
Note: * the benchmark for Czech equity funds was PX index.
Source: Own compilation
The value of t-statistic for the test of equal means in two populations is -
1.2025. It means that Czech mutual funds achieved results lower than the
return from the benchmark. However, the lack of statistical significance
(compare with the 1.7459 critical value) suggests that these findings should
30
be treated with reserve. The study uses a dispersion map for evaluating
performance of the analysed financial intermediaries. Figure 1 presents a
graph in which the y-axis stands for return, and the x-axis represents the
values of standard deviation showing risk levels in the total study period. We
also provided the values of χ2
-statistic (the Bartlett’s test), which are given in
the upper right-hand corner.
Figure 1 Risk-performance mapping for Czech equity funds and the level
of homogeneity of variances
Note: Value of χ2 test= 67.1179; the number of degree of freedom: 37; the critical
value of significance level (α=0.05): 52.1923; the coefficient of variation = 5.49.
Source: Own compilation
In the case of Czech equity funds, some entities generate better raw rates of
return than their competitors; these rates are obtained at a higher risk level
(see figure 1). The reported return dispersion allows for indicating better or
worse managed funds. However, at this point, we should refer back to the
findings presented in table 3, where the average returns differ significantly
from the benchmark (PX). It also has to be noted that the dispersion analysis
concerns the average annual performance of all equity funds regardless of
their market entrance periods. The value of dispersion measure calculated as a
coefficient of variation for Czech equity funds was 5.49 and means high
variability.
By comparing the returns’ variances of individual funds using the Bartlett’s test
it is possible to conclude that the dispersion of returns is significant, and the
null hypothesis about the equality of variances in subpopulations could be
rejected. The value of the calculated statistic (χ2
=67.1179) exceeded the
theoretical value for the assumed significance level. It means that in the case
of Czech mutual funds the variances are heterogeneous. In other words, the
returns are characterized by a different level of variability.
-0,40
-0,30
-0,20
-0,10
0,00
0,10
0,20
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09
Return
Risk
31
3.2 Hungarian Mutual Funds
On the basis of gathered data, we recognized 109 equity funds operated in
Hungary at the end of 2015. Within the entire time horizon of the study, we
registered 1064 observations depending on the return measure used. The
study uses raw return, market-adjusted return, Sharpe ratio and Jensen’s
alpha. The results of return and risk evaluation for Hungarian entities are
shown in table 4.
Table 4 Return and risk evaluation for Hungarian equity funds in given periods
and the value of t-statistic testing the difference between the returns
of mutual funds and benchmark means in the total period under study
Period r Rm SR Alfa SD
Benchmark*
Return Risk
2000 -0.0763 0.0513 -0.5541 -0.0146 0.0353 -0.1276 0.0791
2001 -0.1233 -0.0602 -0.4978 -0.0199 0.0393 -0.0632 0.0592
2002 -0.0530 -0.1640 -0.3319 -0.0124 0.0348 0.1110 0.0715
2003 0.1827 -0.0223 0.1886 0.0072 0.0306 0.2050 0.0600
2004 0.2284 -0.3173 0.1305 0.0125 0.0290 0.5456 0.0260
2005 0.2371 -0.1885 0.3828 0.0134 0.0304 0.4256 0.0819
2006 0.1112 -0.0695 0.0262 0.0063 0.0385 0.1807 0.0542
2007 -0.0350 -0.0786 -0.3680 -0.0085 0.0349 0.0435 0.0519
2008 -0.3394 0.1654 -0.6786 -0.0535 0.0633 -0.5049 0.0845
2009 0.4165 -0.2656 0.2658 0.0325 0.0616 0.6821 0.0935
2010 0.1619 0.1534 0.2253 0.0089 0.0395 0.0085 0.0700
2011 -0.0998 0.1120 -0.2405 -0.0144 0.0636 -0.2118 0.0704
2012 0.0917 0.0131 0.0038 0.0024 0.0393 0.0786 0.0537
2013 -0.0083 -0.0118 -0.0781 -0.0041 0.0378 0.0035 0.0281
2014 0.0747 0.1899 0.1191 0.0018 0.0534 -0.1152 0.0458
2015 -0.0132 -0.4705 -0.0548 0.0018 0.0507 0.4573 0.0584
2000-2003 -0.0067 -0.0540 -0.2689 -0.0090 0.0349 0.0313 0.0675
2004-2007 0.1268 -0.1571 0.0237 0.0052 0.0335 0.2989 0.0535
2008-2011 0.0402 0.0502 -0.0813 -0.0045 0.0571 -0.0065 0.0796
2012-2015 0.0392 -0.0513 0.0004 0.0004 0.0452 0.1060 0.0465
2000-2015 0.0456 -0.0356 -0.0497 -0.0014 0.0464 0.1074 0.0618
Value of the
Welch’s t-
statistic
-0.9902
The number of
degree of freedom
15
The minimal critical
value /t/ to obtain
the significance level
of 10%
1.7530
Note: * the benchmark for Hungarian equity funds was BUX index.
Source: Own compilation
As we can see, the rates of return on investment in Hungarian equity funds
were positive in several periods, depending on the market situation. However,
it should be noted that just as in the case of Czech funds, returns
outperformed the benchmark only in six out of sixteen yearly periods. This was
shown particularly well by market-adjusted return and refers to the years
2000, 2008, 2010-2012 and 2014 and to the subperiods representing market
cycles. The two remaining performance measures revealed a relatively strong
32
dynamics of market trend related changes in several yearly periods. Fund
returns as opposed to equity index experienced lower ups and downs,
particularly during drastic market changes. The Sharpe ratio for the average
annual return within the entire period under study was generally negative. The
values of Jensen’s alphas2
were positive in nine out of sixteen yearly periods.
However, the alphas for the entire time horizon were below 0. The final
findings seem to support the hypothesis concerning the lack of ability to
achieve abnormal returns. Moreover, the risk level analysis for the discussed
funds done by using standard deviation, showed that the average volatility of
fund returns was higher only in three yearly periods (2004 and 2013-2014).
Hence, the findings are related with the fact that the portfolios of equity funds,
being less diversified than stock index, are characterized by lower variability.
The calculated value of t-statistic is lower than the critical value at the minimal
level of significance. Hence, there is a lack of evidence to reject the null
hypothesis about the equality of funds’ returns and benchmark means. The
negative value of the Welch’s t-test corresponds well with the results from
table 4 for Hungarian mutual funds, which suggest that funds’ returns
underperform the benchmark.
The study uses a graphic tool for performance evaluation, which is namely a
return-risk map. Figure 2 presents the average annual rates of return and the
values of standard deviation for individual Hungarian equity funds in the total
study period. This part also presents the findings concerning the level of
variances homogeneity.
Figure 2 Risk-performance mapping for Hungarian equity funds and the level
of homogeneity of variances
Note: Value of χ2 test= 209.2638; the number of degree of freedom: 145; the critical
value of significance level (α=0.05): 174.101; the coefficient of variation = 1.02.
Source: Own compilation
2
The values of Jensen’s alphas should be treated with reserve. Out of 1064 estimated
parameters only 153 (approx. 14%) were statistically significant for Hungarian equity
funds.
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18
Return
Risk
33
The average annual performance of individual Hungarian equity funds, both in
terms of return and risk, is presented in figure 2. The results of the analysis
show that a small group of funds received higher returns at a relatively limited
risk. As mentioned before, the average annual returns were much lower than
the returns from the benchmark (BUX). The position of outliers with discrete
returns near 0.2 and/or with the risk level above 0.15 results from comparing
the average performance of the entities that have different longevity periods.
Accordingly, the results should be treated with reserve. The coefficient of
variation for Hungarian equity funds returns equals 1.02 and indicates a rather
high variability.
The values of χ2
-statistic form the Bartlett’s test provided arguments for
rejecting the hypothesis about variances equality. This indicates that in
relation to Hungarian funds the return dispersion is significant, which means
that there is relatively large heterogeneity of variances.
3.3 Polish Mutual Funds
The constructed database enabled us to obtain information about equity funds
operated in Poland. At the end of the period under study, there had been 153
entities in the market; the total number of observations amounted to
maximum 1033 within the entire time horizon. Table 5 presents the average
annual values of the measures of return and risk.
As can be seen in table 5, we measured the effectiveness of asset
management by using classic raw returns, market-adjusted returns, Sharpe
ratio and Jensen’s alpha. The performance of Polish mutual funds was positive
in the majority of periods. In order to compare the results with the stock
index, we used the second of the performance measures. Three out of six
yearly periods, in which the analysed entities outperformed the benchmark
(WIG), overlapped with upward tendencies in the equity market (2007 and
2013-2014). However, while evaluating performance over consecutive market
cycles, we noted that the obtained results always failed to beat the
benchmark. The sign preceding the yearly values of Sharpe ratios suggests
that after including the differences in risk level, the returns of Polish funds
were characterized by a relatively high volatility. However, the mean value of
the risk-adjusted returns was negative in the entire time horizon. The values
of Jensen’s alphas3
, in turn, were slightly positive in ten out of sixteen yearly
periods. The findings concerning the average income generated by Polish
funds are in line with the efficient market hypothesis. The measurement risk
produced results concerning the volatility of funds’ returns. The average
annual value of standard deviation, which equals 0.0427 seems to be relatively
low, particularly when the average risk form the benchmark is higher.
However, the level of unsystematic risk in the analysed sample was generally
3
The findings obtained by means of Jensen’s alphas should be treated carefully. Out of
1033 estimated parameters only 263 (approx. 25%) were statistically significant for
Polish equity funds.
34
the highest in the periods of sharp decline and strong growth in the local
equity market.
The test for differences between the means indicated that the funds’ returns
are lower than the potential income from the benchmark (the value of the tstatistic
was -0.8004). Nevertheless, these results were statistically
insignificant.
Table 5 Return and risk evaluation for Polish equity funds in given periods
and the value of t-statistic testing the difference between the returns
of mutual funds and benchmark means in the total period under study
Period r Rm SR Alfa SD
Benchmark*
Return Risk
2000 0.1165 0.1295 -0.0866 0.0085 0.0607 -0.0131 0.0641
2001 -0.1430 0.0770 -0.4393 0.0008 0.0530 -0.2199 0.0712
2002 -0.0040 -0.0360 -0.1460 -0.0036 0.0475 0.0319 0.0708
2003 0.3661 -0.0831 0.3944 0.0038 0.0538 0.4492 0.0771
2004 0.2142 -0.0652 0.4924 0.0013 0.0242 0.2794 0.0264
2005 0.2168 -0.1198 0.2882 -0.0050 0.0372 0.3366 0.0506
2006 0.4146 -0.0014 0.4917 0.0051 0.0469 0.4160 0.0598
2007 0.1049 0.0011 0.0677 0.0019 0.0508 0.1039 0.0600
2008 -0.5092 0.0015 -0.9072 -0.0090 0.0654 -0.5107 0.0750
2009 0.4447 -0.0238 0.4124 0.0036 0.0632 0.4685 0.0897
2010 0.1670 -0.0207 0.2584 0.0023 0.0388 0.1877 0.0470
2011 -0.2120 -0.0036 -0.5090 -0.0083 0.0467 -0.2083 0.0488
2012 0.1474 -0.1150 0.1828 -0.0027 0.0379 0.2624 0.0436
2013 0.1010 0.0204 0.1539 0.0006 0.0397 0.0806 0.0458
2014 0.0039 0.0014 -0.0417 -0.0013 0.0298 0.0026 0.0316
2015 -0.0318 0.0639 -0.1290 0.0028 0.0351 -0.0962 0.0272
2000-2003 0.1030 -0.0132 -0.0338 0.0011 0.0533 0.0620 0.0708
2004-2007 0.2252 -0.0346 0.2920 0.0012 0.0435 0.2840 0.0492
2008-2011 -0.0067 -0.0121 -0.1547 -0.0028 0.0522 -0.0157 0.0651
2012-2015 0.0485 -0.0016 0.0300 0.0000 0.0354 0.0623 0.0371
2000-2015 0.0507 -0.0077 -0.0070 -0.0007 0.0427 0.0981 0.0556
Value of the
Welch’s t-
statistic
-
0.8004
The number of
degree of
freedom
15
The minimal critical
value /t/ to obtain
the significance
level of 10%
1.7530
Notes: * the benchmark for Polish equity funds was WIG index.
Source: Own compilation
As mentioned before, the dispersion analysis used the risk-return mapping.
Figure 3 presents the average yearly rates of return and the values of
standard deviations for individual funds in the total study period. Moreover,
the paper presents the results from homogeneity of variances testing.
35
The dispersion analysis presented in figure 3 seems to be relatively schematic.
Most of the entities achieved slightly positive discrete returns at the average
level of risk. Some funds have a marginally higher average performance than
their competitors. However, as mentioned before, it was hard to obtain returns
exceeding the benchmark, particularly over longer periods of time, which
supports the hypothesis about the unachievable abnormal returns. The value
of variation coefficient for Polish equity funds was 0.84 and indicates a
moderate dispersion.
Figure 3 Risk-performance mapping for Polish equity funds and the level
of homogeneity of variances
Note: Value of χ2 test= 180.3188; the number of degree of freedom: 142; the critical
value of significance level (α=0.05): 170.809; the coefficient of variation = 0.84.
Source: own compilation.
The variance homogeneity analysis, conducted in accordance with the
approach proposed by Bartlett, provided arguments to reject the null
hypothesis about the lack of differences in variations for individual funds. The
value of χ2
-statistic marginally exceeded the critical value for the assumed
level of significance. Hence, it could be concluded that the returns achieved by
Polish funds are characterised by different variability in the total period under
study.
Conclusions
The financial markets in new EU member states, such as the CEE ones, might
be perceived as less efficient. Accordingly, the conclusions concerning the
more developed markets, indicating that mutual funds are unable to
outperform, may have no application to the emerging markets. These
cognitive and practical aspects of analysing the performance of collective
investment companies are the reason for addressing the issue discussed in the
present paper.
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1
Return
Risk
36
The aim of the study was to evaluate mutual fund performance on the basis of
returns and risk levels. To this end, we used the following selected measures
of return mentioned in the reviewed empirical literature: discrete return,
market-adjusted return, Sharpe ratio and Jensen’s alpha. The measurement of
risk, in turn, was done by using the values of standard deviation. Moreover,
we employed a graphic method, the so-called risk-return map, for presenting
return collated with risk levels, and decided to use statistical hypothesis
testing to examine the homogeneity of their variability.
The study sample comprised 294 equity funds (domestic and foreign ones)
operated in the Czech Republic (32 entities), Hungary (109 entities) and
Poland (153 entities). The time horizon was the 2000-2015 period, with
market cycles distinguished in given years. Having analysed the collected data,
we noted that mutual funds were unable to outperform their benchmarks in
terms of average return. However, the tests provided statistically insignificant
evidence for rejecting the hypothesis about equality of return means in mutual
funds and applied benchmarks. Furthermore, the level of risk in funds,
calculated as volatility of returns, was lower than the mean value of
benchmark’s standard deviation. The study has also shown that the variability
of mean risk-adjusted return depends on the short term market situation.
Moreover, we noted that the average annual investment results of funds in the
Czech Republic, Hungary as well as Poland in the short periods of upward
tendencies in equity markets were, in general, worse than the returns
achieved form PX, BUX and WIG index respectively. As for the periods of
downward trends in the local securities markets, the funds operated in less
liquid markets did not lose as much as the mentioned indices.
The dispersion analysis indicates the existence of individual entities which
received higher returns than their competitors at a relatively low level of risk.
However, the mentioned results were unable to outperform benchmarks. The
assumption about the variance homogeneity of mutual funds was rejected on
the basis of tests. The diversity of return variances observed in the case of
Czech, Hungarian as well as Polish funds could be due to the fact that
domestic and foreign mutual funds were analysed jointly and in the analysed
samples of funds there was no distinction between various investment
strategies (passive or active). The article is an introduction to the evaluation of
mutual funds’ effectiveness and provides the basis for further studies and
analyses in this area.
Acknowledgements
The paper was written with financial support from the National Science Centre,
Poland (Narodowe Centrum Nauki) - Decision no. DEC-2014/15/D/HS4/01227.
Project: “Determinants of Mutual Fund Performance: Managerial characteristics
and fund attributes”.
37
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