The Long-Run Performance of German Stock Mutual Funds

The Long-Run Performance of German Stock Mutual Funds
Richard Stehle / Olaf Grewe
Draft: May 15, 2001
Humboldt-Universität zu Berlin
Wirtschaftswissenschaftliche Fakultät
Institut für Bank-, Börsen- und Versicherungswesen
Spandauer Strasse 1
D - 10178 Berlin
Phone +49 30 2093-5761
Fax
+49 30 2093-5666
e-mail [email protected]
[email protected]
We thank Anja Ibisch for excellent research assistance and many helpful comments. We have
benefited from discussion with Stefan Mayer and other participants of the 7th Annual Meeting
of the German Finance Association, Konstanz, October 2000. The financial support of the
Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 373, Teilprojekt C1) is gratefully acknowledged.
The Long-Run Performance of German Stock Mutual Funds
Abstract
We examine the risk-adjusted performance of open-end mutual funds which invest mainly in
German stocks. After briefly discussing the institutional environment in which these funds
operate, we focus on the benchmark problem and the risk adjustment problem. Our data set
includes all German funds sold to the public in 1972, our performance analysis covers the time
period 1973 to 1998.
In our empirical analysis, we first look at the rates of return of individual funds and at the
unweighted average rates of return of all funds in our sample. When we apply the Sharpe and
Jensen measure to the latter time series in the traditional way, the funds underperform the
appropriate benchmarks by approximately 1.5 % per year, which is significant both from the
statistical and the economic perspective. Applying the Sharpe and the Jensen measure in the
traditional way creates a bias from the perspective of long-term investors, because the analysis is based on the arithmetic, not the geometric mean return. To avoid this bias we look, in a
second step, at the returns of investors who risk adjust their fund investments ex-ante by borrowing or lending with the objective, that the future risk of his levered portfolio matches that of
the chosen benchmark. When we again apply the Sharpe and the Jensen measure to the
unweighted average rates of return, the underperformance is reduced by 40 %. For large
funds, on the average, the underperformance is less than for small funds. When we look at the
value-weighted means of individual fund returns, the underperformance nearly disappears.
The Long-Run Performance of German Stock Mutual Funds
1. Introduction
Starting with the landmark studies of Sharpe (1966) and Jensen (1968), a large number of
studies found that US stock mutual funds – when risk is properly taken into account – underperform the market. The results of studies on funds concentrating on German stocks are less
clear-cut. Kaserer/Pfau (1993) and Scherer (1994) find that these funds underperform the market. Steiner/Wittrock (1994) and Reichling/Trautmann (1997) get a positive average performance for one index, a negative for another. Several of them suffer from a serious benchmark
problem. Their data on mutual funds reflects the total after-tax return of a German investor with
a marginal income tax rate of 0%, while the indices they use as benchmarks reflect a marginal
income tax rate of 36%. Some studies use indices that do not take dividends into account.
After briefly discussing the institutional environment in which these funds operate, we focus on
the benchmark problem and the risk adjustment problem. Our data set includes all 18 German
stock mutual funds concentrating on German stocks sold to the public in 1972, our analysis
covers the years 1973 to 1998. There is no survivorship problem, the 18 funds all still exist
today.
Using proper benchmarks, tax-adjusted versions of the DAX and the DAX100, we find that with
one exception all included funds underperform both benchmarks, when we use the performance measures suggested by Sharpe (1966) and Jensen (1968) in the traditional way. The
time-series of the unweighted averages of the individual fund returns underperforms the
benchmarks by approximately 1.5% per year according to these measures. For most financially educated long-term investors such an underperformance would hardly be tolerable1.
From the perspective of long-term investors, these measures are biased against the funds,
however, because they are explicitly or implicitly based on the arithmetic means of the underlying returns. A better measure of the long-run return of an investment is the geometric mean
return. Because the difference between the arithmetic and the geometric mean depends on
the standard deviation of the underlying return series, this difference is considerably larger for
the benchmarks than for all included funds.
In a second step of our analysis, in order to avoid the bias associated with the arithmetic mean,
we look at the returns of investors who risk adjust their fund investments ex-ante by borrowing
or lending with the objective, that the future risk of the levered portfolio matches that of the
chosen benchmark. When we apply the traditional measures of fund performance to the timeseries of the risk adjusted returns of the individual funds and to the unweighted average fund
returns, the underperformance is reduced by 40 %.
1
Gruber (1996) discusses the puzzle that in the US fund growth has been tremendous and persistent despite the well documented underperformance in this market.
For large funds, on the average, the underperformance is less than for small funds. Therefore,
in addition to looking at the unweighted means of individual fund returns, we also look at their
value-weighted means, using assets under management as weights, with the result, that the
underperformance nearly disappears. The volume-weighted mean of the returns of the individual funds in a given month or year is identical to the return mutual fund investors have
achieved in the aggregate. The result, that the aggregate returns for all mutual fund investors,
when properly risk-adjusted, nearly matches that of a direct investment in the stock market is
of crucial importance for evaluations of the mutual fund industry as a whole.
In section 2 the institutional environment in which German funds operate is discussed. Section
3 contains the sample description, summary statistics on the included funds, and a discussion
of the benchmark indices. In section 4 we outline the risk adjustment procedure and present
the results for the individual funds and for the aggregate returns. Section 5 contains a summary of the main results.
2. The German Mutual Fund Market
At the end of 1997 68 German firms based in Germany offered shares of 1343 open-end
mutual funds to the public. In addition to these ”Publikumsfonds” the firms (”Kapitalanlagegesellschaften” or ”Fondsgesellschaften”) offered 4208 Spezialfonds to institutional investors.
Typically the Fondsgesellschaften manage and market the Publikumsfonds themselves, but
there are many cases in which others do the management or the marketing.
The oldest of these firms, ”Allgemeine Deutsche Investment GmbH (ADIG)” was founded in
1949, its first two funds were started in 1949. Figure 1 shows total assets under management
(in the bottom two lines, nominal and real in prices of 2000) and the market shares of the different categories of German Publikumsfonds. Nominally an equivalent of 5 billion Euro were
invested at the end of 1970 in Publikumsfonds managed by German Fondsgesellschaften
which corresponds to approximately 13 billion Euro based on the level of consumer prices at
the end of 2000. At the end of 2000 298 billion Euro were invested in these funds, thus their
real growth rate between 1960 and 2000 was 11% per year.
Until 1960 stock funds dominated the market. At the beginning of the sixties real estate funds
and bond funds came into existence which became very popular in the seventies and eighties.
Money market funds came into existence at the beginning of the nineties, ”Altersvorsorgefonds” in 1998. Literally translated ”Altersvorsorge” is making financial provisions for old age.
These funds may hold both stocks and real estate. In 1990 stock funds were at an all-time low
with respect to their market share but started a dramatic come-back. At the end of 2000 54% of
the amount invested in German Publikumsfonds were in stock funds (see figure 1).
Of the 68 German Fondsgesellschaften based in Germany 64 are members of the Bundesverband Deutscher Investmentfonds (BVI), which promotes their interest in many ways. Until
recently most of the data on German mutual funds was collected and supplied by the BVI.
Their data generally only includes funds managed by member firms.
Starting around 1987 most German Fondsgesellschaften started subsidiaries in Luxembourg.
Without any doubt a number of good reasons exists for basing these subsidiaries in Luxembourg. However, many market observers believe that tax evasion by German investors was an
important motive. Figure 2 shows that at the end of 2000 nearly 1/3 of the capital managed
directly or indirectly by German Fondsgesellschaften was legally based in Luxembourg.
In spite of the more than twentyfold increase of the total volume invested in German mutual
funds from 1970 to 2000, the Fondsgesellschaften control only a small portion of the money
managed by German financial institutions on behalf of their clients.
Major competitors are life insurance companies (major product: life insurance contracts), home
loan banks (home savings contracts), commercial banks, savings and loan banks, and credit
unions (the latter three offer savings and term accounts). While the market share of savings
accounts and term accounts at commercial banks, savings and loan banks, and credit unions
decreased continually since 1970, 33.1% of the 1685 billion Euro managed by financial institutions on behalf of their clients is still deposited in these accounts at the end of 2000 (see figure
2). Not included in this figure are all direct investments by German investors, that is direct
investments in securities2 or real estate.
Initially all Fondsgesellschaften were owned by banks. Some of them are fully controlled by a
single bank or a single banking group. Examples are DIT Deutscher Investment-Trust which is
owned by Dresdner Bank and DWS Deutsche Gesellschaft für Wertpapiersparen which is a
subsidiary of Deutsche Bank AG. DEKA Deutsche Kapitalanlagegesellschaft belongs to the
savings and loan banking group, Union Investment to the credit union group. Some have more
than one owner. Besides banks, insurance companies are often owners today.
Shares of mutual funds traditionally were sold by the banks that owned the funds or by independent sales organizations. Normally the shares are kept in the custody of the bank that sold
them or in the custody of the Fondsgesellschaft.
The German mutual fund industry is highly regulated. German Fondsgesellschaften must
observe the ”Gesetz über Kapitalanlagegesellschaften” (KAGG),3 and the ”Kreditwesengesetz”, their non-German counterparts doing business in Germany the ”Auslandsinvestmentgesetz”. Also the EC UCITS Directive of 1985 must be observed. Important general
regulations are:
-
Stock or bond Publikumsfonds must be open-end4, that is, the funds shares can be
redeemed at all times at net asset value.
2
3
That is investment in exchange-listed stocks and bonds, shares of partnerships, unlisted securities.
The KAGG exists since 1970. Recently it was amended by the 3. Finanzmarkt-Förderungsgesetz
of April 1, 1998.
-
Money market funds officially exist since 1995.
-
Fondsgesellschaften must be organized as separate entities and have the legal form of
Gesellschaft mit beschränkter Haftung (GmbH) or Aktiengesellschaft (AG).
-
German Fondsgesellschaften are supervised by the Bundesaufsichtsamt für das Kreditwesen
-
Money resulting from the sale of mutual fund shares, and the securities held by a mutual
fund must be kept in a custodian account at a regular bank (‚Depotbank‘), which must be
legally independent from the mutual fund. The Depotbank also determines the net asset
value and acts as a supervisor of the Fondsgesellschaft in many ways.
Also law restricts the investment behavior of mutual funds. Important portfolio restrictions are:
-
In principle, only securities traded in organized markets may be included in the portfolios of
Publikumsfonds, other securities may have a maximum share of 10% of the portfolio (§ 8,1
and 8,2 KAGG)
-
Bank deposits and money market securities may be included up to 49% of the portfolio (§
8,3 KAGG)
-
In principle, securities of one issuer may only make up 5% of the portfolio. In case of
exceptions the upper limit is 10% and the total value of all exceptions must not exceed
40% of the portfolio‘s value. Securities issued by members of an economic entity that
legally is a ”Konzern” are treated as securities issued by the same issuer (§ 8a,1 KAAG)
-
All mutual funds managed by a specific Fondsgesellschaft may only control 10% of the
votes in the stockholder’s meeting (§ 8a,3 KAAG)
-
Precious metals or securities based on precious metals may not be included in the portfolios (§ 8,4 KAAG)
-
Under certain conditions up to 5% of the portfolio may be invested in other mutual fund
portfolios (§ 8b,1 KAGG)
-
Futures and options may only be included if the underlying securities are in the portfolio (§
8f,1 KAAG)
-
Only 10% of the portfolio may be financed by debt and this may only be done for the shortterm (§9,4 KAAG).
3. Description of the Initial Sample, Rates of Return, Benchmark Indices
The BVI, in its statistics, distinguishes between stock funds, bond funds, mixed funds, money
4
A small number of exchange-listed companies concentrate their activities on investing in stocks.
To some extent, these companies resemble closed-end mutual funds. Closed-end real estate
funds are permitted and were very popular in the past 20 years.
market funds, and real estate funds. While bonds funds, by their charter, are often not allowed
to invest in stocks, funds labeled stock funds by the BVI typically may and often do hold bonds.
At the end of 1960 19 stock funds existed, 1970: 42, 1980: 71, 1990: 165, 1997: 415 and 2000:
449. Of the 449 (415) stock funds that existed at the end of 2000 (1997), 88 (112) concentrate
on German stocks, 89 (83) have an international portfolio, 112 (57) focus on European stocks,
17 (25) on North- and South-American stocks, 24 (40) on stocks from the Far-East, 37 (68)
only invest in a more specific region or in a specific country, 65 (30) only include stocks from a
specific industry in their portfolio, and 17 invest according to the market capitalization of stocks
or have a variable investment objective.
We have price and dividend data starting in 1971. In our empirical analysis we concentrate on
those mutual funds which predominantly invest in German stocks. Unfortunately the official
descriptions of the investment policies are vague and the actual investment policies change
over time. Appendix A contains a summary of the official investment policies. We include in
our sample those funds that were officially labeled "stock fund with a concentration on Germany" in January 1972 as well as other funds that existed at that time which had more than 50
% of their assets invested in German stocks. All of the 18 funds in our sample were offered by
BVI member firms.
While the issue of survivorship bias has found extensive coverage in the literature investigating
the US mutual fund industry (e.g. Carhart (1997)), this bias is of minor importance for the German market. The 18 stock mutual funds in our initial sample all still exist. In a separate paper
we will look at a larger sample of 50 funds for the time period 1994 to 1998. Of the 50 funds
included in the larger sample only two ceased to exist (DWS Bayern and Bethmann Univ. Taunus). For two more funds the Kapitalanlagegesellschaft changed (Progress-Universal and Privatfonds).
Figure 3 shows for some of the included funds the portfolio compositions at the end of their fiscal years for the four asset categories German stocks, foreign stocks, bonds, and ”other”. The
latter category includes short-term bank deposits. The graph shows that the asset mix of some
funds changes drastically over time. DIT-Fonds für Vermögensbildung (DIT), for example, was
nearly fully invested in German stocks at the end of 1975 and after 1988. At the end of 1982,
on the other hand, DIT had invested more than 80 % in bonds and only 10 % in German
stocks. While the DIT fund’s behaviour was extreme, most funds increased their stock investment during the last 30 years, for example MK Alfakapital. Several funds permanently were
nearly fully invested in German stocks, for example Unifonds. Several maintain a relative constant mix of stocks and bonds through time, for example Fondra, several others include bonds
or foreign stocks from time to time.
In 1972, the 18 funds in our initial sample together had close to 5 billion marks assets under
management, at the end of 1997 close to 29. Figure 4 shows total assets under management
for the individual years and the fractions managed by the individual funds. The eight largest
funds in 1972 - Concentra, Investa, Unifonds, Deka-Fonds, Fondak, Adifonds, Fondra, and
Adiverba together controlled more than 95 % of total assets under management at the end of
the year. At the end of 1997 the eight largest funds in our sample had close to 70 % of the total
assets managed by our sample firms. At the end of that year several funds that have started
after January 1972 (and therefore are not included in our sample) belonged to the group of the
10 largest funds concentrating on German stocks, for example FT Frankfurt-Effekten-Fonds,
DWS Deutschland, BfG Invest Aktienfonds, Provesta, ADIG-Aktien-Deutschland. The 18 fund
in our sample, at the end of 1997, controlled 58.8 % of the total assets under management by
all 112 funds concentrating on German stocks.
Of the 18 funds in our sample Deka-Fonds could increase its market share most between 1972
and 1998, Fondra suffered the largest loss in market share. By 1998 three more large funds
existed in our sample, DIT, Thesaurus, and Ring-Aktienfonds DWS. Five of the included funds
were extremely small throughout our observation period: HANSAsecur, HWG-Fonds, MAIN IUNIVERSAL-FONDS, Oppenheim Privat, and Privatfonds.
Most funds pay dividends annually, a few retain dividends fully. Thesaurus (managed by DIT)
is an important member of the latter group. In both groups shareholders obtain immediately or
at the time when their income tax obligation is settled – this may be several months or even
years later – a cash or quasi-cash payment (Körperschaftsteuergutschrift) which results from
the fact that the corporate income tax on dividends is taken into account in the calculation of
the personal income tax. From 1977 to 1995 this additional payment was in general 56.25% of
the cash dividend.
Starting point of our calculations are monthly rates of return supplied by the BVI.5 These
returns are based on net asset values per share and include dividends and the Körperschaftsteuergutschrift mutual fund shareholders receive. Like most recent studies on the US market,
for example Gruber (1996), Carhart (1997) and Wermers (2000), we use - in Fama's (1976,
page 20) terminology - simple returns, not continuously compounded returns. Looking at continuously compounded returns (that is, at ln(1 + return)) may offer certain advantages when we
analyse individual stocks or individual mutual funds. When we want to average across funds,
the use of logarithmic returns creates problems, since the arithmetic mean of logarithmic
returns corresponds to the geometric mean of the corresponding raw returns. In particular,
averaging logarithms across firms is not compatible with any economically intuitive investment
strategy.
In figure 5 the monthly rates of return of the 18 funds are plotted and compared to the rate of
change of the DAX. The DAX contains, roughly speaking, the 30 largest German stocks. Its
rate of change reflects the rate of return on a value-weighted portfolio of the included stocks.
The figure shows the tendency that the DAX had the highest return in upward markets and the
5
Additional data was supplied by Finanz-Computer-Service (FCS). We thank the BVI and Dieter
Reitz from FCS for supplying the data and for explaining many peculiarities of the mutual fund
industry to us.
lowest in downward markets, a phenomenon already observed by Poschadl (1981, p. 200) and
Lerbinger (1984, p. 69). There was one month with an upward movement of the index higher
than 15 % (July 1997). Only three (out of 18) funds beat the index in this month and only by a
small amount. There were three months with a market decline larger than 15%: October 1987,
September 1990, and August 1998. In these months the index performed worse than most
mutual funds. The graph also shows that monthly rates of return on mutual funds have a small
negative skewness.
Table 1 contains summary statistics for the monthly rates of return on the 18 stock mutual
funds included in our initial sample. It confirms the visual impressions based on figure 5. All
funds have a standard deviation of the monthly rates of return (see column Sigma) that is
smaller than that of the four DAX benchmarks that will be discussed in greater detail below.
The skewness of monthly rates of return is negative for all funds. For all funds the kurtosis which mesures the thickness of the tails - is significantly higher than 3, the population value for
the normal distribution. The summary statistics presented in table 1 are all based on the total
time series of the monthly rate of return observations per fund.
Since we have seen in figure 3 that the asset mix for some funds changes drastically over
time, it is unlikely that the underlying probability distributions are constant over time. Included
in figure 3 is also a rolling estimate of the ratio of the standard deviation of the rates of return of
the DAX and of the specific fund. The ratio is calculated for each year-end and based on the
24 recent observations. Figure 6 shows these ratios for all funds except the DIT fund which
already is included in figure 3. For this fund the ratio is exceptionally high in 1984. The magnitude of this ratio allows a few interesting insights into fund behaviour over time:
a) On the average, the ratios decline over time. Before 1986 only one fund temporarily has a
ratio below 1.0, from 1996 to 1998 the ratio is below 1.0 for several funds. A possible reason for the decline of the ratio in the nineties is, that the DAX has become the most important benchmark for these funds. An important strategy to avoid an underperformance with
respect to the index is its full replication.
b) Several times a number of funds show a similar development of the ratio.
c) Until the middle of the nineties, the ratio is considerably higher than 1.0 for most funds,
that is, the standard deviation of the rate of return on the DAX portfolio is considerably
higher than that of the funds. A major reason for this is the fact, that the funds are not fully
invested in stocks but also hold bonds and bank deposits. Traditionally, an important reason for holding bank deposits was the requirement to redeem shares at all times at net
asset volume. But the ratio is also often larger than unity when the funds are nearly fully
invested in German stocks. Major reasons for this are probably
-
that the funds normally may only allocate 5 % of the market value of their portfolio to
an individual security, while normally several stocks included in the DAX have a higher
weight,
-
that funds invested more in small DAX stocks than the amount implied by the DAX
weight and also invest in non DAX stocks and foreign stocks to some extend.
In the remaining parts of the paper we will concentrate on annual rates of return because
investors in mutual funds typically have a long-term investment horizon. In the calculation of
annual rates of return it is implicitly assumed that dividends and the Körperschaftsteuergutschrift are fully reinvested in fund shares at the end of the month in which dividends are paid.6
Figure 7 shows the annual returns of the included 18 funds and compares these returns with
the rate of return of the DAX portfolio. With annual returns the tendency that the DAX has the
highest return in upward markets and the lowest return in downward markets is even stronger
than with monthly returns.
In the process of the calculation of the net asset values all costs borne by the funds are
included, especially the administrative expenses the Fondsgesellschaft receives from the
fund's cash flow (usually between .5 and 1.2 % per year of the asset value), custodian costs
payable to the custodian bank (usually between 0.02 to .1% per year) and transaction costs
resulting from portfolio restructurings. The latter costs are not documented by the funds, they
are implicitely included in the transaction prices.
Costs borne by the mutual fund shareholders are load fees (officially 5 to 7.5 % for the funds in
our sample) at the time of purchase, and an annual account fee which is payable by the shareholder to the bank where he keeps his fund certificates. Appendix B contains more detailed
information about these costs. The costs payable by the shareholders are not included in the
rate of return calculation.
Table 2 contains summary statistics for the annual rates of return of the individual funds
included in our initial sample. The table is basically an extension of similar tables by Steiner/
Wittrock (1994), Wittrock/Steiner (1995) and Reichling/Trautmann (1997).7 Column ’Mean a’
shows the arithmetic means
1 T
a
r i = --- ∑
r
T t = 1 it
6
To transform monthly into annual rates of return, we use the formula 1 + rit =
(3.1)
∏j = 1 ( 1 + ritj )
12
where r it is the rate of return on fund i in year t and r itj is the rate of return of fund i in year t and
7
month j
Scherer (1993) and Scherer (1994) include similar tables (on page 24 and 195, respectively). In
these tables the identity of the funds is disguised to some extent. Minor differences between these
studies are that some use logarithmic returns instead of raw returns (that is ln ( 1 + r it ) instead of
r it ), some look at annualized returns (monthly returns x 12) instead of exact annual returns, some
at annualized logarithmic returns.
of the annual returns, column ’Sigma’ the standard deviation
1 - T
a 2
----------r
(
–
r
)
T – 1 ∑t = 1 it i
σi =
(3.2)
of the 26 annual returns for each fund around their means.
Column ’Mean g’ shows the geometric means
g
1 + ri =
T
∏t = 1
( 1 + r it )
1⁄T
(3.3)
of the annual returns.
All columns are in %. The table demonstrates that the performance of the individual funds over
26 years from January 1973 to December 1998, differs considerably. Investa, the fund with the
best ”raw” performance, has an arithmetic mean of the annual rates of return of 13.7%, the
worst performer has 6.7%. The other funds have mean annual returns between 9.4 and
13.1%. The table also shows that the standard deviations of the funds differ considerably. The
highest standard deviation is 22.9%, the lowest 14.3%. The four DAX time series have considerably higher standard deviations, 24.4 to 26.2 %.
The arithmetic mean of the annual rates of return and their standard deviation are important
numbers for investors with an investment horizon of one year. If the rates of return are serially
uncorrelated and their probability distributions are stable over time, the historic arithmetic
mean return is the best predictor for the future one-year returns. The geometric mean, on the
other hand, is an important number for a long-term investor, in our case for an investor with an
investment horizon of 26 years. The difference between the arithmetic mean and the geometric mean depends on the autocorrelation and the standard deviation of the process generating
the rates of return. The difference between the means is highest for Deka-Fonds (2.1 percentage points), the fund with the highest standard deviation, it is lowest for Fondra, the fund with
the lowest standard deviation (0.9 percentage points).
While the one-dimensional fund rankings based on arithmetic mean and geometric mean are
similar, important differences exist. Deka-Fonds ”beats” Plusfonds according to the arithmetic
mean, according to the geometric mean it is the other way around. According to the geometric
mean return HWG-Fonds ranks 11th, according to the geometric mean 15th.
All funds have annual rates of return that exhibit a small positive skewness, which is the rule
for annual returns on stock portfolios. We have already noted that monthly fund returns exhibit
a negative skewness, which is also the rule for monthly returns on stock portfolios.8 The kurtosis of all funds is very close to 3, that is, the thickness of the tails is very close to the normal
distribution.
8
As a consequence annualized rates of return (monthly rates of return x 12) also exhibit negative
skewness.
The column Size ’98 in table 2 shows that enormous differences exist with respect to fund size.
The largest stock mutual fund with a concentration on Germany at the end of 1998 was
DekaFonds, whose assets under management on December 31, 1998, was 7.6 billion marks.
Privatfonds, on the other hand, only had a volume of 8.4 million marks. There is a clear tendency, that the large funds have higher average returns.
In addition to looking at the summary statistics of the time series of the unweighted arithmetic
means of the annual fund return9, we also include summary statistics for weighted average of
these returns, in which the assets under management at the beginning of each year,
expressed as a fraction of total assets under management by the included funds, are used as
weights. Note however that the arithmetic mean of the weighted average of the arithmetic
mean returns is 12.5 %, 1.2 percentage point higher than the arithmetic mean of the
unweighted returns. The strategy of investing in each fund according to its assets under management would also have resulted in a higher standard deviation, a higher geometric mean
return, a higher skewness, and a higher kurtosis than the strategy of investing equal portfolio
proportions in all funds.
We use three versions of the DAX as benchmarks:
-
”DAX nach Deutsche Börse AG”. Mella constructed this time series, often it is called
”Mella-DAX”. Mella linked the official DAX that started January 1988 together with its predecessors, the Börsenzeitungsindex (BZ-Index, 1981-1987) and the Hardy-Index (9/1959
– 1981). Both indices also focused on German Blue Chips. The BZ index, like the DAX
included 30 stocks, the Hardy-Index only 24. A major weakness of the Hardy-Index is that
it did not include dividends. Since more than 50 % of the Mella-DAX consists of the HardyIndex, the omission of dividends in the latter index reduces the total performance of the
Mella-DAX considerably. A weakness of the BZ index is that it implicitly weighs the rates of
return of the included stock equally. From 1981 to 1987 the small stocks in the BZ index
had relatively low rates of return, the large stock in the index had higher rates of return. As
a consequence, the BZ index would have underperformed the DAX if the latter had existed
at that time. In the DAX the rates of return are market-value weighted.
-
”DAX nach Stehle u.a.” In this time series the official DAX is linked with a DAX replication.
Stehle/Huber/Maier (1996) discuss the problems of such a replication and estimate a time
series that is free of a survivorship bias for the years between 1954 and 1987.102
-
”DAX 0%”. A major weakness of the first two series is that both do not include the Körperschaftsteuergutschrift which existed after 1977. Economically they reflect the rate of return
of a German investor with a marginal income tax rate of 36 % between 1977 and 1994,
30% after 1994.113 The DAX 0% time series, described in Stehle (2000), is based on the
9
10
Stehle/Huber/Maier (1996) discuss this problems in detail.
The name ‚DAX nach Stehle u.a.‘ was given by the Deutsches Aktieninstitut e.V. which uses it in
its publications.
official DAX and the DAX replication by Stehle/Huber/Maier (1996)124. It includes the
Körperschaftsteuergutschrift. Economically this time series reflects the rate of return of a
taxable German investor with a marginal income tax rate of 0 %, hence the abbreviation
DAX 0%.
The bottom rows of table 2 show summary statistics for the three DAX time series, which illustrate this effect. Between January 1973 and December 1998 annual rates of return have a
geometric mean of 9.0% (Mella-DAX), 10.7 % (DAX nach Stehle u.a.) and 12.4 % (DAX 0%).
Because of the fact that in the ”Mella-DAX” the rates of return on individual stocks are
weighted equally before 1987, the standard deviation of the annual rates of return is only
24.4% compared to 26.0% of DAX nach Stehle u.a. The relatively low standard deviation of the
”Mella” time series leads to a smaller difference of the arithmetic and the geometric mean (2.5
percentage points compared to 2.8 of the DAX 0%). The differences in weighting also influence the higher moments of the empirical distribution of the different DAX time series. The
skewness of the ”Mella” time series is considerably lower than that of the three DAX series in
which market value weights are used throughout.
In our context only the DAX 0% is a correct benchmark because the mutual fund data by the
BVI also includes the Körperschaftsteuergutschrift. An alternative to using BVI data in combination with the DAX 0% is to exclude the Körperschaftsteuergutschrift from the BVI data and
then use an index that also does not include the Körperschaftsteuergutschrift, for example the
DAX or the DAFOX. Wittrock/Steiner (1995) and Steiner/Wittrock (1994) follow this procedure.
Several prior studies on the German market, especially Scherer (1994) and Reichling/Trautmann (1998) use BVI-data in combination with an index that does not include the Körperschaftsteuergutschrift (see table 1). The DAFOX, one of the standard benchmarks in the
empirical research on the German stock market, includes the relevant universe of stocks, it is
market value weighted, includes dividends but not the Körperschaftsteuergutschrift. Thus
results based on the combination of BVI data and the DAFOX are biased in favor of the funds.
Reichling/Trautmann (1998), for example, use a roughly similar sample and time period than
we do. They report in their table 1 that the DAFOX outperforms the average fund by .92 % per
year in a one-dimensional comparison based on the arithmetic mean return.
The bias in favor of the funds is even larger when the ”Mella-DAX”, the index of the Frankfurter
Wertpapierbörse (FWB) or the CDAX is used, because these time series do not include dividends at all for a large part of the observation period. Reichling/Trautmann (1998) report in
their table 1 that the funds, on average, outperform the ”Mella-DAX” by .72 % per year and the
CDAX by .70 %, while we conclude that the DAX 0% outperforms the unweighted average of
the fund returns by 3.9 % per year in raw returns.
11
In addition to the two mentioned time series Stehle has constructed a DAX 36 % time series which
continues to use a marginal income tax rate of 36 % after 1994 and a DAX 56 % time series which
reflects a marginal income tax of 56 %. These series are not used in the present study.
12 Stehle (2000) gives an English summary.
This might be one of the reasons why the ”Mella-DAX” index is so popular with Kapitalanlagegesellschaften. Usually long-term performance evaluations in the German financial press
are also based on this index.
The last row of table 2 contains summary statistics for an alternative benchmark we use, the
DAX 100 at a marginal tax rate of 0%. This time series, after 1987 is based on the DAX 100 of
the Deutsche Börse AG, a market-value weighted index of the 100 largest German stocks. The
official index is adjusted for the tax effects mentioned above, for the years before 1987 we use
a replication. The DAX100 0% has a higher skewness than the ”Mella” time series and a
slightly lower standard deviation. Compared to the DAX 0% both values are lower. As a consequence of a negative size effect after 1990, the arithmetic and the geometric mean return of
the DAX100 0% are lower than that of the DAX 0%.
4. Risk-Adjusted Performance
Assume that the risk of a portfolio is properly measured by the standard deviation of its rates of
return. The differences between the standard deviations of the individual funds summarized in
table 2 demonstrate the need for an analysis that takes return and risk differences into
account. Most studies of mutual fund performance build upon the procedures originally suggested by Sharpe (1966), Treynor (1965) and Jensen (1968). While Sharpe proposes to use
the overall risk of the funds’ portfolios, Treynor and Jensen use the systematic risk or beta of
an asset as additional element in performance evaluation.
The reward-to-variability or Sharpe ratio is calculated according to equation (4.1). The Sharpe
ratio is the appropriate performance measure for an individual whose total wealth is invested in
the fund. In addition to the assumption that risk is properly measured by the standard deviation, no major assumption is necessary. In particular, the Sharpe ratio is a proper measure of
fund performance, even if the capital asset pricing model does not hold.
rp – rf
SR p = -------------σp
(4.1)
SR p denotes the Sharpe ratio of fund p, r p its average rate of return, σ p its standard
deviation and r f the average risk-free rate of return.
where
Table 2 also includes the Sharpe ratios based on annual returns for the 18 funds in our sample
(see column Sharpe), calculated in the traditional way. The time-series of the unweighted averages of fund returns have a Sharpe ratio of .26, which is considerably higher than the Sharpe
ratio of the Mella-DAX (.21) but considerably lower than the Sharpe ratio of the two DAX series
which are properly adjusted to include the Körperschaftsteuergutschrift, the DAX 0% and the
DAX100 0%. Both have Sharpe ratios of .34. Only one fund (Investa) has the same Sharpe
ratio as the latter two indices, all others have a lower Sharpe ratio. The difference between the
Sharpe ratio for the time-series of the unweighted averages of fund returns and the Sharpe
ratio of the two relevant versions of the benchmarks translates into an underperformance of 2.36 % per year according to the M-square measure proposed by Modigliani/Modigliani
(1997).
Jensen suggested to use the intercept of a linear regression of the excess returns of fund on
the excess return of the market portfolio as the risk-adjusted measure of fund’s performance.
The model to be estimated is
r pt – r ft = α p + β p ( r mt – r ft ) + ε t
where r mt is the rate of return of the market portfolio at time t and
term.
(4.2)
ε t a random disturbance
The Jensen measure (Jensen’s alpha) is based on the perspective of an individual, whose
investment in a specific mutual fund is only a small fraction of his over-all portfolio. This measure is only appropriate if the capital asset pricing model holds.
Performance estimates based on the Jensen measure calculated in the traditional way are
included in table 5 in the columns "annual returns". When the DAX 0 % is used as benchmark,
the underperformance of the unweighted average of fund returns is -1.5% (statistically significant at the 10% level), or -1.6% when the DAX100 0 % is used, respectively. This is considerably more than the underperformance reported by Reichling/Trautmann (1998) and Kaserer/
Pfau (1993). Their estimates are only slightly negative, when the DAFOX is used, which does
not include the Körperschaftsteuergutschrift, while the BVI data they use does. The performance estimates of these and other studies on German stock mutual funds are summarized in
table 3.
Estimates of the Sharpe measure, calculated in the traditional way, are based on the arithmetic
average of monthly, quarterly, or annual rates of return of mutual funds. The values calculated
for the individual funds are compared with the corresponding values for the market portfolio,
which is typically approximated by an actual stock market index or portfolios based on a specific universe of stocks. This implies that the performance evaluation is based on the perspective of an investor with a monthly, quarterly or annual time horizon. For an investor with a
longer time horizon, for example ten-year time horizon, the geometric mean returns for tenyear time intervals would be the proper input in the estimation of the Sharpe measure. Unfortunately the available data for non-overlapping time periods is not sufficient to make meaningful
estimates. In traditional estimates of the Jensen measure, the arithmetic mean return is used
implicitily.
An additional weakness of performance measures calculated in the traditional way is that an
ex-post perspective is used. If a specific fund has an identical mean excess return as the chosen benchmark but a lower standard deviation, the argument is, that investors could have
achieved a higher return than the chosen benchmark with an identical risk exposure by lever-
ing their fund investment properly. Note that in this line of argument the proper leverage factor
is only identified ex-post, performance evaluation is based on hindsight.
Instead of using the standard ex-post perspective we follow the ex-ante perspective of investors who want to invest a given amount of money, their equity investment, in the stock market,
either by investing directly in a portfolio that corresponds to the DAX portfolio or by investing
their money in a mutual fund. By looking at past returns investors realize that the mutual funds
typically have a lower risk than the DAX portfolio. To make the two strategies comparable with
respect to risk they have to borrow and invest the borrowed money in addition to their equity in
the chosen fund.
If
σ̂ i is the investors’ estimate of the future standard deviation of the rate of return on fund i,
σ̂ M their estimate of the standard deviation of the rate of return of the DAX portfolio, the
amount of borrowing needed to achieve an identical risk exposure, expressed as a fraction of
( σ̂ M ⁄ σ̂ i ) – 1 . The investors’ total investment in fund i, also expressed as a
fraction of their equity, is ( σ̂ M ⁄ σ̂ i ) . The adjusted rate of return, that is the rate of return on the
their equity is
levered portfolio based on fund i in time period t, is:
r it∗ = r it ( σ̂ M ⁄ σ̂ i ) – r f [ ( σ̂ M ⁄ σ̂ i ) – 1 ]
(4.3)
In order to make this procedure operational, we need values for the investors’ estimate of the
future standard deviation of the funds and of the chosen benchmark portfolio. We use naïve
estimates, the historical standard deviations of the monthly rates of return during the past 24
month, that is, the ratios presented in figure 6. Leverage adjustments are made at the beginning of each calendar year, based on the standard deviations during the past 24 months. In a
few cases this ratio is higher than 2.0, especially for the DIT fund in 1984. In these cases we
limit the amount of borrowing to the amount of the equity investment.
Table 4 shows summary statistics for the adjusted returns, that is, for the annual returns of the
levered investment strategies for our sample of 18 German stock mutual funds, using both the
DAX 0% and the DAX100 0% as benchmark portfolios. The ex-post standard deviations of the
annual rates of return of the levered investment strategies (see column ”Sigma”) are higher for
all funds, sometimes considerably higher. The standard deviation of the unweighted average
fund returns is now nearly identical to that of the chosen benchmark index. All standard deviations are within three percentage points of the benchmark. For all funds the arithmetic means
of the adjusted returns are higher than the corresponding means of the ”raw” returns, in some
cases the differences are large. The geometric mean returns are also higher for all funds
except one.
The column "Sharpe" in table 4 shows the Sharpe measures of the levered investment strategies. Note that the Sharpe measure of the unweighted average of the adjusted fund returns is
.29, which is considerably higher than the average based on the raw returns. According to the
Sharpe measure two funds had a better performance than the DAX 0%, Investa and Concentra.
Table 5, in the columns "adjusted returns", shows the Jensen measures for the adjusted
returns. The Jensen’s alpha of the unweighted average of the adjusted fund returns amounts
to -.9 % when the DAX 0% is used as benchmark, to -1.2% when the DAX100 0% is used as
benchmark. The comparable measures for unadjusted returns are –1.5% and –1.6%.
Regardless whether we use raw returns and estimate the Sharpe and the Jensen measure in
the traditional way or use adjusted returns in the calculation of these measures, the large German stock mutual funds, on the average, have performed better than the small ones. Weighting them equally in the calculation of the industry average does not seem appropriate when
evaluating the fund industry as a whole. Therefore, in addition to looking at the performance
measures of the unweighted average of the individual fund returns, we have included, in all
tables, performance measures of the value-weighted average of the individual fund returns,
using the fraction of each fund’s share of total assets under management at the beginning of
each year as weights. When we judge performance by the performance measures for valueweighted averages based on the adjusted fund returns, the underperformance nearly disappears.
5. Conclusions
Our first important result is, that the rates of return of the mutual funds and the rates of return
of the chosen benchmark both must include identical return components. Either both must
include dividends and the Körperschaftsteuergutschrift or both must exclude these return components.
Our second important result is that the performance estimates are not very sensitive with
respect to the benchmark choice. The performance measures based on the DAX, which
includes the 30 largest German stocks, and the performance measures based on the DAX100,
which includes the 100 largest German stocks, are very similar in most cases.
Our third and most important result is that when we look at an investment strategy in which the
investment in a specific fund ex-ante has the same risk as the chosen benchmark, the average
underperformance is small when we weight the individual fund returns equally. The average
performance is neutral, when we weight the individual fund returns according to fund size,
measured by assets under management.
Literature
Bayer, J. (1994): Die Performance deutscher Aktienfonds mit Anlageschwerpunkt Deutschland
unter besonderer Berücksichtigung der Meßproblematik, Diplomarbeit, University Augsburg.
Bullock, H. (1959): The Story of Investment Companies, New York.
BVI Bundesverband Deutscher Investment-Gesellschaften e.V., Ed. (1998): Investment 98.
Daten, Fakten, Entwicklungen, Frankfurt am Main.
Carhart, M. (1997): On Persistence in Mutual Fund Performance, Journal of Finance 52, 5782.
DAI Deutsches Aktieninstitut e.V., Ed. (1997): DAI-Factbook 1997. Statistiken, Analysen und
Grafiken zu Aktionären, Aktiengesellschaften und Börsen, Frankfurt am Main, 3-25.
Elton, E.J. / Gruber, M.J. (1995): Modern Portfolio Theory and Investment Analysis, 5th ed.,
New York.
Göppl, H. / Schütz, H. (1994): Die Konzeption eines Deutschen Aktienindex für Forschungszwecke (DAFOX), Discussion paper 162, University of Karlsruhe (TH).
Grinblatt, M. (1992): The Persistence of Mutual Fund Performance, Journal of Finance 47,
1977-1984.
Gruber, M.J. (1996): The Growth in Actively Managed Mutual Fund, Journal of Finance 51,
783-810.
Ibisch, A (1999): Altersvorsorge in deutschen Aktien: Direktanlage versus Investmentfonds,
Humboldt University Berlin.
Janßen, B. / Rudolph, B. (1992): Der Deutsche Aktienindex DAX. Konstruktion und Anwendungsmöglichkeiten, Frankfurt am Main.
Jensen, M.C. (1968): The Performance of Mutual Funds in the Period 1945-1964, Journal of
Finance 23, 389-416.
Kaserer, C., Pfau, S. (1993): Perfomance deutscher Aktienfonds, Die Bank 10, S 596-600
Lerbinger, P. (1984): Die Leistungsfähigkeit deutscher Aktieninvestmentfonds, Zeitschrift für
betriebswirtschaftliche Forschung 36, 60-73.
Linhardt, H. (1935): Die Britischen Investment Trusts, Berlin/Wien.
Mella, F. (1988): Dem Trend auf der Spur – Der Deutsche Aktienmarkt 1959-1987 im Spiegel
des Index Börsen-Zeitung, Deutscher Aktienindex, Frankfurt am Main.
Modigliani, F. / Modigliani, L. (1997): Risk-Adjusted Performance, The Journal of Portfolio
Management, 45-54.
Möhlmann, J. (1993): Theoretische Grundlagen und Messung zweidimensionaler Perfor-
mancemessung von Investmentfonds, Stuttgart.
Mühlbradt, F. W. (1986): Die Leistungen von Wertpapier-Investmentfonds in Deutschland –
Überlegungen zur Neukonzipierung eines Beurteilungskalküls, Aktiengesellschaft 2, 3645.
Reichling, P. / Trautmann, S. (1998): External Performance Attribution with the Exponential
Performance Measure, Working paper, University of Mainz.
Scherer, B. (1993): Timing deutscher Investmentfonds – Eine empirische Analyse, Dissertation, University Giessen.
Scherer, B. (1994): Timing deutscher Investmentfonds. Jahrbuch für Nationalökonomie und
Statistik 213/2, 187-208
Sharpe, .W.F. (1966): Mutual Fund Performance, Journal of Business 39/1, Part II, 119-38.
Stehle, R. (1998): Aktien versus Renten, Handbuch zur Altersversorgung, Frankfurt am Main,
815-831.
Stehle, R. (2000): The DAX, a long-term view, vision + money 15, 42-45.
Stehle, R. / Huber, R. / Maier, J. (1996): Die Rückberechnung des DAX für die Jahre 1955 bis
1987, Kredit und Kapital 29, 277-304.
Steiner, M. / Wittrock, C. (1994): Timing-Aktivitäten von Aktieninvestment-fonds und ihre Identifikation im Rahmen der externen Performance-Messung, Zeitschrift für Betriebswirtschaft
64, 593-618.
Treynor, J.L. (1965): How to Rate Management of Investment Funds, Harvard Business
Review 43, 63-75.
Wermers, R. (2000): Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transactions Costs, and Expenses, Journal of Finance 55, 1655-1695
White, M. (1980): A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct
Test for Heteroscedasticity, Econometrica 48, 817-838.
Wittrock, C. / Steiner, M. (1995): Performance-Messung ohne Rückgriff auf kapitalmarkttheoretische Renditeerwartungsmodelle. Eine Analyse des Anlageerfolges deutscher Aktieninvestmentfonds, Kredit und Kapital 28/1, 1-45.
100%
Luxembourg Mutual funds
90%
7,1%
German Mutual funds
19,7%
Life insurance
80%
70%
Home savings
60%
31,2%
market
share 50%
in %
40%
8,9%
30%
Savings and term accounts
20%
33,1%
10%
0%
1970
1972
1974
1976
1978
78
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
210
389
861 nominal
341
495
861 real in prices of
2000
Total assets in bill.
Fig 1: Total assets under management by German mutual funds (bottom lines), market shares of mutual fund types
100%
16%
Real estate funds
90%
"Altersvorsorgefonds"
7%
80%
1%
Money market funds
70%
21%
60%
Bond mutual funds
market
share
in % 50%
40%
Stock mutual funds*
30%
20%
54%
10%
0%
1950
1955
1960
1965
1970
5
13
Source: Bundesbank (* incl. Mixed funds)
1975
1980
1985
1990
1997
1998
1999
2000
17
65
298 nominal
27
82
298 real, in prices
Total assets under Management in bill.
Fig 2: Total amount of indirect investments (bottom line), market shares of different types of indirect investments
of 2000
4.5
100%
90%
4
80%
3.5
70%
3
60%
2.5
50%
2
40%
1.5
30%
1
20%
10%
Germ. Stocks
For. Stocks
Bonds
Standard Deviation Ratio
0%
0.5
0
’71 ’72 ’73 ’74 ’75 ’76 ’77 ’78 ’79 ’80 ’81 ’82 ’83 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98
Fig 3.a: Investment behavior of selected funds at the end of their fiscal years, Fondra
100%
4.5
90%
4
80%
3.5
70%
3
60%
2.5
50%
2
40%
1.5
30%
1
20%
10%
Germ. Stocks
For. Stocks
Bonds
Others
0.5
Standard Deviation Ratio
0%
0
’71 ’72 ’73 ’74 ’75 ’76 ’77 ’78 ’79 ’80 ’81 ’82 ’83 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98
Fig 3.b: DIT-Fonds für Vermögensbildung
4.5
100%
90%
4
80%
3.5
70%
3
60%
2.5
50%
2
40%
1.5
30%
1
20%
10%
Germ. Stocks
For. Stocks
Bonds
Others
0.5
Standard Deviation Ratio
0%
0
’71 ’72 ’73 ’74 ’75 ’76 ’77 ’78 ’79 ’80 ’81 ’82 ’83 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98
Fig 3.c: UniFonds
4.5
100%
90%
4
80%
3.5
70%
3
60%
2.5
50%
2
40%
1.5
30%
1
20%
10%
Germ. Stocks
For. Stocks
Bonds
Others
0.5
Standard Deviation Ratio
0
0%
’71 ’72 ’73 ’74 ’75 ’76 ’77 ’78 ’79 ’80 ’81 ’82 ’83 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98
Fig 3.d: MK Alfakapital
100%
35000
30000
80%
25000
60%
20000
15000
40%
10000
20%
5000
0%
0
’72 ’73 ’74 ’75 ’76 ’77 ’78 ’79 ’80 ’81 ’82 ’83 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98
Adifonds
Deka-Fonds
Fondra
Investa
Oppenheim Privat
Ring-Aktienfonds DWS
Total assets under management
Adiverba
DIT-Fonds f. Vermögensbildung
HANSAsecur
MAIN I
Plusfonds
Thesaurus
Concentra
Fondak
HWG-Fonds
MK Alfakapital
Privatfonds
Unifonds
Fig 4: Assets under management by the 18 funds in our initial sample
The line shows total assets under management by the 18 funds, the colums each fund’s individual share
Rates of return of funds
Rate of return of DAX
.2
.15
.1
.05
0
-.05
-.1
-.15
-.2
-.25
-.3
Dec/72 Dec/74 Dec/76 Dec/78 Dec/80 Dec/82 Dec/84 Dec/86 Dec/88 Dec/90 Dec/92 Dec/94 Dec/96 Dec/98
Date
Fig 5: Monthly rates of return of the DAX and the 18 funds in our sample
2.7
2.5
2.3
2.1
1.9
1.7
1.5
1.3
1.1
.9
Dec/72 Dec/74 Dec/76 Dec/78 Dec/80 Dec/82 Dec/84 Dec/86 Dec/88 Dec/90 Dec/92 Dec/94 Dec/96 Dec/98
Date
Fig 6: Ratio of the standard deviation of the DAX and the 18 included funds, based on 24 prior monthly observations
Rates of return of funds
Rate of return of DAX
.14
.12
.1
.08
.06
.04
.02
0
-.02
-.04
-.06
-.08
1972
1974
1976
1978
1980
1982
1984 1986
Year
Fig 7: Annual rates of return of the DAX and the 18 funds in our sample
1988
1990
1992
1994
1996
1998
Table 1: Descriptive statistics for monthly rates of return of 18 German stock mutual funds in our
initial sample
The sample includes all funds that operated in January, 1972 or earlier. Sample period is 01/73 to 12/98, all funds still operate today.
WKN: Wertpapierkennnummer
Size ’91: Assets under management as of December 31, 1991, in Mio. DM
Mean a: Arithmetic mean of monthly returns
Sigma: Standard deviation of monthly returns
Mean g: Geometric mean of monthly returns
#
Name
WKN
Size ’91 Begin
End
Mean a
Sigma
Mean g
Skewness
Kurtosis
1
Adifonds
847103
487,9
01/73
12/98
0,99
4,86
0,87
-0,564
5,4
2
Adiverba
847106
716,8
01/73
12/98
0,91
4,37
0,81
-0,647
6,7
3
Concentra
847500
1113,3
01/73
12/98
0,99
4,80
0,88
-0,552
5,1
4
DIT-Fonds f. Verm.
847506
593,7
01/73
12/98
0,89
3,89
0,82
-0,701
6,0
5
Deka-Fonds
847450
1488,9
01/73
12/98
0,96
4,96
0,84
-0,550
5,0
6
Fondak
847101
688,0
01/73
12/98
0,88
4,65
0,77
-0,635
5,8
7
Fondra
847100
352,3
01/73
12/98
0,76
3,28
0,70
-0,673
5,9
8
HANSAsecur
847902
13,7
01/73
12/98
0,51
4,57
0,40
-1,303
10,8
9
HWG-Fonds
10 Investa
849143
9,8
01/73
12/98
0,81
3,41
0,75
-0,863
6,2
847400
1411,7
01/73
12/98
1,04
4,71
0,93
-0,521
5,0
11 MAIN I
849134
24,7
01/73
12/98
0,84
4,52
0,73
-0,798
6,1
12 MK Alfakapital
847770
257,8
01/73
12/98
0,79
4,43
0,69
-0,539
6,0
13 Oppenh. Privat
848550
30,9
01/73
12/98
0,74
4,16
0,65
-1,092
8,1
14 Plusfonds
847108
227,1
01/73
12/98
0,95
4,30
0,86
-0,649
6,1
15 Privatfonds
975221
12,6
01/73
12/98
0,82
4,25
0,73
-0,603
6,7
16 Ring-Aktienf.
847405
353,6
01/73
12/98
0,82
4,48
0,71
-0,923
6,7
17 Thesaurus
847501
367,0
01/73
12/98
0,92
4,69
0,81
-0,673
5,2
18 Unifonds
849100
1738,0
01/73
12/98
0,95
4,59
0,84
-0,650
5,2
01/73
12/98
0,87
4,38
0,77
-0,719
6,2
01/73
12/98
0,94
4,58
0,84
-0,614
5,5
DAX 0 % (Stehle u.a.)
01/73
12/98
1,12
5,38
0,98
-0,558
5,0
DAX (Mella)
01/73
12/98
0,86
5,33
0,72
-0,436
4,7
DAX nach Stehle
01/73
12/98
1,00
5,37
0,85
-0,536
5,0
DAX100 0% (Stehle u.a.)
01/73
12/98
1,09
5,13
0,96
-0,598
5,1
Interest rate
01/73
12/98
0,51
0,21
0,51
0,000
0,0
Unweighted ar. mean
Weighted ar. mean
9887,8
Table 2: Descriptive statistics for annual rates of return of 18 German stock mutual funds in our initial
sample
The sample includes all funds that operated in January, 1972 or earlier. Sample period is 01/73 to 12/98,
all funds still operate today. The weighted average mean is based on assets under management as of December 31, 1991.
KAG: Kapitalanlagegesellschaft (Managing firm)
WKN: Wertpapierkennnummer
Size ’91: Assets under management as of December 31, 1991, in Mio. DM
Mean a: Arithmetic mean of the annual returns (Annual returns are calculated from monthly returns by proper compounding.)
Sigma: Standard deviation of the annual returns
Mean g: Geometric mean of the annual returns
Sharpe: Sharpe’s reward-to-variability measure
Rank: Rank according to Sharpe’s measure
#
Name
KAG
ADIG
WKN
847103
Size ’91 Mean a Sigma Mean g
487.9
12.9
Sharpe
1
Adifonds
0.30
2
Adiverba
ADIG
847106
716.8
3
Concentra
DIT
847500
1113.3
4
DIT-Fonds f. Verm.
DIT
847506
593.7
5
Deka-Fonds
DeKa
847450
1488.9
6
Fondak
ADIG
847101
688.0
11.6
21.3
9.7
0.25
7
Fondra
ADIG
847100
352.3
9.7
14.3
8.8
0.24
8
HANSAsecur
HANSA
847902
13.7
6.7
20.0
5.0
0.02
9
HWG-Fonds
Univ-Inv.
849143
9.8
10.5
15.7
9.4
0.27
Rank Skewness Kurtosis
21.7
10.9
4
0.531
2.8
12.3
21.9
10.2
0.27
8
0.302
3.4
13.1
22.0
11.1
0.31
3
0.531
2.7
11.6
17.8
10.3
0.30
5
0.847
3.0
12.7
22.9
10.6
0.28
7
0.566
3.3
11
0.459
3.3
12
0.266
2.9
18
0.509
3.6
10
0.251
2.4
10 Investa
DWS
847400
1411.7
13.7
21.5
11.7
0.34
1
0.389
2.7
11 MAIN I
Univ-Inv.
849134
24.7
10.9
20.0
9.2
0.23
13
0.307
2.4
12 MK Alfakapital
Mün.-Kap.
847770
257.8
10.6
21.1
8.6
0.20
16
0.261
2.5
13 Oppenh. Privat
Oppenh.
848550
30.9
9.4
17.2
8.1
0.18
17
0.243
2.2
14 Plusfonds
ADIG
847108
227.1
12.4
19.2
10.8
0.32
2
0.462
2.7
15 Privatfonds
Metzler
975221
12.6
10.6
19.1
9.1
0.23
14
0.562
2.6
16 Ring-Aktienf.
DWS
847405
353.6
10.7
20.2
8.9
0.22
15
0.056
2.5
17 Thesaurus
DIT
847501
367.0
12.2
21.9
10.2
0.27
9
0.538
2.9
18 Unifonds
Union-Inv.
849100
1738.0
12.4
20.6
10.6
0.30
6
11.3
19.9
9.6
0.25
Weighted ar. mean
12.3
21.0
10.5
0.29
0.449
2.9
DAX 0 % (Stehle u.a.)
15.2
26.2
12.4
0.34
0.544
3.6
Unweighted ar. mean
549.3
0.381
2.7
0.415
2.8
DAX (Mella)
11.5
24.4
9.0
0.21
0.349
2.5
DAX nach Stehle
13.5
26.0
10.7
0.28
0.563
3.6
DAX100 0% (Stehle u.a.)
14.6
24.4
12.1
0.34
0.491
3.3
Table 3: Studies on the performance of German Stock mutual funds.
Ln returns: logarithmic returns
KSt: Körperschaftssteuer included in fund returns
Div/KSt: dividends included/Körperschaftssteuer included in index)
Sample
size
Time period
covered
Return
interval
Ln
returns
Lerbinger (1984)
7
1970-1979
annual
no
not rel. random
Mühlbradt (1986)
11
1976-1983
annual
no
not rel.
1/1981-1/1993
monthly
yes
no
DAFOX
monthly
yes
yes
Mella-DAX
FWB
yes
no
DAFOX
Author(s), year
KSt
Index
Div/KSt
Jensen’s
Alpha
Timing
Persiste
nce
-
-
no
portfolios
Kaserer/Pfau (1993)
Scherer (1994)
26
6/1974-1/1990
Steiner/Wittrock (1994)
16
5/1974-12/1991
annualized
monthly
annualized
Wittrock/Steiner (1995)
21
5/1974-12/1991
monthly,
-
Mella-DAX
yes
no
DAFOX
no
yes
DAFOX
-
-
yes/no
-.05 %
-
-
partly/no
negative
negative
-
no/no
negative
negative
-
yes/no
negative
no
-
partly/no
positive
no
-
yes/no
-
no
no
annualized
Reichling/Trautmann (1998)
monthly
annualized
yes/no
-.08 %
negative
CDAX
partly/no
.94 %
negative
-
Mella-DAX
partly/no
1.47 %
positive
-
Table 4: Descriptive statistics for adjusted annual returns of the 18 German stock mutual funds in our
initial sample
The sample includes all funds that operated in January, 1972 or earlier. Sample period is 01/73 to 12/98,
all funds still operate today.
Adjusted returns are returns on the equity investment in a levered portfolio. (The amount borrowed or lent at the riskless
rate of interest is determined ex-ante with the objective that the standard deviation of the levered portfolio matches that
of the chosen benchmark.)
Weights according to table 2.
Adjusted (DAX 0%) annual returns
#
Name
WKN
Mean a
Sigma
Adjusted (DAX100 0%) annual returns
Mean g Sharpe Rank Mean a
Sigma
Mean g Sharpe Rank
1
Adifonds
847103
14.5
25.3
12.0
0.32
7
13.7
23.7
11.5
0.31
7
2
Adiverba
847106
15.1
28.2
11.7
0.31
8
14.1
26.2
11.2
0.30
8
3
Concentra
847500
15.5
26.4
12.8
0.35
2
14.6
24.6
12.2
0.34
2
4
DIT-Fonds f. Verm.
847506
16.1
29.4
13.0
0.33
4
15.7
28.7
12.8
0.33
3
5
Deka-Fonds
847450
14.3
26.1
11.6
0.31
10
13.5
24.3
11.1
0.30
9
6
Fondak
847101
13.7
25.2
11.1
0.29
11
12.9
23.5
10.6
0.28
11
7
Fondra
847100
13.8
26.4
11.0
0.28
12
12.9
24.6
10.4
0.27
12
8
HANSAsecur
847902
7.2
23.6
4.8
0.04
18
6.9
22.3
4.7
0.03
18
9
HWG-Fonds
849143
14.8
25.5
12.1
0.33
5
14.0
23.9
11.6
0.32
5
10 Investa
847400
15.9
25.4
13.3
0.38
1
15.0
23.6
12.7
0.37
1
11 MAIN I
849134
13.0
25.5
10.2
0.26
13
12.3
23.9
9.8
0.25
13
12 MK Alfakapital
847770
12.1
27.1
8.7
0.21
16
11.4
25.9
8.3
0.20
16
13 Oppenh. Privat
848550
10.4
23.4
7.9
0.18
17
10.0
22.4
7.8
0.17
17
14 Plusfonds
847108
16.1
29.3
12.9
0.33
3
15.0
27.0
12.2
0.32
4
15 Privatfonds
975221
13.9
29.2
10.8
0.26
14
13.0
26.9
10.3
0.25
14
16 Ring-Aktienf.
847405
13.1
26.6
10.0
0.26
15
12.4
24.9
9.7
0.24
15
17 Thesaurus
847501
14.7
27.3
11.7
0.31
9
13.8
25.4
11.2
0.30
10
18 Unifonds
849100
14.5
25.1
11.9
0.33
6
13.7
23.4
11.4
0.32
6
Unweighted ar. mean
13.8
26.4
11.0
0.28
13.0
24.7
10.5
0.27
Weighted ar. mean
14.7
26.3
11.9
0.32
13.9
24.6
11.4
0.31
DAX 0 % (Stehle u.a.)
15.2
26.2
12.4
0.34
14.6
24.4
12.1
0.34
6.3
2.6
6.3
DAX100 0% (Stehle u.a.)
Interest rate
Table 5: Jensen’s alphas of the 18 German stock mutual funds in our initial sample
The sample includes all funds that operated in January, 1972 or earlier. Sample period is 01/73 to 12/98, all funds still operate
today.
Adjustment based on standard deviation of past 24 monthly returns
Regressions based on the 26 annual returns between 1973 and 1998
*: denotes significance at 10% level
WKN: Wertpapierkennnummer
α: Jensen’s (1968) alpha
Intercept of a linear regression of the fund’s excess returns on the excess returns
of the respective market portfolio
β: Beta with respect to the chosen market portfolio
R2: R-squared of the regression
Market portfolio: DAX100 0%
Annual returns
#
Name
WKN
α
β
Market portfolio: DAX 0%
Adjusted annual returns
R2
α
β
R2
Annual returns
α
β
R2
Adjusted annual
returns
α
β
R2
1
Adifonds
847103
-0.8
0.887
0.97
-0.4
0.945
0.95
-0.8
0.824
0.96
-0.1
0.938
0.94
2
Adiverba
847106
-1.2
0.868
0.93
-0.6
1.016
0.90
-1.2
0.806
0.92
-0.2
1.012
0.89
3
Concentra
847500
-0.6
0.891
0.97
0.2
0.978
0.95
-0.6
0.825
0.95
0.5
0.971
0.94
4
DIT-Fonds f. Verm.
847506
-0.3
0.669
0.82
0.9
1.029
0.79
-0.2
0.608
0.78
1.2
0.963
0.75
5
Deka-Fonds
847450
-1.3
0.931
0.97
-0.8
0.967
0.95
-1.2
0.862
0.96
-0.5
0.961
0.94
6
Fondak
847101
-1.9 * 0.868
0.98
-1.2 *
0.940
0.95
-1.8 * 0.802
0.96
-0.9
0.931
0.94
7
Fondra
847100
-1.5 * 0.591
0.95
-1.5 *
0.973
0.92
-1.5 * 0.550
0.95
-1.1
0.972
0.92
8
HANSAsecur
847902
-6.0 * 0.781
0.91
-6.4 *
0.843
0.86
-6.0 * 0.723
0.89
-6.4 * 0.830
0.86
9
HWG-Fonds
849143
-1.0
0.624
0.90
0.1
0.912
0.86
-1.0
0.577
0.88
0.4
0.905
0.86
10
Investa
847400
0.1
0.878
0.98
0.8
0.948
0.96
0.1
0.817
0.97
1.2
0.945
0.96
11
MAIN I
849134
-1.9 * 0.792
0.92
-1.7 *
0.928
0.90
-1.9
0.729
0.89
-1.4
0.913
0.88
12
MK Alfakapital
847770
-2.7 * 0.845
0.92
-3.0 *
0.981
0.84
-2.7 * 0.780
0.90
-2.7
0.951
0.83
13
Oppenh. Privat
848550
-2.5 * 0.674
0.89
-3.3 *
0.847
0.86
-2.5 * 0.624
0.88
-3.2 * 0.825
0.86
14
Plusfonds
847108
-0.3
0.777
0.93
0.0
1.052
0.90
-0.3
0.718
0.92
0.4
1.054
0.89
15
Privatfonds
975221
-1.8
0.738
0.86
-1.6
1.005
0.84
-1.8
0.686
0.85
-1.3
1.010
0.83
16
Ring-Aktienf.
847405
-2.1
0.793
0.89
-1.6
0.925
0.82
-2.1
0.739
0.89
-1.4
0.920
0.82
17
Thesaurus
847501
-1.5 * 0.893
0.98
-0.8
1.007
0.95
-1.5
0.823
0.95
-0.5
0.999
0.93
18
Unifonds
849100
-0.9 * 0.843
0.98
-0.3
0.933
0.95
-0.8
0.782
0.97
0.0
0.925
0.94
-1.2
0.851
-1.5
0.592
-0.9
0.872
Unweighted ar. mean
-1.6
0.642
U. bound of 95% C.I.
-2.2
-2.0
-2.2
-1.8
L. bound of 95% C.I.
-0.9
-0.3
-0.9
0.0
Weighted ar. mean
-1.0
U. bound of 95% C.I.
-1.3
0.850
-0.8
-0.4
0.966
-1.3
-0.9
0.788
-0.5
-0.1
L. bound of 95% C.I.
-0.6
0.1
-0.6
0.4
0.956
Appendix A: Official Investment Guidelines of the Mutual Funds in our Sample
All mutual funds in our sample are offered by German ”Fondsgesellschaften”. Their charters
contain provisions that they are supposed to invest in German securities mainly, in general
stocks are mentioned first.
An exception with regard to the official concentration on German stocks is Adiverba, whose
official orientation is ”international”. Exceptions with respect to mentioning stocks first are the
three mixed funds Fondra, HWG, and Plusfonds. Privatfonds was a mixed fund before 1989,
then it was declared a stock fund.
Approximately half of the funds may also invest in foreign securities, but those investments are
nearly always restricted in some way. Fondra, for example, may invest in German as well as
foreign bonds, convertible bonds (“Wandelschuldverschreibungen” and “Optionsanleihen”) but
only in German stocks. Several funds, for example Fondak, Fondra, and Adifonds allow in
exceptional circumstances investments in foreign securities up to 25 % of the assets. RingAktienfonds DWS is also an exception, it does not have any geographical restrictions. In the
time period 1971 to 1999 the official investment guidelines were relatively stable with regard to
the geographical orientation. Some funds increased their emphasis on German securities,
notably Oppenheim Privat, whose official investment orientation was changed to 100 % German stocks in 1989.
The funds are not limited to specific industries, except for Adiverba, whose main emphasis is
insurance and bank shares. Most funds emphasize in their official statements that a broad
diversification as well as a flexible orientation are intended. Very often it is explicitely stated
that the stocks should come from different industries, and that a positive development in the
long-run should be expected. HANSA+secur is an exception in this respect. It explicitely stays
away from extraordinary growth chances, according to the official description of their investment policy, to avoid the high risks associated with extraordinary growth chances. This fund
announced a significant change of the investment policy in 1995. Since the beginning of the
seventies it invested in German and in international securities without restriction. Since 1995
the focus is on the stocks of medium-sized German companies (”MID-DAX-Werte” ).
In addition the investment guidelines of most funds in our sample change at the beginning of
the nineties in so far as warrants were included as eligible securities and also that larger
investments in bonds became admissible. In 1971 in most funds bank deposits, bonds, and
money market securities were only admitted up 20 to 25 % of the fund assets. This amount
increased in the nineties, usually up to a maximum of 49 % of the fund assets.
During the entire time period the basic rule was that only stock quoted or traded in the top two
segments of German stock exchanges (Amtlicher Handel und geregelter Markt) could be
bought.
Typically the restrictions with respect to borrowing also changed. Only a few funds were
allowed to use credit at the beginning of the seventies, for example Unifonds. At the end of the
nineties in almost all funds short-term credit up to 10 % of total assets is allowed in exceptional
cases – it only requires the approval of the custodian bank at which securities are deposited.
Sources: Vademecum der Investmentfonds, various issues, 1970–1996, Hoppenstedt-Fondsführer, 1998-2000
Appendix B: Fee structure of the funds in our sample
Table B1 shows the official initial loads and the administrative expenses for the funds in our
sample for two selected years, 1988 and 1998. The table shows that the official loads did not
change in this time period for the funds in our sample. In fact, for most funds in our sample the
loads remained identical after 1971.
Interesting exceptions to this rule are Concentra, Thesaurus, DIT, which are all managed by
the same ”Fondgesellschaft”. In the seventies all three funds had a 6 % load fee, from 1980 to
1986 their load was 2.5 %, after 1987 it was 5 %. MK Alfakapital and Ring-Aktienfonds DWS
had a higher load fee before 1980 than in the years after 1980 (8.5 % and 6.5 %, respectively).
The table also shows that the administrative expenses varied more than the load fees. A good
example is Ring-Aktienfonds DWS: From 1971 to 1975 the administrative expenses were 1 %
per year, in the following 10 years .5 %. Starting in 1987 they doubled again, after three years
they went down to .5 %.
A general tendency does not exist. For several funds the administrative expenses decreased
by .3 percentage points over the years. For other funds, examples are Deka-Fonds and Concentra, the administrative expenses increased strongly, in some cases they doubled.
(Sources: Vademecum der Investmentfonds, various issues, 1970 - 1996, HoppenstedtFondsführer, 1998 - 2000)
Table B.1: Loads and annual administrative expenses of the mutual funds in our sample for
the years 1988 and 1998
Load in %
1988
Administrative expenses in % p.a.
1998
1988
1998
Adifonds
5
5
0.9
0.9
Adiverba
5
5
0.9
0.9
Concentra
5
5
0.5
0.7
DIT-Fonds f. Verm.
5
5
0.5
0.7
Deka-Fonds
5.26
5.26
0.5
1.2
Fondak
5
5
0.9
0.6
Fondra
5
5
0.9
0.6
HANSAsecur
5
5
0.96
0.96
HWG-Fonds
4
4
0.5
0.5
Investa
5
5
0.5
0.5
7.53
7.53
1
1
MAIN-I
MK Alfakapital
Oppenheim Privat
5
5
1
1
Plusfonds
5
5
1
0.6
Privatfonds
5
5
1
0.5
4.71
4.712
1
0.5
Thesaurus
5
5
0.5
0.7
Unifonds
5
5
0.55
0.55
Ring-Aktienfonds