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composition of open-end funds. Bond funds constitute 58% of the assets in closed-end funds, and
stock funds 42% of the assets. If we restrict the analysis to funds holding domestic assets, the
percentages are 68% to bonds and 32% to equity.
1.3 Exchange-Traded Funds
Exchange-traded funds are a recent phenomenon, with the first fund (designed to
duplicate the S&P 500 Index) starting in 1993. They are very much like closed-end funds with
one exception. Like closed-end funds, they trade at a price determined by supply and demand
and can be bought and sold at that price during the day. They differ in that at the close of the
trading day investors can create more shares of ETFs by turning in a basket of securities which
replicate the holdings of the ETF, or can turn in ETF shares for a basket of the underlying
securities. This eliminates one of the major disadvantages of closed-end funds, the potential for
large discounts. If the price of an ETF strays very far from its net asset value, arbitrageurs will
create or destroy shares, driving the price very close to the net asset value. The liquidity which
this provides to the market, together with the elimination of the risk of large deviations of price
from net asset value, has helped account for the popularity of ETFs.
2. Issues with Open-End Funds
In this section we will discuss performance measurement, how well active
funds have done, how well investors have done in selecting funds, other characteristics of good-
performing funds, and influences affecting inflows.
2.1 Performance Measurement Techniques
No area has received greater attention in mutual fund research than how to measure
performance. This section starts with a discussion of problems that a researcher must be aware of
when using the standard data sources to measure performance. It is followed by a subsection that
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discusses the principal techniques used in performance measurement of stock funds. The third
subsection discusses performance measurement for bond funds. The fourth subsection discusses
the measurement of timing.
2.1.1 Data Sources, Data Problems, and Biases
While many of the standard sources of financial data are used in mutual fund research,
we will concentrate on discussing issues with the two types of data that have been primarily
developed for mutual fund research. We will focus on the characteristics of and problems with
data sets which contain data on mutual fund returns, and mutual fund holdings. Mutual fund
return data is principally available from CRSP, Morningstar and LIPPER. Mutual fund holdings
data is available on several Thompson and Morningstar databases.
There are problems with the returns data that a researcher must be aware of. First is the
problem of backfill bias most often associated with incubator funds.
3
Incubation is a process
where a fund family starts a number of funds with limited capital, usually using fund family
money. At the end of the incubator period the best-performing funds are open to the public and
poor-performing funds are closed or merged. When the successful incubator fund is open to the
public, it is included in standard databases with a history, while the unsuccessful incubator fund
never appears in databases. This causes an upward bias in mutual fund return data. Evans (2010)
estimated the risk-adjusted excess return on incubator funds that are reported in data sets as
3.5%. This bias can be controlled for in two ways. First, when the fund goes public it gets a
ticker. Eliminating all data before the ticker creation date eliminates the bias. Second,
eliminating the first three years of history for all funds also eliminates the bias at the cost of
eliminating useful data for non-incubator funds.
3
This is developed and analyzed in Evans (2010). He employed a four-factor model (Fama-French and
momentum) to estimate alpha or risk-adjusted excess return.
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The second problem concerns the incompleteness of data for small funds. Funds under
$15 million in assets and 1,000 customers don‟t need to report net asset value daily. Funds under
$15 million either don‟t report data or report data at less frequent intervals than other funds in
most databases. If they are successful they often enter standard databases with their history,
another case of backfill bias. If they fail, they may never appear (see Elton, Gruber & Blake
(2001)). This, again, causes an upward bias in return data. It can be eliminated by removing data
on all funds with less than $15 million in assets.
The third problem, which has never been studied, arises from the difference in the fund
coverage across databases. When CRSP replaced Morningstar data with LIPPER data, over
1,000 funds disappeared from the database. What are the characteristics of these funds? Do the
differences bias results in any way?
The fourth problem is that many databases have survivorship bias. In some databases,
such as Morningstar, data on funds that don‟t exist at the time of a report are not included
(dropped) from the database. Thus, using the January 2009 disk to obtain ten years of fund
returns excludes funds that existed in 1999 but did not survive until 2009. Elton, Gruber & Blake
(1996a) show that funds that don‟t survive have alphas below ones that survive, and excluding
the failed funds, depending on the length of the return history examined, increases alpha by from
35 basis points to over 1%. The CRSP database includes all funds that both survive and fail, and
thus is free of this bias. To use Morningstar data, one needs to start at some date in order to
obtain funds that existed at that starting date and to follow the funds to the end of the time period
studied or to when they disappear.
Holdings data can be found from Morningstar and from Thompson. The most widely
used source of holdings data is the Thompson holdings database since it is easily available in
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computer-readable form. The Thompson database lists only the holdings data for traded equity. It
excludes non-traded equity, equity holdings that can‟t be identified, options, bonds, preferred,
convertibles, and futures.
The Morningstar database is much more complete, including the largest 199 holdings in
early years and all holdings in later years. Investigators using the Thompson database have the
issue of what to do about the unrecorded assets. Usually, this problem is dealt with in one of two
ways. Some investigators treat the traded equity as the full portfolio. Other authors treat the
differences between the aggregate value of the traded equity and total net assets as cash. Either
treatment can create mis-estimates of performance (by mis-estimating betas) that may well be
correlated with other factors. Elton, Gruber and Blake (2010b) report that about 10% of funds in
their sample use derivatives, usually futures. Futures can be used in several ways. Among them
are to use futures with cash to manage inflows and outflows while keeping fully invested, as a
timing mechanism, and as an investment in preference to holding the securities themselves.
Investigators report numbers around 10% for the percentage of securities not captured by the
Thompson database. However, there is wide variation across funds and types of funds. For funds
that use futures sensitivities to an index will be poorly estimated. Likewise, for funds that have
lower-rated bonds use options or convertibles or have non-traded equity, sensitivity to indexes
can be poorly estimated. The problem is most acute when timing is studied. Elton, Gruber and
Blake (2011b) analyze the problem of missing assets when alpha is being calculated, and find
that the superior performing funds are very different depending on whether a complete set of
assets or the Thompson database are used.
2.1.2 Performance Measurement of Index Funds
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Index funds are the easiest type of fund to evaluate because generally there is a well-defined
single index that the fund attempts to match. For example, when evaluating the “Wilshire 2000”
index fund, the fund‟s performance is judged relative to that index. We will concentrate on S&P
500 index funds in the discussion which follows, but the discussion holds for index funds
following other indexes.
There are several issues of interest in studying the performance of index funds. These
include:
1. Index construction
2. Tracking error
3. Performance
4. Enhanced return index funds
2.1.2.1 Index Construction
The principal issue here is how interest and dividends are treated. Some indexes are
constructed assuming daily reinvestment, some monthly reinvestment, and some ignore
dividends. Index funds can make reinvestment decisions that differ from the decisions assumed
in the construction of the index. In addition, European index funds are subject to a withholding
tax on dividends. The rules for the calculation of the withholding tax on the fund may be very
different from the rules used in constructing the index. These different aspects of construction
need to be taken into account in the conclusions one reaches about the performance of index
funds versus the performance of an index.
2.1.2.1 Tracking Error
Tracking error is concerned with how closely the fund matches the index. This is usually
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measured by the residuals from the following regression:
4
()
pt p p t pt
R I e
Where
t
I
is the return on the index fund at time t
p
is the average return on the fund not related to the index
t
I
is the return on the index at time t
pt
e
is the return on portfolio p at time t unexplained by the index (mean zero)
p
is the sensitivity of the fund to the index
pt
R
is the return on the fund at time t
A good-performing index fund should exhibit a low variance of
pt
e
and low autocorrelation
of
pt
e
over time so that the sum of the errors is small. Elton, Gruber and Busse (2004) found
an average
2
R
of 0.999 when analyzing the S&P 500 index funds indicating low tracking
error. The
p
is a measure of how much of the portfolio is invested in index matching assets.
It is a partial indication of performance since it measures in part the efficiency with which the
manager handles inflows and outflows and cash positions.
2.1.2.2 Performance of Index Funds
The
p
is a measure of performance. It depends in part on trading costs since the index fund
pays trading costs where the index does not. Thus we would expect higher
p
for S&P 500 Index
4
Two variants of this equation have been used. One variant is to set the beta to one. This answers the question of
the difference in return between the fund and the index. However, performance will then be a function of beta with
low beta funds looking good when the market goes down. The other variant is to define returns as returns in excess
of the risk-free rate. failure to do this means that alpha will be partially related to one minus beta. However, beta is
generally so close to one that these variants are unlikely to lead to different results.
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funds where trading costs are low and index changes are small relative to small or mid-cap index
funds where index changes are more frequent and trading costs are higher. Second,
p
depends
on management fees. Elton, Gruber and Busse (2004) find that the correlation between future
performance and fees is over -0.75 for S&P 500 index funds. Third, the value of
p
depends on
management skill in portfolio construction. For index funds that are constructed using exact
replication, management skill principally involves handling index changes and mergers although
security lending , trading efficiency, and the use of futures are also important. For indexes that
are matched with sampling techniques, portfolio construction also can have a major impact on
performance. Problems with matching the index are especially severe if some securities in the
index are almost completely illiquid, holding all securities in the index in market weights would
involve fractional purchases, or because some securities constitute such a large percentage of the
index that holding them in market weights is precluded by American law. Finally, European
mutual funds are subject to a withholding tax on dividends which also affects performance and
impacts alpha. Because of fees and the limited scope for improving performance, index funds
almost always underperform the indexes they use as a target.
2.1.2.3 Enhanced Return Index Funds
A number of funds exist that attempt to outperform the indexes they declare as benchmarks.
These are referred to as “enhanced return” index funds. ‟There are several techniques used. First,
if futures exist the fund can match the index using futures and short-term instruments rather than
holding the securities directly. Holding futures and short-term instruments may lead to excess
returns if futures generally deviate from their arbitrage value in a manner that means they offer
more attractive returns. Some index funds have been organized on this premise. Second, if the
fund invests in short-term assets that give a higher return than the short-term assets used in the
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future spot arbitrage relationship, it can give a higher return. Finally, switching between futures
and the replicating portfolio depending on the direction of the futures mispricing might enhance
returns. Alternatively, a manager can attempt to construct an index fund from assets the manager
views as mispriced. For example, the manager can construct a Government bonds index fund
using what the manager believes are mispriced Government bonds. This strategy is more natural
for index funds that can‟t use a replicating strategy because they have to hold securities in
weighs that differ from those of the index.
2.1.3 Performance Measurement of Active Equity Funds
The development of Performance Measurement for equity funds can be divided into two
generations:
2.1.3.1 Early Models of Performance Measurement
Friend, Blume &Crocket (1970) was the first major study to consider both risk and return
in examining equity mutual fund performance. They divided funds into low, medium and high
risk categories where risk was defined alternately as standard deviation and beta on the S&P 500
Index. They then compared the return on funds in each risk category with a set of random
portfolios of the same risk. Comparison portfolios were formed by randomly selecting securities
until random portfolios containing the same number of securities as the active portfolios being
evaluated. The random portfolios were divided into risk ranges similar to the active portfolios,
and differences in return between the actual and random portfolios were observed. In forming
random portfolios, individual stocks were first equally weighted and then market-weighted. The
results were clear for one set of comparisons: mutual funds underperformed equally weighted
random portfolios. The results were mixed for comparisons with market-weighted random
portfolios, where funds in the high risk group appeared to outperform random portfolios. The
advantage of this method over methods discussed below is that it makes no specific assumption
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about equilibrium models or the ability to borrow or lend at a particular rate. On the other hand,
results vary according to how the random portfolios are constructed and according to what risk
ranges are examined, making results often difficult to interpret.
While this type of simulation study is an interesting way to measure performance, it is
easier to judge performance if risk and return can be represented by a single number. The desire
to do so led to the development of three measures that have been widely used in the academic
literature and in industry. The first single index measure was developed by Sharpe (1966).
Sharpe recognized that assuming riskless lending and borrowing the optimum portfolio in
expected return standard deviation space is the one with the highest excess return (return minus
riskless rate) over standard deviation. Sharpe called this the reward to variability ratio. It is now
commonly referred to as the Sharpe ratio.
p
F
p
RR
Where
p
R
is the average return on a portfolio
p
is the standard deviation of the return on a portfolio
F
R
is the riskless rate of interest
This is probably the most widely used measure of portfolio performance employed by
industry. This is true, though, as we discuss below, Sharpe now advocates a more general form
of this model.
A second single index model which has been widely used is the Treynor (1965) measure,
which is analogous to the Sharpe measure but replaces the standard deviation of the portfolio
with the beta of the portfolio. Beta is defined as the slope of a regression of the return of the
14 – Mutual Funds 4-13-11
portfolio with the return of the market. This measures performance as reward to market risk
rather than reward to total risk.
The third single index model is due to Jensen (1968). This model can be written as
()
pt Ft p p Mt Ft pt
R R a R R e
p
a
is the excess return of the portfolio after adjusting for the market
pt
R
is the return on portfolio p at time t
Ft
R
is the return on a riskless asset at time t
Mt
R
is the return on the market portfolio at time t
p
is the sensitivity of the excess return on the portfolio t with the excess return on the market
pt
e
is the excess return of portfolio p at time t not explained by the other terms in the equation
This measure has a lot of appeal because
p
represents deviations from the Capital Asset
Pricing Model and as such has a theoretical basis. The Jensen measure can also be viewed as
how much better or worse did the portfolio manager do than simply holding a combination of the
market and a riskless asset (which this model assumes can be held in negative amounts) with the
same market risk as the portfolio in question.
While these models remain the underpinning of most of the metrics that are used to
measure mutual fund performance, new measures have been developed which lead to a more
accurate measurement of mutual fund performance.
2.1.3.2 The New Generation of Measurement Model
The models discussed in the last section have been expanded in several directions. Single
index models have been expanded to incorporate multiple sources of risk and more sophisticated
models of measuring risk and expected return have been developed
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