ABSTRACT
Over the last 20 years, investors have
come to approach investment decisionmaking
in an increasingly mechanical manner. Optimisers
are filled up with historical return data
and the 'optimal' portfolio follows almost
automatically. In this paper we argue that
such an approach can be extremely dangerous,
especially when alternative investments
such as hedge funds are involved. Proper
hedge fund investing requires a much more
elaborate approach to investment decisionmaking
than currently in use by most investors.
The available data on hedge funds should
not be taken at face value, but should first
be corrected for various types of biases
and autocorrelation. Tools like meanvariance
analysis and the Sharpe ratio that many
investors have become accustomed to over
the years are no longer appropriate when
hedge funds are involved as they concentrate
on the good part while completely skipping
over the bad part of the hedge fund story.
Investors also have to find a way to figure
in the long lockup and advance notice periods,
which make hedge fund investments highly
illiquid. In addition, investors will have
to give weight to the fact that without
more insight in the way in which hedge funds
generate their returns it is very hard to
say something sensible about hedge funds'
future longerrun performance. The tools
to accomplish this formally are not all
there yet, meaning that more than ever investors
will have to rely on common sense and doing
their homework.
1. INTRODUCTION
Hedge funds are on their way to become
the next big thing in investment management.
New funds start up every day, hedge funds
are marketed aggressively to institutions
and, under pressure to make up for recent
losses, many institutional investors are
showing serious interest. The amount of
assets under management by hedge funds has
grown from around $40 billion in 1990 to
an estimated $600 billion in 2003. In line
with this, the number of hedge funds worldwide
has grown to around 6000. In the early days
not much was known about hedge funds. Since
1994, however, a number of data vendors,
hedge fund advisors and fund of hedge funds
operators have been collecting performance
and other data on hedge funds. This has
allowed researchers to take a more serious
look at hedge funds. Although research in
this area is still in its infancy, it has
become clear that hedge funds are a lot
more complicated than common stocks and
investmentgrade bonds and may not be as
phenomenally attractive as many hedge fund
managers and marketers want investors to
believe. Hedge fund investing requires a
much more elaborate approach to investment
decisionmaking than what most investors
are used to. Mechanically applying the same
decisionmaking processes as typically used
for stock and bond investment may lead to
some very nasty surprises.
2. MODERN PORTFOLIO THEORY IN ACTION
Before the arrival of finance theory as
we known it today, finance was a very practical
discipline. Finance students would spend
their time studying accounting, taxation,
law and the writings of Benjamin Graham
and others. With the arrival of Harry Markowitz's
meanvariance analysis, Bill Sharpe's CAPM
and Gene Fama's efficient market hypothesis
things changed, however. From a practical
discipline, finance very quickly reinvented
itself as a branch of neoclassical price
theory, concentrating on the analysis of
abstract little 'toy worlds' where most
of what makes life complicated is simply
assumed away in an attempt to come to the
essence of things. At the same time, computers
and databases started to evolve up to a
point where nowadays every investor has
access to extensive computing power and
market data. All this has had a profound
impact on the way investment decisions are
being taken. Meanvariance optimisers play
an important part in modern investment management
and essentially take over a substantial
portion of the responsibility for the asset
allocation decision. Likewise, performance
evaluation relies heavily on theoretical
concepts such as the Sharpe ratio and Jensen's
alpha. All these tools have become so common
that many investors tend to apply them in
a purely mechanical fashion, giving little
or no thought to their underlying assumptions.
The same is true for the required inputs.
Often, means, and especially variances and
correlations coefficients are simply calculated
from downloaded historical return data with
little or no consideration for the sometimes
very specific factors that generated the
data in question.
The way in which the basic concepts of
modern finance are used in practice leaves
a lot to be desired. Despite this, their
application in the stock and bond markets
does not appear to be without some merit.
There are a number of reasons for this.
First, return data on stocks and bonds often
covers a long time period and tends to be
of good quality. Second, stock and bond
returns tend to exhibit statistical characteristics
that are very much in line with what is
assumed in theory. Third, stock and bond
markets typically tend to offer relatively
good liquidity. When we move away from stocks
and bonds and into the realm of alternative
investments then the situation changes dramatically,
however. Serious data problems, complex
return generating processes, nonnormal
return distributions, low transparancy and
substantial illiquidity all have to be taken
into account properly. If not, investors
risk selfdeception. They will see miracles
where there are none and vice versa. In
the sections that follow we will discuss
these matters in greater detail focusing
on hedge funds and the typical way in which
'sophisticated' investors look at them.
3. HEDGE FUND DATA
With the hedge fund industry still in its
infancy and hedge funds under no formal
obligation to disclose their results, gaining
insight in the performance characteristics
of hedge funds is not straightforward. Fortunately,
many funds nowadays release performance
as well as other administrative data to
attract new and to accommodate existing
investors. These data are collected by a
number of data vendors and fund advisors,
some of which make their data available
to qualifying investors and researchers.
The available data on hedge funds are not
without problems though. Here are some of
them:
An unknown universe.
Most hedge funds only report into one or
two databases. As a result, every database
covers a different subset of the hedge fund
universe and different researchers may arrive
at quite different conclusions simply because
different databases were used.
No independent auditing.
Most databases are of relatively low quality
as most data vendors simply pass on the
data supplied by the fund managers and their
administrators without any independent verification.
This means that before any serious research
can take place, one must check the data
for a number of possible errors and either
correct these or delete the funds in question
altogether.
Backfill bias.
Hedge fund databases tend to be backfilled,
i.e. although typically funds only start
reporting to a database some time after
their actual startup, when they do, their
full track record is included in the database.
Since only funds with good track records
will eventually decide to report, this means
that the available data sets are overly
optimistic about hedge fund performance.
As shown in Posthuma and Van der Sluis (2003),
on average actual hedge fund returns may
be 4% per annum lower than reported.
Survivorship bias.
Most data vendors only supply data on funds
that are still in operation. However, disappointing
performance is a major reason for hedge
funds to close down. As shown in Amin and
Kat (2003), this means that the data available
to investors will overestimate the returns
that investors can realistically expect
from investing in hedge funds by 24% per
annum. In addition, concentrating on survivors
only will lead investors to underestimate
the risk of hedge funds by 1020%.
Markingtomarket problems.
Since many hedge funds invest in illiquid
assets, their administrators have great
difficulty generating uptodate valuations
of their positions. When confronted with
this problem, administrators will either
use the last reported transaction price
or a conservative estimate of the current
market price, which creates artificial lags
in the evolution of these funds' net asset
values. As we will discuss in more detail
in section 4, this will lead to very substantial
underestimation of hedge fund risk, sometimes
by as much as 3040%.
Limited data.
Since most data vendors only started collecting
data on hedge funds around 1994, the available
data set on hedge funds is very limited.
The available data on hedge funds also span
a very special period: the bull market of
the 1990s and the various crises that followed
combined with the spectacular growth of
the hedge fund industry itself. This sharply
contrasts with the situation for stocks
and bonds. Not only do we have return data
over differencing intervals much shorter
than one month, we also have those data
available over a period that extends over
many business cycles. This has allowed us
to gain insight into the main factors behind
stock and bond returns and also allows us
to distinguish between normal and abnormal
market behaviour. The return generating
process behind hedge funds on the other
hand is still very much a mystery and so
far we have little idea what constitutes
normal behaviour and what not.
With institutional interest in hedge funds
on the increase another question that arises
is when the hedge fund industry will reach
capacity. While the industry has experienced
strong growth over the last five years in
terms of assets under management, hedge
funds themselves are showing lower returns
every year. This could be an indication
that there are no longer enough opportunities
in the global capital markets to allow hedge
funds to continue to deliver the sort of
returns that we have seen so far.
4. HEDGE FUND RISK
Markingtomarket problems tend to create
lags in the evolution of hedge funds' net
asset values, which statistically shows
up as autocorrelation in hedge funds' returns.
As discussed in Brooks and Kat (2002) for
example, this autocorrelation causes estimates
of the standard deviation of hedge fund
returns to exhibit a systematic downward
bias. The second column in table 1 shows
the average 1month autocorrelation found
in the returns of individual hedge funds
in some of the usual strategy groups over
the period 19942001. The table shows that
the problem is especially acute for convertible
arbitrage and distressed securities funds,
which makes sense as these funds' assets
will typically be the most difficult to
value. One way to correct for the observed
autocorrelation is to 'unsmooth' the observed
returns by creating a new set of returns
which are more volatile but whose other
characteristics are unchanged. One method
to do so stems from the real estate finance
literature, where due to smoothing in appraisals
and infrequent valuations of properties,
the returns of direct property investment
indices suffer from similar problems as
hedge fund returns (see Geltner (1991, 1993)).
The third and fourth column of table 1 show
the average standard deviations of the original
as well as the unsmoothed returns on individual
hedge funds belonging to the different strategy
groups. From the table we see that the difference
between the observed and the true standard
deviation can be very substantial. For distressed
securities funds the true standard deviation
is almost 30% higher than observed. For
convertible arbitrage funds the difference
is even higher.
Table 1: Average 1Month
Autocorrelation and Standard Deviations
Original and Unsmoothed Individual Hedge
Fund Returns

AC (1) 
Original SD 
Unsmoothed SD

Merger Arbitrage 
0.13 
1.75 
2.02 
Distressed Securities

0.25 
2.37 
3.05 
Equity
Market Neutral 
0.08 
2.70

3.04 
Convertible Arbitrage

0.30 
3.01 
4.00 
Global Macro 
0.03 
5.23 
5.37 
Long/short Equity

0.09 
5.83 
6.37 
Emerging Markets 
0.15 
8.33 
9.75 
A second reason why many investors think
hedge funds are less risky than they really
are results from the use of the standard
deviation as the sole measure of risk. Generally
speaking, risk is one word, but not one
number. The returns on portfolios of stocks
and bonds risk are more or less normally
distributed. Because normal distributions
are fully described by their mean and standard
deviation, the risk of such portfolios can
indeed be measured with one number. Confronted
with nonnormal distributions, however,
it is no longer appropriate to use the standard
deviation as the sole measure of risk. In
that case investors should also look at
the degree of symmetry of the distribution,
as measured by its socalled 'skewness',
and the probability of extreme positive
or negative outcomes, as measured by the
distribution's 'kurtosis'. A symmetrical
distribution will have a skewness equal
to zero, while a distribution that implies
a relatively high probability of a large
loss (gain) is said to exhibit negative
(positive) skewness. A normal distribution
has a kurtosis of 3, while a kurtosis higher
than 3 indicates a relatively high probability
of a large loss or gain. Since most investors
are in it for the longer run, they strongly
rely on compounding effects. This means
that negative skewness and high kurtosis
are extremely undesirable features as one
big loss may destroy years of careful compounding.
Table 2: Average Skewness
and Kurtosis of Individual Hedge Fund Returns

Skewness 
Kurtosis 
Merger Arbitrage 
0.50 
7.60 
Distressed Securities

0.77 
8.92 
Equity
Market Neutral 
0.40 
5.58

Convertible Arbitrage

1.12 
8.51 
Global Macro 
1.04 
10.12 
Long/short Equity

0.00 
6.08 
Emerging Markets 
0.36 
7.83 
Table 2 shows the average skewness and
kurtosis found in the returns of individual
hedge funds from various strategy groups.
From the table it is clear that the average
hedge fund's returns tend to be far from
normally distributed and may exhibit significant
negative skewness as well as substantial
kurtosis. Put another way, hedge fund returns
may exhibit relatively low standard deviations
but they also tend to provide skewness and
kurtosis attributes that are exactly opposite
to what investors desire. It is this whole
package that constitutes hedge fund risk,
not just the standard deviation.
The skewness and kurtosis properties of
hedge funds should not come as a complete
surprise. If we delve deeper into the return
generating process it becomes obvious that
most spread trading and pseudoarbitrage
will generate these features by their very
nature as the profit potential of trades
will typically be a lot smaller than their
loss potential. Consider a merger arbitrage
fund for example. When a takeover bid is
announced the share price of the target
will jump towards the bid. It is at this
price that the fund will buy the stock.
When the takeover proceeds as planned the
fund will make a limited profit equal to
the difference between the relatively high
price at which it bought the stock and the
bid price. When the takeover fails, however,
the stock price falls back to its initial
level, generating a loss that may be many
times bigger than the highest possible profit.
Spread traders are confronted with a similar
payoff profile. When the spread moves back
to its perceived equilibrium value they
make a limited profit, but when the market
moves against them they could be confronted
with a much larger loss. This is why strategies
like this are sometimes referred to as "picking
up nickels in front of a steamroller".
Of course, there is no reason why a trader
could not get lucky and avoid getting hit
by the steamroller for a long period of
time. This does not mean that the risk was
never there, however. It always was. It
just never materialized so it does not show
from the trader's track record.
5. HEDGE FUND SHARPE RATIOS
To evaluate hedge fund performance many
investors use the Sharpe ratio, which is
calculated as the ratio of the average excess
return and the return standard deviation
of the fund being evaluated. When applied
to raw hedge fund return data, the relatively
high means and low standard deviations offered
by hedge funds lead to Sharpe ratios that
are considerably higher than those of most
benchmarks. Whilst this type of analysis
is widely used, it is not without problems.
First, survivorship bias, backfill bias
and autocorrelation will cause investors
to overestimate the mean and underestimate
the standard deviation. Second, the Sharpe
ratio does not take account of the negative
skewness and excess kurtosis observed in
hedge fund returns. This means that the
Sharpe ratio will tend to systematically
overstate true hedge fund performance. There
tends to be a clear relationship between
a fund's Sharpe ratio and the skewness and
kurtosis of that fund's return distribution.
High Sharpe ratios tend to go together with
negative skewness and high kurtosis. This
means that the relatively high mean and
low standard deviation offered by hedge
funds is not a free lunch. Investors simply
pay for a more attractive Sharpe ratio in
the form of more negative skewness and higher
kurtosis.
Figure 1: Tradeoff
between Median, Standard Deviation and Skewness.
Figure 2: Sharpe Ratios
for Different Skewness Levels.
Another way to look at this is to use ordinary
put and call options to create distributions
that have exceedingly nonnormal characteristics.
Starting with the (approximately normal)
return distribution of the index we can
increase the skewness of that distribution
by buying puts on that index for example.
Likewise, we can reduce skewness by selling
calls on that index. When we calculate the
median (for skewed distributions this is
a better measure of location than the mean),
standard deviation and skewness of such
distributions and plot those graphically
we obtain a graph as in figure 1, which
shows the median return as a function of
the standard deviation and skewness. From
the graph we see that for a given level
of standard deviation lower (higher) skewness
produces a higher (lower) median. Alternatively,
we could of course say that for a given
median lower skewness produces a lower standard
deviation and vice versa. From the graph
in figure 1 we can derive (medianbased)
Sharpe ratios for different skewness levels.
The result is shown in figure 2, where the
slope of each line equals the Sharpe ratio
for the given level of skewness. Obviously,
the lower the skewness level, the higher
the Sharpe ratio will be. This shows how
wrong it can be to evaluate fund managers
that produce returns with different degrees
of skewness with the same benchmark Sharpe
ratio. Different skewness levels require
different benchmark Sharpe ratios, higher
when skewness is negative and lower when
skewness is positive. If not, the good guys,
that produce positively skewed returns,
will end up being punished while the bad
guys are rewarded.
6. HEDGE FUND ALPHAS
Another performance measure often used
is Jensen's alpha. The idea behind alpha
is to first construct a portfolio that replicates
the sensitivities of a fund to the relevant
return generating factors and then compare
the fund return with the return on that
portfolio. If the fund produces a higher
average return, this can be interpreted
as superior performance since both share
the same return generating factors. The
main problem with this approach lies in
the choice of return generating factors.
As mentioned before, we have little idea
what factors really generate hedge fund
returns. As a result, investors that calculate
hedge funds' alphas are likely to leave
out one or more relevant risk factors. This
will produce excess return where in reality
there is none. Good examples of often forgotten
but extremely important risks are credit
and liquidity risk. So far, no study of
hedge fund performance has correctly figured
in credit or liquidity risk as a source
of return, despite the fact that some hedge
funds virtually live off it.
Table 3: Regression
Individual Hedge Fund Alphas on Autocorrelation
Coefficients

Average Alpha

Average AC (1) 
Regression
Coefficient 
Merger Arbitrage 
1.20

0.13 
1.1356 
Distressed Securities

0.89

0.25 
0.8720 
Equity Market Neutral

0.40 
0.08 
0.3112 
Convertible Arbitrage

0.97

0.30 
1.2975 
Global Macro 
0.26

0.30 
0.2864 
Long/short Equity

0.94

0.09 
0.8954 
Emerging Markets 
0.33

0.15 
0.3680 
Providing liquidity can be expected to
be compensated by a higher average return.
However, when this is not taken into account,
we will find alpha where there is in fact
none. Table 3 provides a simple example.
For individual funds in the various strategy
groups, table 3 shows (a) the average alpha
assuming the stock and bond market are the
only relevant risk factors, and (b) the
average 1month autocorrelation coefficient
found in these funds monthly returns. Since
the autocorrelation found in hedge fund
returns primarily stems from markingtomarket
problems in illiquid markets, we can use
the autocorrelation coefficient as a measure
of the liquidity risk taken on by a fund.
From the table we see that there tends to
be a positive relationship between alpha
and autocorrelation. This is also confirmed
by the last column, which shows the results
of regressing individual funds' alphas on
their autocorrelation coefficients. All
regression coefficients are positive and
significant (tvalues not reported), meaning
that in every category the funds that take
most liquidity risk also tend to be the
funds with the highest alphas.
The above makes it very clear that when
it comes to hedge funds, traditional performance
evaluation methods like the Sharpe ratio
and alpha can be extremely misleading. A
high Sharpe ratio or alpha should not be
interpreted as an indication of superior
manager skill, but first and foremost as
an indication that further research is required.
One can only speak of superior performance
if such research shows that the manager
in question generates the observed excess
return without taking any unusual and/or
catastrophic risks. Unfortunately, simply
studying a manager's past returns will not
be enough. Apart from the fact that most
hedge fund managers do not have much of
a track record to study, extreme events
only occur infrequently so that it is hard
if not impossible to identify the presence
of catastrophic risk from a relatively small
sample of returns. Consider the following
example. A substantial portion of the outstanding
supply of catastrophelinked bonds is held
by hedge funds. These bonds pay an exceptionally
high coupon in return for the bondholder
putting (part of) his principal at risk.
Since the world has not seen a major catastrophe
for some time now, these bonds have performed
very well and the available return series
show little skewness. However, this does
not give an accurate indication of the actual
degree of skewness as when a catastrophe
does eventually occur, these bonds will
produce very large losses.
There are no shortcuts to hedge fund selection.
After properly controlling for the risks
involved, small funds do not perform better
than larger funds, young funds do not perform
better than older funds, closed funds do
not perform better than open funds, etc.
Proper hedge fund selection is first and
foremost a matter of asking the right questions
and doing one's homework. There are various
due diligence question lists available on
the internet and more and more institutions
develop their own. The use of such lists
harbours its own risks, however. First,
it may lead to a more and more mechanical
application where getting all the questions
answered becomes more important than correctly
interpreting the answers. Second, in an
attempt to offload as much responsibility
and job risk as possible, especially institutional
investors will add more and more questions
to the list, thereby wasting more and more
of hedge fund managers' time. When setting
up a due diligence procedure, investors
must remember that one of the most important
goals is to obtain proper insight in the
true riskreturn profile (including the
relationship with other asset classes) of
the strategy followed. This means asking
a lot of detailed questions about the strategy
and risk management procedures followed,
going home and studying the latter under
many different scenarios. Common sense and
doing one's homework are crucial in alternative
investments.
7. HEDGE FUND DIVERSIFICATION
For riskaverse investors, diversification
is often said to be the only true free lunch
in finance. Unfortunately, this does not
include hedge funds. Although combining
hedge funds into a basket will substantially
reduce the standard deviation of the return
on that portfolio, it can also be expected
to lower the skewness and raise the correlation
with the stock market.
Table 4: Individual
Hedge Fund and Hedge Fund Portfolio Risks

Individual Hedge
Funds 
Portfolio of Hedge
Funds 

Standard
Deviation 
Skewness 
Corr S&P 500

Standard
Deviation 
Skewness 
Corr S&P
500 
Merger Arbitrage 
1.75 
0.50 
0.47

1.04 
2.19 
0.56 
Distressed Securities

2.37 
0.77 
0.37

1.54 
2.60 
0.47 
Equity Market Neutral

2.70

0.40

0.07

1.14 
0.41 
0.19 
Convertible Arbitrage

3.01 
1.12 
0.19

1.64 
1.35 
0.38 
Global Macro 
5.23 
1.04 
0.14 
2.43 
0.87 
0.37 
Long/short Equity

5.83 
0.00 
0.35 
2.95 
0.29 
0.63 
Emerging Markets 
8.33 
0.36 
0.44

6.15 
0.65 
0.67 
Table 4 shows the standard deviation, skewness
and correlation with the S&P 500 of
the average individual hedge fund in the
various strategy groups as well as an equallyweighted
portfolio of all funds in each group. From
the table we see that forming portfolios
leads to a very substantial reduction in
standard deviation. With the exception of
emerging market funds, the portfolio standard
deviations are approximately half the standard
deviations of the average individual fund.
This signals that the degree of correlation
between funds in the same strategy group
must be quite low. Apparently, there are
many different ways in which the same general
strategy can be executed. Contrary to standard
deviation, skewness is not diversified away
and actually drops further as portfolios
are formed. With the exception of equity
market neutral funds, the portfolio skewness
figures are lower than for the average individual
fund, with especially merger arbitrage and
distressed securities funds standing out.
Despite the lack of overall correlation,
it appears that when markets are bad for
one hedge fund, they tend to be bad for
other funds as well. Finally, comparing
the correlation with the S&P 500 of
individual funds and portfolios we clearly
see that the returns on portfolios of hedge
funds tend to be much more correlated with
the stock market than the returns on individual
funds. Although individual hedge funds may
be more or less market neutral, the portfolios
of hedge funds that most investors actually
invest in definitely are not.
8. HEDGE FUNDS AND EQUITY
It is often argued that given their relatively
weak correlation with other asset classes,
hedge funds can play an important role in
risk reduction and yield enhancement strategies.
Again, this diversification service does
not come for free, however. Although the
inclusion of hedge funds in a portfolio
may significantly improve that portfolio's
meanvariance characteristics, it can also
be expected to lead to significantly lower
skewness as well as higher kurtosis. Table
5 shows what happens to the standard deviation,
skewness and kurtosis of the portfolio return
distribution if, starting with 50% stocks
and 50% bonds, we introduce hedge funds
(modelled by the average equallyweighted
random portfolio of 20 funds) in a traditional
stockbond portfolio. As expected, when
hedge funds are introduced the standard
deviation drops significantly. This represents
the relatively low correlation of hedge
funds with stocks and bonds. This is the
good news. The bad news, however, is that
a similar drop is observed in the skewness
of the portfolio return. In addition, we
also observe a rise in kurtosis.
Table 5: Effects of
Combining Hedge Funds with Stocks and Bonds
% HF 
SD 
Skewness 
Kurtosis 
0 
2.49 
0.33 
2.97 
5 
2.43 
0.40 
3.02 
10 
2.38 
0.46 
3.08 
15 
2.33 
0.53 
3.17 
20 
2.29 
0.60 
3.28 
25 
2.25 
0.66 
3.42 
30 
2.22 
0.72 
3.58 
35 
2.20 
0.78 
3.77 
40 
2.18 
0.82 
3.97 
45 
2.17 
0.85 
4.19 
50 
2.16 
0.87 
4.41 
Especially the skewness effect goes far
beyond what one might expect given the hedge
fund skewness results in table 4. When things
go wrong in the stock market, they also
tend to go wrong for hedge funds. Not necessarily
because of what happens to stock prices
(after all, many hedge funds do not invest
in equity), but because a significant drop
in stock prices will often be accompanied
by a widening of credit spreads, a significant
drop in market liquidity, higher volatility,
etc. Since hedge funds are highly sensitive
to such factors, when the stock market drops,
hedge funds can be expected to show relatively
bad performance as well. Recent experience
provides a good example. Over the year 2002,
the S&P 500 dropped by more than 20%
with relatively high volatility and substantially
widening credit spreads. Distressed debt
funds, at the start of 2002 seen by many
investors as one of the most promising sectors,
suffered substantially from the widening
of credit spreads. Credit spreads also had
a negative impact on convertible arbitrage
funds. Stock market volatility worked in
their favour, however. Managers focusing
on volatility trading generally fared best,
while managers actively taking credit exposure
did worst. Equity market neutral funds suffered
greatly from a lack of liquidity, while
long/short equity funds with low net exposure
outperformed managers that remained net
long throughout the year. As a result, overall
hedge fund performance in 2002 as measured
by the main hedge fund indices was more
or less flat.
9. HEDGE FUNDS AND MEANVARIANCE ANALYSIS
When studied in a meanvariance framework,
the inclusion of hedge funds in a portfolio
appears to pay off impressive dividends:
equitylike returns with bondlike risk.
Since meanvariance analysis only looks
at the mean and standard deviation, however,
it skips over the fact that with hedge funds
more attractive, meanvariance attributes
tend to go hand in hand with less attractive
skewness and kurtosis properties. In addition,
it skips over the significant coskewness
between hedge funds and equity.
Table 6: MeanVariance
Optimal Portfolios


Std. Dev. 
Mean 
% Stocks 
% Bonds 
% HFund 
Skew 
Kurtosis 
2 
0.77 
32.79 
67.21 

0.04 
3.23 
2.5 
0.95 
50.31 
49.69 

0.34 
2.97 
3 
1.10 
64.68 
35.32 

0.55 
3.24 
3.5 
1.23 
77.86 
22.14 

0.68 
3.57 
4 
1.36 
90.44 
9.56 

0.77 
3.86 

Stocks, Bonds
and Hedge Funds 
2 
0.92 
18.07 
26.81 
55.12 
0.82 
4.39 
2.5 
1.06 
29.95 
10.75 
59.30 
0.99 
5.26 
3 
1.20 
45.07 
0 
54.93 
1.07 
5.47 
3.5 
1.30 
67.08 
0 
32.92 
1.00 
4.81 
4 
1.39 
86.14 
0 
13.86 
0.89 
4.32 
We performed two standard meanvariance
optimisations; one with only stocks and
bonds and one with stocks, bonds and hedge
funds as the available asset classes. The
results of both optimisations can be found
in table 6. Starting with the case without
hedge funds (top panel), we see that moving
upwards over the efficient frontier results
in a straightforward exchange of bonds for
stocks. Since stocks have a higher mean
than bonds, the mean goes up. While this
happens, the skewness of the return distribution
drops in a more or less linear fashion as
stock returns are more negatively skewed
than bond returns. The kurtosis of the return
distribution remains more or less unchanged.
Next, we added hedge funds and recalculated
the efficient frontier (bottom panel). Moving
over the efficient frontier, we see that
at first bonds are exchanged for stocks
while the hedge fund allocation remains
more or less constant. When the bond allocation
is depleted, the equity allocation continues
to grow but now at the expense of the hedge
fund allocation. Similar to the case without
hedge funds, if we increase the standard
deviation, the mean goes up, while the skewness
of the return distribution goes down. Unlike
what we saw before, however, skewness drops
as long as bonds are being replaced by equity
but rises again as hedge funds start to
be replaced by equity. The lowest level
of skewness is reached when the bond allocation
reaches 0%, which is in line with our earlier
observation that in terms of skewness hedge
funds and equity are not a good mix.
Comparing the case with and without hedge
funds we see a significant improvement in
the mean, especially for lower standard
deviations. However, we also see a major
deterioration in skewness and kurtosis,
with the largest change taking pace exactly
there where the mean improves most. From
this it is painfully clear that standard
meanvariance portfolio decisionmaking
is not appropriate when hedge funds are
involved as it completely ignores these
effects. When hedge funds are involved investors
need a decisionmaking framework that also
incorporates the skewness and kurtosis of
the portfolio return distribution. Since
portfolios with low skewness will tend to
exhibit the most attractive meanvariance
properties, meanvariance optimisers are
essentially nothing more than skewness minimizers.
When bringing together different assets
or asset classes in a meanvariance framework,
we implicitly assume that these are comparable
in terms of liquidity and the quality of
the inputs used. With stocks and bonds this
assumption is often justified. When alternative
investments are introduced, however, this
is no longer true. Many hedge funds employ
long lockup and advance notice periods.
Such restrictions are not only meant to
reduce management costs and cash holdings
but also allow managers to aim for longerterm
horizons and invest in relatively illiquid
securities. As a result, hedge fund investments
are substantially less liquid than stocks
or bonds. In addition, since the available
hedge fund data cover such a short and exceptional
period we have little idea what the return
generating process behind hedge funds looks
like and what constitutes normal behaviour
and what not. This illiquidity and additional
uncertainty should be properly incorporated
in the portfolio optimization process. If
not, hedge funds are artificially made to
look good and consequently too much money
will be allocated to them.
10. CONCLUSION
Proper hedge fund investing requires a
much more elaborate approach to investment
decisionmaking than currently in use by
most investors. The available data on hedge
funds should not be taken at face value,
but should first be corrected for various
types of biases and autocorrelation. Tools
like meanvariance analysis and the Sharpe
ratio that many investors have become accustomed
to over the years are no longer appropriate
when hedge funds are involved as they concentrate
on the good part while completely skipping
over the bad part of the hedge fund story.
Investors also have to find a way to figure
in the long lockup and advance notice periods,
which make hedge fund investments highly
illiquid. In addition, investors will have
to give weight to the fact that without
more insight in the way in which hedge funds
generate their returns it is very hard to
say something sensible about hedge funds'
future longerrun performance. The tools
to accomplish this formally are not there,
meaning that more than ever investors will
have to rely on good oldfashioned common
sense and doing their homework. Given the
lemminglike behaviour of especially institutional
investors, however, for most this may well
turn out to be too much to ask for.
It has also become clear that hedge funds
are not the miracle cure that many investors
think or have been told they are. Again,
this boils down to a matter of common sense.
Anyone who is well calibrated to the world
we live in will have extreme difficulty
believing that there is a significant (and
growing) number of people that are able
to systematically beat the market to such
an extent that even after deducting "2
plus 20" or even more the investor
is left with a superior return. Hedge funds
offer investors a way to obtain a lower
standard deviation and/or higher expected
return but only at the cost of lower skewness
and higher kurtosis. Whether the resulting
portfolio makes for a more attractive investment
than the original is purely a matter of
taste, not a general rule.
