The hedge-fund return patterns are more important than historical returns.

In our first article about hedge funds for Financial
Advisor, we indicated that the pattern of returns was more important
than historical return levels in selecting hedge funds.(1) The pattern
of returns is a good proxy for understanding the risk of the strategy
even though there are many other ways of defining risk. Some are
statistically based, while others are explained in terms of dollar
loss.

Equally important is the expression of risk that
manifests itself in a comfort level. Which expression of risk is
correct? Most important, how should an investor in hedge funds use the
various ways of describing risk to determine which is a suitable
investment?

This article will discuss some of the most useful
and frequently used measures of risk. We will describe their importance
and influence, but also highlight their flaws so that the investor can
be aware of some commonly used measures that may be misleading. The
investor can then determine which measures of risk are most appropriate
for his investment objectives.

Each investor has a different set of criteria that
determine the success or failure of her investments. Such criteria may
include achieving a wealth goal, avoiding loss, maintaining some
liquidity in order to provide for planned or unexpected spending needs,
or avoiding volatility in order to sleep better. In other words, the
definition of risk is idiosyncratic and thus different for each person
depending on one's needs, biases and perceptions. There is no right or
wrong measure of risk nor does just one measure address the question of
"What is a risky investment?" However, if a measure is used
incorrectly, inappropriate investments may be made.

Quantitative Measures Of Risk-What They Are And How They Are Used

The ubiquitous measure of risk is volatility or
standard deviation. It is the statistical measure of how much variation
(noise) there is around an average value or outcome. For example, based
on the average, one may expect that the S&P 500 Index will deliver
a return of 10% over time.(2) However, in any given year, the market
can deliver more than 10% or less, even negative returns. The measure
of volatility around the 10% return has been 15% per year. Hence, one
may conclude that the market is expected to return 10% per year +/-15%
in any given year and be correct two-thirds of the time.(3)

This is a wide variation of returns in any given
year and yet many investors accept this volatility, expecting an
average return of 10% in the long run, not realizing that bad periods
may coincide with the need for funds or that several bad periods in a
row may cause the investor excess anxiety and lead to a decision to not
invest. The use of standard deviation as described above is a useful
notion but relies on the premise that over time returns follow a normal
(bell shaped) distribution, with returns above average as likely as
returns below the average. The idea that most outcomes over time occur
around a central measure, with few outlying events, is why the use of
the traditional measure of standard deviation is useful. But is it a
realistic measure of hedge fund returns?

The notion of normality is quite useful in many
investment situations. However hedge funds, for the most part, defy the
concept of normal return patterns. Specifically, there may be a greater
tendency to have large losses than large gains, or a larger likelihood
that returns are significantly better or worse than would be expected.
The return distribution that has a greater downside is said to have
negative skewness. The distribution that has a greater gain or loss
than would be expected from a normal distribution is said to have
excess positive kurtosis, or is leptokurtic. Chart 1 compares a
distribution that has negative skewness with a normal curve that has
the same mean and standard deviation. Chart 2 shows a distribution that
has the same mean and standard deviation but is leptokurtic and thus
has fat tails. If an investor is only considering the mean and standard
deviation, and there is skewness, kurtosis or both, the investor will
be frequently surprised, and if the returns are negatively skewed those
surprises could be quite unpleasant.

Table 1 details the monthly average return, standard
deviation of returns, the measures of skewness and kurtosis, and the
annualized Sharpe Ratio (definition following) for each of the 12 most
popular hedge fund strategies.(4,5) As can be observed, many hedge
fund strategies have negative skewness (greater downside events) and
all have positive excess kurtosis (6) (performance events which are
greater than a normal event), making the use of standard deviation and
the reliance upon normal distributions much less relevant for
understanding the true risk of hedge fund investments.(7) More
importantly, if the investor only considers the mean and standard
deviation she will most likely underestimate the possibility of large
losses.

The lack of normality has significant implications
for the way asset allocation is frequently determined and hedge funds
are evaluated. Usually, mean-variance optimization is used to build a
portfolio of different strategies to determine the asset allocation for
the degree of risk the investor is willing to take. However,
mean-variance optimization assumes that the returns are normally
distributed. This is a weakness in the analysis because if the returns
are not normally distributed the resulting allocations will not be
optimal and future returns will not be within expectations.

Another risk measure that is commonly used is the
Sharpe Ratio, also shown in Table 1.(8) However, the Sharpe Ratio also
assumes that the return pattern is normally distributed. As we noted
before, this assumption can be misleading if there is skewness and
kurtosis. For example, if we assume an annual 4% risk-free return, the
annualized Fixed-Income Arbitrage Sharpe Ratio is 1.75. Thus, an
investor looking at Table 1 might reasonably assume that Fixed-Income
Arbitrage is an attractive low-risk strategy-a large return per unit of
risk. But if the investor considered the large negative skewness and
very large positive excess kurtosis of Fixed-Income Arbitrage, the
investor would reach a different conclusion. This is particularly
important if one is concerned about large dollar losses.

The histogram of monthly returns and a fitted
probability distribution for Fixed-Income arbitrage are shown in Chart
3.(9) It can be seen that the performance experience is clustered about
the mean, but there have been large losses. Thus, while most of the
time the returns were within acceptable ranges, there were big
surprises that had large negative consequences.

The results displayed in Table 1 and Chart 3 are
based on averages for the strategies. Within each strategy, many funds
exhibit return distributions that are much more radical than what is
shown by the averages. Specifically within fixed-income arbitrage,
three funds have been in existence for three or more years that have
negative skewness in excess of -5 and excess kurtosis greater than 50.

Table 2 illustrates, for each of the 12 major hedge
fund strategies, what percentage of each has significant skewness and
kurtosis. Table 2 also shows the wide range of skewness and kurtosis
for funds within the strategy. For example, in Fixed-Income Arbitrage,
29% (close to one in three) of the funds we examined had measures of
significant skewness, while 40% (two in five) of the funds had
significant measures of kurtosis. The chances are fairly high, in our
opinion, that investors will be disappointed relative to expectation
with many of the managers they select.

Other Risk Measures To Consider

If hedge fund returns are not normally distributed
and the use of means, standard deviations and Sharpe Ratios can be
misleading, are there other measures an investor should consider? We
will discuss two additional risk measures that are getting more
attention, as they are particularly useful when returns are not
normally distributed.

Semi-deviation measures the volatility of the
returns that occur below the average return. Table 3 depicts the
monthly standard deviation and semi-deviation measures. Generally, if
the returns have negative skewness the semi-deviation will be greater
than the standard deviation, as can be seen with the Event Driven,
Convertible Arbitrage, Fixed-Income Arbitrage, Distressed and Value
strategies.(10) Those strategies that have positive skewness generally
will have a semi-deviation smaller than the standard deviation. When
selecting funds within a strategy or when building a portfolio of
different strategies, using semi-deviation instead of standard
deviation may result in a bias that exhibits less negative or more
positive skewness, resulting in a better investment experience.

However, how many investors define their return
objectives around an average experience? A second risk measure builds
on the idea of semi-deviation, but captures the downside risk relative
to a minimum return expectation. This measure is known as downside
deviation. In our example in Table 3 we provide the downside deviation
measures for each of the 12 strategies for an investor who has a return
objective of 10%.

The concept of downside deviation is best captured
in the statistic known as the Sortino Ratio. The Sortino Ratio also
measures return per unit of risk, similar to the Sharpe Ratio; however,
the ratio uses downside deviation as its risk component versus standard
deviation in the Sharpe Ratio calculation.

Depending upon the ratio used, each of the
strategies listed in the previous table would have a different rank.
Table 4 lists the ranking for each strategy using both the Sharpe and
Sortino Ratios. For example, convertible arbitrage is the least risky
when looking at the Sharpe Ratio, while small cap is the least risky
when considering the Sortino Ratio. While it is difficult to draw any
definitive conclusions, the Sortino Ratio will tend to favor those
strategies that have high compound returns and low negative skewness
and kurtosis (i.e., small cap). For most investors, a ratio built
around their targeted returns and incorporating the effects of skewness
should be attractive.

What If Liquidity Is Important?

For investors who may have liquidity requirements
and therefore cannot be exposed to periodic losses, and for those
investors who are inclined to sell their investments after experiencing
unexpected losses, either Value at Risk (VaR) and/or drawdown are
important measures.

VaR is based on the probability distribution of
periodic returns (weekly or monthly, for example) and is expressed in
dollars lost at a given probability level. It is the limit of the
amount that the investor can expect to lose over the periodic interval
at the stated confidence interval. Thus, VaR can be thought of as the
"pain threshold" expressed in dollars, and the probability of this
occurrence under normal conditions.

What makes this measure useful is that an investor
can assess how much money could be lost over any time period of
interest. The calculation of VaR takes into account the pattern of
returns to create a probability distribution from which one can
estimate the future experience. Because return patterns for hedge funds
are not normally distributed, one must be careful in using VaR
estimates, which may assume normality.

If this measure is provided to you, ask whether or
not the underlying return patterns have a normal distribution
experience or if there is evidence of skewness to the shape of the
return pattern. Our previous example using Fixed-Income Arbitrage
underscores just how much one can underestimate volatility and
skewness. A VaR calculation used alone, without understanding some of
the other risk concepts suggested so far, could lead to underestimating
the potential for losing money.

Drawdown is another "pain threshold" concept.
Drawdown measures the amount of capital that is lost from the peak of
performance to the trough of performance. Some funds can have large
(well in excess of 25%) and frequent drawdowns. Obviously, for the
investor who has a bias against the loss of capital or who may
have a periodic need for liquidity, a tendency for large drawdowns
should be avoided. What may not be so obvious, but may be considered an
important point in hiring or keeping a manager, is the speed of the
drawdowns. If one fund has a tendency for large drawdowns that occur
over several months, it may be less of a concern because the investor
will have adequate time to redeem assets reducing the potential for
loss. On the other hand, if a fund exhibits a tendency for large
drawdowns that occur over very short periods, it should probably be
avoided because the investor will not be able to get out due to lockups
and infrequent redemption opportunities.

Understanding drawdown is also an important investment consideration
because recouping capital loss is difficult. For example, if a fund
lost 75% of its capital, it needs to gain back 300% just to break even.

Drawdown also has business risk implications, which
are important to all investors. This number inflicts pain not only to
the investor in terms of dollars lost, but also to the investment
manager who is highly dependent on performance fees to run the
business. Most funds have a "high water mark" which prevents them from
being paid a performance fee until losses are fully recovered. Thus, if
a fund has a large drawdown and does not earn its performance fee, it
will not be able to retain high-quality investment professionals, which
could lead to continued poor performance. Small funds, in particular,
may be highly dependent on performance fees to pay some of their
business and organization costs. In the absence of performance the
business may fold.

Business Risk-An Important Component

While business risk is closely tied with capital
drawdowns for the reasons described previously, investors should also
be cognizant of other forms of business risk that can lead to
disappointing performance. If a fund is not well managed or the staff
does not perceive the opportunity for an attractive career, staff
defections will occur, which at a minimum will be a distraction to
senior management. At the worst, poor management can lead to poor
performance and the vicious circle continues until the firm needs to
close its doors. Investors considering hedge funds must look beyond the
returns and the statistics. They should conduct comprehensive due
diligence to ensure that they are investing in a business that is well
managed and will remain intact, in order to ensure that their
investment will have a good chance of meeting return expectations over
reasonable periods of time.

The risk of selecting a firm which will not be
around in three years is high. We believe that it is important to
evaluate a company as one would a business, and assess the following:
What is the business plan? What is the infrastructure to support such a
plan? How are the employees paid? How much staying power does the firm
have if there is a year of bad performance? What about two years of bad
performance? Conduct a background check. While SEC registration for
hedge funds will be mandatory beginning in 2006, this registration
requirement will only provide a small level of comfort to assess
business risk and will not substitute for thorough due diligence by
experienced analysts.

Conclusion

Understanding risk when investing in a hedge fund is
extremely critical. We know that the traditional measures of risk
(volatility, standard deviation of returns and Sharpe Ratios) do not go
far enough in helping to frame investors' expectations. Other measures,
such as drawdown, Sortino Ratio and VaR, can provide additional insight
into a fund's level of risk.

In framing any analysis or discussion, it is helpful
to understand that there are other considerations to contemplate when
measuring and thinking about risk. Perhaps, though, the most important
consideration is the need for any investor to take a step back and
reconsider why she is considering a hedge fund investment, and then ask
again whether or not a particular strategy fits the risk profile, which
may lead to a successful investment.