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.

    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.

Eileen Cohen is a portfolio manager in U.S. equities for JP Morgan Fleming Asset Management in New York. William H. Overgard is president of WHO Investment Consulting in Wilton, Conn., and can be reached at (203) 834 2871.