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Futures Lab: Insight on how to make the tails of the distribution work for you in hedge fund investing

Tuesday, March 10, 2009


Making the Tails Work for You

A study by three researchers from Graham Capital Management shows that systematic macro and dedicated short bias investments have a positive skew – fat right tails – while most other hedge fund strategies have a negative skew. The authors, Peter Park, Oguz Tanrikulu and Guodong Wang, conclude that conventional measures are not accurate indicators of risk. Below is an edited excerpt from their paper.

The most commonly used metric of hedge fund strategy performance is the Sharpe ratio. This is the ratio between the annualized return and annualized volatility; it implicitly assumes that volatility is a full measure of risk. When returns are normally distributed, the Sharpe ratio is an appropriate measure of reward versus risk.

But when returns are not normally distributed, the Sharpe ratio by itself may lead to a mis-estimation of the potential reward versus risk. One way to analyze this issue is to look at skew, which measures a distribution's symmetry. A skew of zero indicates that the distribution is symmetric; negatively skewed distributions have thicker left tails than right, whereas positively skewed distributions have thinner left tails than right.

All else being equal, an investor would prefer strategies with the most positive skew—thick right tail and thin left tail. These would be strategies with large positive returns and the fewest occurrence of large negative returns.

Another method of measuring this characteristic is the ratio of upside to downside volatility. A low upside-to-downside volatility ratio implies that the underlying strategy has large losses more frequently than large gains. This undesirable property can also be detected through a negative skew with high excess kurtosis—a fat left tail.

The table below contains annualized statistics for major hedge fund style indexes based on monthly returns data from January 1994 to December 2008. The starting date is chosen to coincide with the beginning of CSFB/Tremont hedge fund data, which is used for all strategies except systematic global macro.

The Barclays Systematic Traders Index was chosen to represent systematic global macro. Funds in this strategy may also be classified as global macro, managed futures or trend-following/Commodity Trade Advisor. CSFB/Tremont does not report an appropriate index for this strategy.

We find that most strategies have a low upside/downside volatility ratio, with only systematic traders and dedicated short bias having a ratio around or above one. A low upside/downside volatility ratio would indicate that the distribution of returns is skewed towards the left. This is confirmed by analyzing skewness. Of the styles with low upside/downside volatility ratios, most have negative skew, as shown in the table.

To summarize, except for systematic traders and dedicated short bias, hedge fund styles have low upside/downside volatility, most have negative skew, and most have high excess kurtosis.

Descriptive Statistics of Monthly Returns
  Annualized ReturnUpside/Downside VolSkew
Systematic Traders 6.8%0.90.22
Equity Market Neutral5.6% 0.1-11.9
Fixed Income Arb3.5%0.2-4.6
Event Driven9.6%0.3-2.7
Long/Short Equity9.7% 0.70.02
Convertible Arb5.5%0.3-3.5
Dedicated Short Bias-
Emerging Markets 6.7%0.7-0.7

Given the skew statistics, it is likely that monthly returns are not normally distributed. Thus it is not surprising that both systematic traders and dedicated short bias are in the bottom half of strategies when the Sharpe ratio is the metric used to measure performance.

A statistical test showed that only systematic trader returns are likely to be normally distributed. For all other strategy types, we can reject the null hypothesis of a normal distribution at the 99% confidence level. We can conclude that the Sharpe ratio is not a good measure of reward per unit risk.

It is highly probable that when a Sharpe ratio calculated from monthly returns is used to assess risk, the estimated risk is too high for systematic traders and dedicated short bias, while it is too low for the remaining strategy types.

This article was published in Opalesque Futures Intelligence.
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