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Alternative Approaches to Calculating Value-at-Ris

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NEW YORK ( Fund blowups slant hedge fund performance measures, causing ?fat tails? in the distribution of returns. Methods that take account of this issue give better results in estimating value-at-risk, but some are difficult to use, a new study shows.

Suleyman Gokcan, vice president and head quantitative analyst at Citigroup?s fund of funds unit, and Turan Bali, associate professor of finance at Baruch College of the City University of New York, compared four models, including the common ?thin-tailed? normal distribution, using strategy-level monthly index data.

?We tested if the return distributions of the strategies are normal. For most of them, we found that they are not normal. There is strong skewness, mostly negative, as well as kurtosis,? explained Mr. Gokcan. ?So, you should not assume the distribution is normal in estimating VaR. The other distributions take into account this skewness and kurtosis, in one way or another.?

Two of the alternatives to the normal distribution performed best. But one, the Cornish-Fisher expansion in computing VaR thresholds for hedge fund index returns, is easier to obtain.

Catastrophic Market Risk

Value-at-Risk shows how much the investor likely will lose if something goes wrong. It is a measure of the maximum expected loss on a portfolio over a given period with a certain degree of probability. This metric became popular especially after the Long-Term Capital Management episode, which drew attention to the effect of catastrophic market risk on hedge funds.

One of the articles cited in the new study found that LTCM severely underestimated its risk due to its reliance on short-term history and risk concentration. While statistical analyses of the tails of the distribution can sound abstract, these are ways of addressing a question of great importance to hedge fund investors.

To determine which model best approximates the actual distribution, Messrs. Gokcan and Bali calculated VaR for monthly HFR index data covering 17 hedge fund strategies from January 1990 to June 2002. Two different measures of deviation between the calculated and historical returns indicate much greater errors for the normal distribution than the other three methods.

One of these alternatives, the fat-tailed generalized error distribution, led to higher errors than the other two, an extreme value approach that approximates the tails of the distribution asymptotically and the Cornish-Fisher expansion that takes into account the skewness and kurtosis exhibited by the data in question.

?The extreme value approach and Cornish-Fisher were the two best models, but Cornish-Fisher is easier to estimate, so for practical reasons it is preferable,? said Mr. Gokcan. ?It does not require as large a number of observations as the extreme value model. Also, in the extreme value method some restrictions have to be put on the parameters.?

Cornish-Fisher also can be applied to normally distributed data because in the formula the skewness and kurtosis parameters disappear, he pointed out. ?Although the extreme value approach provides slightly more accurate estimates of the actual VaR thresholds, practitioners may still be willing to use the Cornish-Fisher expansion because of its simplicity,? the authors conclude.

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