Intelligent Hedge Fund Investing
Successfully Avoiding Pitfalls through Better Risk Evaluation
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Turan G. Bali and Suleyman Gokcan


Non-Normally distributed returns are the norm in financial return series. The most widely documented departure from Normality is too many large returns, both positive and negative (and high autocorrelation in large returns). This non-Normal reality is a problem for traditional parametric risk measurement, which relies on the assumption of Normality.

If returns were Normally distributed, then a 2.5 daily standard deviation loss event would happen about one day a year. In practice, a rule of thumb is to expect a 4 standard deviation loss event about once a year.

Bali and Gokcan put forward an alternative parametric approach to VaR estimation that is robust to these types of deviations from the Normal probability distribution.

In the usual parametric VaR calculation, the standard deviation of portfolio returns is multiplied by a constant, e.g., 2.33, which is based on the known quantiles of the Normal distribution. In their alternative method, this multiplicative constant is modified to incorporate information about the skewness and excess kurtosis in the return distribution.

Bali and Gokcan examine the returns to 17 hedge fund strategy indexes, all of which exhibit statistically significant departures from Normality, including the negative skewness we have come to expect in hedge fund returns.

They show that their alternative to the standard parametric VaR results in a very close correspondence to the empirically observed tail percentiles they examine, much closer than the usual parametric approach, which significantly underestimates the empirical tail percentile. Their estimates are also better than when they estimate VaR using an extreme value approach, a result they argue that is further enhanced by the greater ease of applying their approach.

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  1. Other research by Turan G. Bali:
    SSRN website
  2. Homepage of Turan G. Bali:

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