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The Difficulties in Measuring the Benefits of Hedge Funds Authors: Andreas Signer, Laurent Favre Source: Journal of Alternative Investments, volume 5, number 1 Date: Summer 2002 |
Abstract
It has been widely demonstrated that associating hedge funds with traditional investment improves the efficient frontier: it procures a greater return for the same risk, or a lower risk for the same return. This article contains a recap of the published research on the subject, but here the authors consider the specific problem of hedge fund risk measurement. Most of the studies have used the mean-variance approach, but this approach only considers the first two moments of the distribution of returns and is therefore only suitable for normal distributions. The return distributions of hedge funds frequently exhibit negative skewness and positive kurtosis, so these higher moments of the distribution have to be taken into account when evaluating the risk of hedge funds. Not considering those factors leads to an exaggerated shift in the efficient frontier. This article begins with a description of the limitations of mean-variance analysis for hedge funds and then presents a solution with a new risk measure called modified value-at-risk, which is appropriate for non-normally distributed returns.
Value-at-risk enables the risk of loss to be quantified, but it can only be calculated with an explicit formula for normal distributions. The authors propose using the Cornish-Fisher expansion to adjust VaR for non-normal distributions. The Cornish-Fisher expansion gives the critical value for the level of probability considered, taking skewness and kurtosis into account. The VaR calculation is then carried out using the normal distribution formula, but replacing the critical value for the probability with the value calculated through the Cornish-Fisher expansion.
To illustrate the use of this risk measure, the authors consider an optimisation problem which involves minimising the volatility for a given return when returns are not normally distributed. The objective function is written using the modified critical value for the probability, with the critical value, volatility, skewness and kurtosis all dependent on the optimal weights. The objective function so defined allows us to calculate the portfolio with the minimum modified VaR for a given return, taking return asymmetries and extreme returns into account. It should be noted that this optimisation problem does not require the covariance matrix. A study was performed with a portfolio made up of hedge funds, Swiss equities, international equities and domestic and foreign bonds, over the period 1994-2000. The result shows that when skewness and kurtosis are taken into account, the efficient frontier is less high on the graph, which demonstrates that the risk is underestimated when skewness and kurtosis are not considered.
Finally, as the essential problem for an investor is to determine whether it is useful to include hedge funds in a traditional portfolio, the authors underline how important the consideration of skewness and kurtosis is for that choice. For example, if the skewness and kurtosis of the hedge fund portfolio are less favourable than those of the traditional portfolio, the benefit of including hedge funds will be lower than a simple mean-variance analysis would have led us to believe.
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