Introducing the normal equivalent to evaluate hedge fund performance

I develop normal equivalents to assess the impact of non-normal return distributions on investor utility using the power utility function. From Taylor series approximations and simulated return data generated from both a non-central t distribution and normal distribution, I find that the statistical rejection of normality is not strong enough to determine that a sample distribution is economically meaningful. A sample of 373 hedge funds, of which 86% reject normality using the Jarque-Bera test, with complete monthly data from 1996 to 2005 is analyzed with the normal equivalents. As a stand alone investment, only 4% of them have return distributions that would cause an investor to be willing to trade ten basis points (per month) for the normal distribution. It does not appear that managers are taking positions that are utility detracting, which would have negative skewness and excess kurtosis, because there are a nearly equal number being utility enhancing (7) as utility detracting (9). The Sharpe ratio's use of the standard deviation to measure risk is generally robust; 90% of the funds had Sharpe ratios that were between 3.9% underestimated and 4.5% overestimated. None of the Sharpe ratios computed with normal equivalents were statistically different than the standard Sharpe ratio. Overwhelmingly, this sample made a positive contribution to a portfolio of stocks and T-bills, even though funds with different strategies impacted the allocations of stocks and T-bills differently. Also, even though 78% of these constructed portfolios reject normality, none of them have non-normality that would substantially impact the utility of an investor. The Sharpe ratio is overestimated for these portfolios by between 0.7% and 2.6% (all positive due to the negative skewness of the portfolios). Hedge fund rankings based on the Sharpe ratio are reasonable for this group if considered as a member of a portfolio, but analysts using it to compare funds as a stand alone investment should be more cautious.