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Abstract:
In this paper we investigate the claim that hedge funds offer investors a superior risk-return trade-off. We do so using a continuous time version of Dybvig's (1988a, 1988b) payoff distribution pricing model. The evaluation model, which does not require any assumptions with regard to the return distribution of the funds in question, is applied to the monthly returns of 77 hedge funds and 13 hedge fund indices over the period May 1990-April 2000. The results show that as a stand-alone investment hedge funds do not offer a superior risk-return profile. We find 12 indices and 72 individual funds to be inefficient, with the average efficiency loss amounting to 2.76% per annum for indices and 6.42% for individual funds. Part of the inefficiency cost of individual funds can be diversified away. Funds of funds, however, are not the preferred vehicle for this as their performance appears to suffer badly from their double fee structure. Looking at hedge funds in a portfolio context results in a marked improvement in the evaluation outcomes. Seven of the 12 hedge fund indices and 58 of the 72 individual funds classified as inefficient on a stand-alone basis are capable of producing an efficient payoff profile when mixed with the S&P 500. The best results are obtained when 10-20% of the portfolio value is invested in hedge funds

Abstract:
Using monthly return data on 455 hedge funds over the period 1994-2001 we study the diversification effects from introducing hedge funds into a traditional portfolio of stocks and bonds. Our results indicate that although the inclusion of hedge funds may significantly improve a portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds includes a definite trade-off between profit and loss potential and suggests that, contrary to popular belief, hedge funds might be more suitable for institutional than for private investors. Our results also emphasize the fact that to have at least some impact on the overall portfolio, one has to make an allocation to hedge funds which exceeds the typical 1-3% that many institutions are currently considering.

Hedge funds, diversification, skewness, kurtosis, portfolio

Abstract:
Using monthly return data over the period June 1994 - May 2001 we investigate the performance of randomly selected baskets of hedge funds ranging in size from 1 to 20 funds. The analysis shows that increasing the number of funds can be expected to lead not only to a lower standard deviation but also, and less attractive, to lower skewness and increased correlation with the stock market. Most of the change occurs for relatively small portfolios. Holding more than 15 funds changes little. The population average appears to be a good approximation for the average basket of 15 or more funds. With 15 funds, however, there is still a substantial degree of variation in performance between baskets, which dissolves only slowly when the number of funds is increased. Survivorship bias is largely independent of portfolio size and thus cannot be diversified away. Finally, our efficiency test indicates that one only needs to combine a small number of funds to obtain a substantially more efficient risk-return profile than that offered by the average individual hedge fund.

Hedge fund, portfolio, diversification, survivorship bias, efficiency

Abstract:
Hedge funds exhibit a high rate of attrition that has increased substantially over time. Using data over the period 1994-2001, we show that lack of size, lack of performance and an increasingly aggressive attitude of old and new fund managers alike are the main factors behind this. Although attrition is high, survivorship bias in hedge fund data is quite modest, which reflects the relatively small difference in performance between surviving and defunct funds. Concentrating on survivors only will overestimate the average hedge fund return by around 2% per annum. For small, young, and leveraged funds, however, the bias can be as high as 4-6%. We also find significant survivorship bias in estimates of the standard deviation, skewness and kurtosis of individual hedge fund returns. When not corrected for, this will lead investors to seriously overestimate the benefits of hedge funds. We find fund of funds attrition to be much lower than for hedge funds. Combined with a small difference in performance between surviving and defunct funds of funds, this yields relatively low survivorship bias estimates for funds of funds.

Hedge fund, attrition, survivorship bias

Abstract:
We study the diversification effects from introducing hedge funds into a traditional portfolio of stocks and bonds. Our results make it clear that in terms of skewness and kurtosis equity and hedge funds do not combine very well. Although the inclusion of hedge funds may significantly improve a portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds includes a definite trade-off between profit and loss potential. Our results also emphasize that to have at least some impact on the overall portfolio, investors will have to make an allocation to hedge funds which by far exceeds the typical 1-5% that many institutions are currently considering.

Hedge funds, asset allocation, diversification, skewness, kurtosis, optimization, mean-variance

Abstract:
We present an extension of the traditional Sharpe ratio to allow for the evaluation of non-normal return distributions. Combining earlier work in this area with stochastic simulation, we develop a procedure that allows for the construction of a benchmark for the evaluation of the performance of funds with a non-normal return distribution, while maintaining the operational ease of the Sharpe ratio. Similar to the latter, our procedure only requires the risk-free rate of interest rate, the distribution of the market index and an assumption about the type of return distributions to be evaluated. Unlike the Sharpe ratio, however, we are not restricted to normality but are able to handle any reasonable type of distribution. Since our benchmarking procedure is based on the no-arbitrage assumption, it also provides insight into the conditional arbitrage-free value of one distributional parameter in terms of another. We show that in case of the Johnson Su distribution the relationship between skewness and mean return is more or less flat. Skewness and median return on the other hand exhibit a strong negative relationship.