Does gain-loss analysis outperform mean-variance analysis?: evidence from portfolios of hedge funds and passive strategies



Publishing details

IFA Working Paper

Authors / Editors

Agarwal V; Naik N Y


Publication Year



The supporters of hedge funds make their case by describing the diversification benefits offered by hedge funds using the traditional mean-variance framework, which is of limited use if returns are not normally distributed, as is the case with hedge funds. Recently, Bernardo and Ledoit (2000) propose gain-loss analysis, which does not require returns to be normally distributed, as an alternative to the mean-variance analysis. Since gain-loss analysis does not require returns to be normally distributed, it can be applied in case of diverse situations ranging from portfolio optimisation with assets having non-normal returns to performance evaluation of managers who use derivatives - situations where traditional metrics like Sharpe ratio and mean-variance frontier offer little help. Using the gain-loss framework, this paper compares the out-of-sample performance of gain-loss efficient and mean-variance efficient tangency portfolios comprising of ten hedge fund strategies and eight passive investment strategies (covering equities, bonds, currencies and commodities). In order to shed light on the differences between gain-loss and mean-variance analyses, it compares the efficient frontiers generated by the two approaches when the set of assets include S&P 500 Composite index and call and put options with different exercise prices on the S&P 500 index. When we specify the investment opportunity set to be the S&P500 index, and pure call or put options on the S&P500 with different strike prices, the gain-loss efficient frontier marginally dominates the mean-variance efficient frontier for all portfolio standard deviations below 12% per annum. Further, when we examine the out-of-sample performances of gain-loss and mean-variance efficient portfolios with same expected volatility, we find that unconditionally the returns on the gain-loss efficient portfolio do not dominate that on the mean-variance portfolio. But, interestingly, when we divide the market returns into five quintiles and compare the returns on the two efficient portfolios, we find that in the highest quintile (lowest quintile) the gain-loss efficient portfolio significantly outperforms (underperforms) the mean-variance portfolio conditional on the state of the equity market. One reason for the lack of overwhelming evidence of dominance of the gain-loss efficient portfolios could be the low non-normality at the hedge fund index level. On the whole, the results suggest that when deviations from normality are small, mean-variance framework provides a good approximation to the more robust and general gain-loss analysis. But when the deviations from non-normality are extremely severe as may be the case for individual hedge funds, it warrants the need for gain-loss analysis.

Publication Research Centre

Institute of Finance and Accounting

Series Number

FIN 305


IFA Working Paper