A Portfolio Performance Index

Abstract

Fund managers may sensibly be averse to earning a time-averaged portfolio return that is less than the average return of some designated benchmark. When a portfolio is expected to earn a higher average return than the benchmark return, the probability that it will not approaches zero asymptotically at a computable exponential decay rate. The probability decay rate is thus proposed here as a new portfolio “performance index.” In the widely analyzed special case in which returns are normally distributed, the new performance-index-maximizing portfolio is the same as the popular Sharpe-ratio-maximizing portfolio. The results of the two approaches generally differ, however, because of nonnormal levels of skewness and/or kurtosis in the portfolio attributable to large asymmetrical economic shocks or investments in options and other derivative securities. An illustrative example will show that the new index is easy to implement and, consistent with empirical evidence on portfolio choice, favors investments with positively skewed returns.