A Portfolio Performance Index
Posted: 8 Oct 2000
This paper models the behavior of a fund manager who selects a portfolio strives to maximize the probability of outperforming an investor-designated benchmark portfolio, on-average, over an uncertain length of time. Surprisingly, the analysis shows that the manager should act as-if she maximizes the expected exponential utility of the portfolio's excess return over the benchmark's. But unlike standard portfolio theory, this manager should maximize expected utility over both the space of portfolios and the utility function's coefficient of risk aversion. Nonetheless, the result is consistent with the usual Sharpe Ratio maximization rule when returns are normally distributed. More realistically, returns are from some unknown distribution. Fortunately, the optimal coefficient of risk aversion and portfolio are easily estimable in this case, using a simple spreadsheet.
Keywords: Portfolio Choice, Fund Management, Endogenous Risk Aversion, Benchmark Investing
JEL Classification: G11, D81
Suggested Citation: Suggested Citation