A Dynamic Model of Active Portfolio Management and Mutual Fund Performance Evaluation

Abstract

We analyze an optimal dynamic portfolio and asset allocation policy for investors who are concerned with the performances of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) and that portfolio managers adopt a mean tracking error analysis similar to Roll (1992), we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a well-diversified benchmark. Unlike the case of constant proportional portfolios for the standard utility maximization, our optimal portfolio policy is state dependent, namely a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio itself. Based on the analysis in this paper, we define a dynamic performance measure which relates portfolio's return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. We study portfolio performances for a sample of U.S. mutual funds with the data from January 2001 to December 2003. To limit biases in the selection of a benchmark for portfolio evaluation, we assume that the benchmark portfolio is the minimum variance portfolio composed of the Dow Jones Industrial Average index and the Nasdaq 100 index components. We find that majority of the mutual funds have substantially under-performed the chosen benchmark. Our model also implies an interesting relationship between performance indices and risk sensitivities. For the three year data, the empirical analysis shows that portfolio performance indices are related to their estimated risk sensitivities in an open-upward quadratic curve.

Keywords: Active portfolio management, benchmark portfolio, growth optimum portfolio, risk sensitivity, mutual fund performance evaluation

JEL Classification: B23, C15, C61, G13