Optimal Utilization of Market Forecasts and the Evaluation of Investment Performance
MATHEMATICAL METHODS IN FINANCE, G. P. Szego, Karl Shell, eds., North-Holland Publishing Company, 1972
34 Pages Posted: 24 Mar 2003
The purpose of this paper is to examine the problem faced by the portfolio manager attempting to optimally incorporate forecasts of future market returns into his portfolio. Given the solution to this problem we then shall focus our attention on the problem involved in measuring a portfolio manager's ability when he is explicitly engaged in forecasting the prices on individual securities (i.e., security analysis) and in forecasting the future course of market prices (i.e., timing activities). We shall consider these problems here in the context of the Sharpe-Lintner mean-variance general equilibrium model of the pricing of capital assets, and in the context of the expanded two factor version of the Sharpe model suggested by Black, Jensen and Scholes (1972) In addition we shall concentrate our attention here on an investigation of just what can and cannot be said about portfolio performance solely on the basis of data on the time series of portfolio and market returns.
In section 2 we outline the foundations of the analysis and its relationship to the general equilibrium structure of security prices given by the Sharpe-Lintner model. In section 3 we briefly summarize the measure of security selection ability suggested by Jensen (1968). Section 4 contains a solution to the problem of the optimal incorporation of market forecasts into portfolio policy and provides the structure for the analysis in section 5 of the measurement problems introduced into the evaluation of portfolio performance by market forecasting activities by the portfolio manager. Section 6 presents the complete development of the model within the two factor equilibrium model of the pricing of capital assets suggested by Black (1970) and Black, Jensen and Scholes (1972). Section 7 contains a brief summary of the conclusions of the analysis.
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