Performance Measures with the Arbitrage Pricing Theory

Two popular measures of portfolio performance are Jensen‘s (1968) coefficient and Treynor and Black‘s (1973) appraisal ratio. Analogous performance measures are developed in an arbitrage pricing theory (APT) framework by extending Connor‘s (1984) equilibrium version of the APT to include a small set of investors with superior information. Estimators of the performance measures are proposed, and their asymptotic distributions derived. It is shown that the Jensen coefficient is an appropriate indicator of superior performance in the equilibrium APT model. Treynor-Black‘s appraisal ratio is found to be a valid measure of level of performance. These 2 performance measures can be estimated consistently from observable variables. A significant advantage of the estimators is that large numbers of securities can be used in estimating factor returns. Also proposed is a new approach to testing whether the correct number of factors has been extracted.