Performance measurement with the arbitrage pricing theory: A new framework for analysis

This paper develops a theory and econometric method of portfolio performance measurement using a competitive equilibrium version of the Arbitrage Pricing Theory. We show that the Jensen coefficient and the appraisal ratio of Treynor and Black are theoretically compatible with the Arbitrage Pricing Theory. We construct estimators for the two performance measures using a new principal components technique, and describe their asymptotic distributions. The estimators are computationally feasible using a large number of securities. We also suggest a new approach to testing for the correct number of factors.