Small sample tests of portfolio efficiency

Abstract

This paper presents an eigenvalue test of the efficiency of a portfolio when there is no riskless asset, complementing the test of Gibbons, Ross, and Shanken (1989). Besides optimal upper and lower bounds, an easily-implented numerical method is provided for computing the exact P-value. Our approach makes it possible to draw statistical inferences on the efficiency of a given portfolio both in the context of the zero-beta CAPM and with respect to other linear pricing models. As an application, using monthly data for every consecutive five-year period from 1926 to 1986, we reject the efficiency of the CRSP value-weighted index for most periods.