Econometrica
journal article
A Test of the Efficiency of a Given Portfolio
Michael R. Gibbons, Stephen A. Ross and Jay Shanken
Econometrica
Vol. 57, No. 5 (Sep., 1989), pp. 1121-1152 (32 pages)
Published By: The Econometric Society
Econometrica
https://doi.org/10.2307/1913625
https://www.jstor.org/stable/1913625
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Abstract

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.

Journal Information

Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics.

Publisher Information

The Econometric Society is an international society for the advancement of economic theory in its relation to statistics and mathematics.

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Econometrica © 1989 The Econometric Society