A Test of the Efficiency of a Given Portfolio

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 pos...

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Bibliographic Details
Published in:Econometrica 1989-09, Vol.57 (5), p.1121-1152
Main Authors: Gibbons, Michael R., Ross, Stephen A., Shanken, Jay
Format: Article
Language:English
Subjects:
Applied sciences
Capital asset pricing models
Capital assets
Decision theory. Utility theory
Econometrics
Economic efficiency
Economic models
Efficiency
Exact sciences and technology
Financial economics
Financial portfolios
Hypotheses
Logical givens
Null hypothesis
Operational research and scientific management
Operational research. Management science
P values
Portfolio analysis
Portfolio management
Standard deviation
Statistics
Stock exchanges
Value weighted index
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Summary: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.
ISSN:0012-9682
1468-0262
DOI:10.2307/1913625