A test of the efficiency of a given portfolio. (English) Zbl 0679.62097

Gibbons, Michael R.; Ross, Stephen A.; Shanken, Jay

Econometrica 57, No. 5, 1121-1152 (1989).

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.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
91G10	Portfolio theory

Keywords:

asset pricing; CAPM; efficiency; portfolio of assets; small sample distribution; power function; sensitivity; portfolio choice; univariate test; diagnostic tools; examples; multivariate approach

Software:

AS 123