A Test of the Efficiency of a Given Portfolio

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

1989-09-01articleEconometrica2,369 citationsclosed

No readable copy stored yet — this record is metadata only.

Financial Markets and Investment Strategies Financial Risk and Volatility Modeling Risk and Portfolio Optimization

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. Copyright 1989 by The Econometric Society.

Citations in this library

Stored only when both papers are in the corpus — 2,369 citations exist upstream.

References

1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*

1973Risk, Return, and Equilibrium: Empirical Tests

1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]

1973An Intertemporal Capital Asset Pricing Model

1981The relationship between return and market value of common stocks

1972Capital Market Equilibrium with Restricted Borrowing

1977A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory

1972The capital asset pricing model: Some empirical tests

Cited by

n.d.Editor's Choice Digesting Anomalies: An Investment Approach

1998Value versus Growth: The International Evidence

2013Value and Momentum Everywhere

2002Differences of Opinion and the Cross Section of Stock Returns

2004The Capital Asset Pricing Model: Theory and Evidence

2012Size, value, and momentum in international stock returns

1999Do Industries Explain Momentum?

1995Market underreaction to open market share repurchases