Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities

This paper proposes a novel test of zero pricing errors for the linear factor pricing model when the number of securities, N, can be large relative to the time dimension, T, of the return series. The test is based on Student t tests of individual securities and has a number of advantages over the existing standardised Wald type tests. It allows for non-Gaussianity and general forms of weakly cross correlated errors. It does not require estimation of an invertible error covariance matrix, it is much faster to implement, and is valid even if N is much larger than T. Monte Carlo evidence shows that the proposed test performs remarkably well even when T = 60 and N = 5;000. The test is applied to monthly returns on securities in the S&P 500 at the end of each month in real time, using rolling windows of size 60. Statistically significant evidence against Sharpe-Lintner CAPM and Fama-French three factor models are found mainly during the recent financial crisis. Also we find a significant negative correlation between a twelve-months moving average p-values of the test and excess returns of long/short equity strategies (relative to the return on S&P 500) over the period November 1994 to June 2015, suggesting that abnormal profits are earned during episodes of market inefficiencies

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 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.