Testing CAPM with a Large Number of Assets

Abstract

This paper is concerned with testing the time series implications of the capital asset pricing model (CAPM) due to Sharpe (1964) and Lintner (1965), when the number of securities, N, is large relative to the time dimension, T, of the return series. In the case of cross-sectionally correlated errors, using a threshold estimator of the average squares of pair-wise error correlations a test is proposed and is shown to be valid even if N is much larger than T. Monte Carlo evidence show that the proposed test works well in small samples. The test is then applied to all securities in the S&P 500 index with 60 months of return data at the end of each month over the period September 1989-September 2011. Statistically significant evidence against Sharpe-Lintner CAPM is found mainly during the recent financial crisis. Furthermore, a strong negative correlation is found between a twelve-month moving average p-values of the test and the returns of long/short equity strategies relative to the return on S&P 500 over the period December 2006 to September 2011, suggesting that abnormal profits are earned during episodes of market inefficiencies.

Keywords: CAPM, testing for alpha, market efficiency, long/short equity returns, large panels, weak and strong cross-sectional dependence

JEL Classification: C12, C15, C23, G11, G12