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

M Hashem Pesaran,Takashi Yamagata

doi:10.2139/ssrn.2973079

Abstract

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.

Highlights

This paper is concerned with testing for the presence of alpha in Linear Factor Pricing Models (LFPM) such as the capital asset pricing model (CAPM) due to Sharpe (1964) and Lintner (1965), or the Arbitrage Pricing Theory (APT) model due to Ross (1976), when the number of securities, N, is quite large relative to the time dimension, T, of the return series under consideration
In support of our conjecture we provide additional Monte Carlo evidence in Table 6, where we present ...nite sample behaviour of the J^ test under the data generating process (DGP) identical to those considered for Table 5, except that betas are generated to be withit IIDN (0; 1), time varying. and set yit =
In this paper we propose a simple test of Linear Factor Pricing Models (LFPM), the J^ test, when the number of securities, N, is large relative to the time dimension, T, of the return series

Summary

Introduction

This paper is concerned with testing for the presence of alpha in Linear Factor Pricing Models (LFPM) such as the capital asset pricing model (CAPM) due to Sharpe (1964) and Lintner (1965), or the Arbitrage Pricing Theory (APT) model due to Ross (1976), when the number of securities, N , is quite large relative to the time dimension, T , of the return series under consideration. Using time series regressions, Jensen (1968) was the ...rst to propose using standard t-statistics to test the null hypothesis that the intercept, i, in the Ordinary Least Squares (OLS) regression of the excess return of a given security, i, on the excess return of the market portfolio is zero.. Using time series regressions, Jensen (1968) was the ...rst to propose using standard t-statistics to test the null hypothesis that the intercept, i, in the Ordinary Least Squares (OLS) regression of the excess return of a given security, i, on the excess return of the market portfolio is zero. The test can be applied to individual securities as well as to portfolios

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Discussion

Conclusion