Testing High-Dimensional Linear Asset Pricing Models

Abstract

We propose in this article a new procedure, based on random projections, for testing widely used linear asset pricing models (Sharpe, 1964; Linter, 1965; Fama and French, 1993). This new testing procedure is particularly suitable when the number of assets N is much larger than the number of observations T, and outperforms the existing methods by admitting the covariance matrix of the idiosyncratic term to be nonsparse. Under some mild conditions, we show theoretically that the test statistic is asymptotically normal as long as min⁡{N,T} goes to infinity. The finite sample performance is investigated by extensive Monte Carlo experiments. The practical utility of the new testing procedure is further justified by treating the U.S. stock market. Employing this new testing procedure, we found that the Fama–French (FF) three-factor model (Fama and French, 1993) is better than the capital asset pricing model (Sharpe, 1964) in explaining the mean–variance efficiency of the U.S. stock market.