A Test of APT with Maximum Sharpe Ratio

摘要

This paper tests the asymptotic arbitrage pricing theory (APT) on individual stocks with the factors extracted by the Connor-Korajczyk method. The asymptotic APT fails if and only if the number of unbounded eigenvalues of the second-moment matrix of excess returns exceeds that of the variance matrix of excess returns by one. A test is developed using this theoretical result based on the eigenvectors extracted using the CK method. The test statistic is shown to be related to the maximum Sharpe ratio among portfolios of all individual stocks. The empirical evidence, supplemented by simulation results, lends support to the implication of the asymptotic arbitrage pricing theory.