Testing the Apt with Maximum Sharpe Ratio of Extracted Factors
37 Pages Posted: 16 Mar 2006
Date Written: 2006
This paper tests the asymptotic arbitrage pricing theory (APT) with the factors extracted from individual stocks. It is shown that 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 result on the eigenvectors extracted by the Connor-Korajczyk (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 that the unconditional pricing error is small.
Keywords: APT, Sharpe ratio, extracted factors, pricing error, eigenvalues
JEL Classification: G12
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