Testing the Apt with Maximum Sharpe Ratio of Extracted Factors

37 Pages Posted: 16 Mar 2006

See all articles by Chu Zhang

Chu Zhang

Hong Kong University of Science & Technology (HKUST) - Department of Finance

Date Written: 2006

Abstract

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

Suggested Citation

Zhang, Chu, Testing the Apt with Maximum Sharpe Ratio of Extracted Factors (2006). Available at SSRN: https://ssrn.com/abstract=890914 or http://dx.doi.org/10.2139/ssrn.890914

Chu Zhang (Contact Author)

Hong Kong University of Science & Technology (HKUST) - Department of Finance ( email )

Clear Water Bay, Kowloon
Hong Kong

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