Testing the Arbitrage Pricing Condition of Apt

Sawyer, Kim R.; Gygax, André

doi:10.2139/ssrn.913696

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Testing the Arbitrage Pricing Condition of Apt

33 Pages Posted: 13 Jul 2006

See all articles by Kim R. Sawyer

Kim R. Sawyer

University of Melbourne - School of Historical and Philosophical Studies

André Gygax

University of Melbourne - Department of Finance

Date Written: May 18, 2006

Abstract

The principal result of APT is the arbitrage pricing condition that expected returns can be approximated by a linear combination of risk with strongly bounded pricing errors. Existing tests of APT either assume the pricing error to be zero or of order one in probability. Neither assumption is consistent with the theory of APT. In this paper, we characterize the pricing errors in terms of orders of probability. Errors consistent with APT are shown to be of order 1/SQRT(N) in probability where N is the number of assets. A test for APT is then a test of the order of the pricing error. We construct such a test based on tests for heteroscedasticity across sequences of assets. In a simulation study for both known and unknown factor structures, we show that this test performs better than existing tests for detecting violations of arbitrage pricing. In a study of US equities from 1978-2002, we find that the strongest evidence for arbitrage pricing is in single-factor models.

Keywords: Arbitrage Pricing Theory, Testing APT, US Equities

JEL Classification: C15, G12

Suggested Citation: Suggested Citation

Sawyer, Kim Russell and Gygax, André, Testing the Arbitrage Pricing Condition of Apt (May 18, 2006). Available at SSRN: https://ssrn.com/abstract=913696 or http://dx.doi.org/10.2139/ssrn.913696