Testing the Arbitrage Pricing Condition of APT

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 stud..