The Number of Arbitrage Pricing Theory Factors: An Assessment of the Power of Multivariate Tests Used

Abstract

In spite of Shanken’s (1982) rejection of its testability, a vast body of literature has developed over the last two decades involving empirical tests of the Arbitrage Pricing Theory. The majority of the earlier studies focused on the determination of the number and pricing of the APT factors. The core methodology employed has involved the use of factor analysis and cross-sectional generalised least squares procedures with conclusions being reached of anywhere between one and nine independently priced factors.

This paper investigates the extent to which prior research conclusions may be influenced by the power of the multivariate tests used. An extensive simulation analysis of a variety of pre-defined priced factor economies is employed. The conclusions are threefold. Firstly, the diversity of past results can to a large extent be explained by the low power of the procedures employed. Secondly, thin trading, with its impact on covariance estimation, biases the results towards a multi factor conclusion being reached. Finally, the existence of moderate levels of non-normalities in the returns distribution does not significantly impact on the results.