A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory: A Reply

THE PAPER BY Dhrymes, Friend, and Gultekin (DFG) in this issue criticizes empirical work on the Arbitrage Pricing Theory (APT) conducted by ourselves, (RR [3]), and by a number of others. We are honored that such eminent professors as DFG have taken an interest in our work. Unfortunately, the DFG paper contains analysis which might foster misconceptions in the casual reader. Our purpose here is to present a brief, nontechnical comment. We are confident that those who are inclined to study the DFG paper in detail will be able to discern its merit for themselves. The introductory section and the concluding Section VIII of DFG stress three points: first, that the method of RR has "major" pitfalls and is "seriously" flawed; second, that individual factors should not be tested for their pricing influence; and third, that more than three to five factors can be found by increasing the size of the group analyzed. We will comment on the reasonableness of the second and third point in some detail. The first is a value judgment and, as such, cannot be disputed on logical grounds. We would be the last to object to a reasoned opinion judiciously drawn by dispassionate and unbiased scholars, but, of course, we do not agree with the particular opinion expressed by DFG. In Sections I and II, DFG repeat the standard development of the APT and make much of the argument that the APT, as a null hypothesis in a statistical test, is independent of any rotation of the factors. They stress their view that the only meaningful tests are those of whether any factors are priced, "rather than those which test whether some of them are priced and others are not." RR raise and analyze precisely this same point,1 and, in fact, our awareness of this issue led us to conduct F-tests of the joint significance of all factor prices (see our Tables IV and VI). Despite the rotation problem, tests of individual factor pricing have meaning. Since the factors are extracted in the order of their importance in explaining the covariance matrix of returns, it is not only perfectly valid, it is also interesting to ascertain if they each have an influence upon pricing. The number of statistically significant estimated priced factors can be different than the number of true factors because of chance rotation in the