Econometrics

Testing the two-parameter asset pricing theory is difficult due to a mathematical equivalence between the individual return/beta’ linearity relation and the market portfolio’s mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio’s composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained. The two-parameter asset pricing theory is testable in principle; but arguments are given here that: (a) No correct and unambiguous test of the theory has appeared in the literature, and (b) there is practically no possibility that such a test can be accomplished in the future. This broad indictment of one of the three fundamental paradigms of modern finance will undoubtedly be greeted by my colleagues, as it was by me, with scepticism and consternation. The purpose of this paper is to eliminate the scepticism. (No relief is offered for the consternation.)

1. The efficient set mathematics.

It has been discussed most usually in terms of ex-ante returns and co variances. To emphasize the purely mathematical nature of the results, however, I should like to state it in terms of an observed sample of returns on N assets. There are only two assumptions:

(A.]) The sample product-moment covariance matrix, V, is non-singular.

(A.2) At least one asset had a different sample mean return from others.

2. A review of some asset pricing theory tests.

Three widely-quoted empirical papers on asset pricing theory are Black, Jensen and &holes (1972), Blume and Friend (1973), and Fama and MacBetb (1973).’ Let us examine what they said they were testing: The statement in Fama and MacBeth is very clear. They refer to a portfolio m which is on the ex-ante efficient frontier as seen by a single investor. This leads to the derivation of an equation identical to (1) but with...