A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm

We propose a new approach to estimating and testing asset pricing models in the context of a bilinear paradigm introduced by Kruskal [18]. This approach is both simple and at the same time quite general. As an illustration we apply it to the special case of the arbitrage pricing model where the number of factors is pre-specified. The data appear to be generally in conflict with a five or seven factor representation of the model used by Roll and Ross [30]. When we consider the number of replications of our test and the large number of observations on which it is performed, the frequency with which we reject the three factor APM does not lead us to conclude that this model is unrepresentative of security returns. Further, the rejection of the five and seven factor versions is to be expected if the three factor version is correct. The paradigm gives insight into the appropriate specification of the model and suggests that there may be a small number of economy wide factors that affect security returns. TESTS OF ASSET PRICING models on the basis of observed stock market data have represented a staple of the financial economics literature of the past twenty years. The early work is reviewed in the famous paper by Jensen [12], and papers by Fama and MacBeth [6]. Rosenberg and Marathe [31], and Roll and Ross [30]. There has been a great deal of confusion regarding what testable propositions are implied by these models (see discussion in Roll [29]). In this paper we show that at a minimum all asset pricing models yet proposed imply a simple easily testable hypothesis which we refer to as the bilinear hypothesis. While specific models may imply further testable propositions, if the bilinear hypothesis is rejected the model is inconsistent with the data and should be rejected. Our test exploits the fact that the economic content of any equilibrium asset pricing model can be expressed in the form of a potentially refutable constraint on the set of parameters of the process generating security returns. This constraint specifies that, given a set of security specific characteristics, there exists a linear relationship common across securities relating expected returns to these