Factor Models as "Explanatory UniÖers" versus "Explanatory Ideals" of Empirical Regularities of Stock Returns

In this paper we investigate whether the empirical regularities of stock returns are independent of each other or whether any one of them implies all the others. If such a regularity exists, it is called 'fundamental' and is usually thought of as a 'deductive explanation' of the others. We demonstrate that such a fundamental regularity of stock returns is the one represented by the single factor model with a stochastically persistent beta coefficient (SFM- AR). Indeed, this regularity alone entails all the usual regularities of stock returns, including conditional heteroskedasticity, leptokurtosis aggregational Gaussianity and aggregational Independence. Hence, SFM-AR may be thought of as an "explanatory unifier" of the empirical regularities of stock returns. However, since the theoretical origins of SFM-AR are weak, its explanatory status falls short of meeting the standards of the 'ideal explanatory text'.