Non‐Standard C.A.P.M.'s and the Market Portfolio

Abstract

RICHARD ROLL (8) CHANGED OUR WAY OF thinking about the CAPM model, both in terms of theoretical content and empirical testing. One of Roll's key contributions was to show that if the were efficient, the SharpeLintner-Mossin or zero beta form of the CAPM must follow. The purpose of this article is to extend Roll's work to non-standard forms of the CAPM. In recent years, the literature has contained over a dozen extensions of the simple CAPM. Of particular interest have been models which incorporate uncertain inflation, differential taxes on income and capital gains, heterogenous expectations, non-marketable assets, missing assets and international securities. In this article we will show that models that have been proposed in each of these areas follow directly from the assumption that investors act as if some particular is efficient. We believe that doing so is important for several reasons. First, it is a generalization of Roll's work which shows that his analysis and many of his conclusions can be extended well beyond his initial contribution. Second, it allows us to derive alternative equilibrium models using only algebra in a very simple and straightforward way. Furthermore, since the derivations are almost exactly parallel, having mastered one, the reader can move easily through the others. Third, we show that the differences between most non-standard forms of the CAPM come about from a difference in which is assumed efficient and an assumption about how to change from the definition of returns used to define the to the usual meaning of returns (dividends plus capital gains). This analysis highlights exactly what are the differences between models and shows that many of the asserted differences are nonexistent. The final reason this paper is important is that it stresses that each model arises directly from the efficiency of a particular version of the portfolio. Therefore, on a theoretical level, one can think about which version of a is likely to be efficient and on an empirical level the correctness of any model is likely to be decided by which market portfolio is efficient. The following sections of the paper are divided by type of non-standard CAPM. The types discussed incorporate non-marketable assets, international assets, inflation, taxes, and heterogenous expectations.