Asset Pricing Models When the Number of Securities Held Is Constrained: A Comparison and Reconciliation of the Mao and Levy Models

Abstract

ln a paper published in 1978, Levy [5] proposed a general capital asset pricing model (GCAPM), which he obtained by maximizing investors1 utility when the number of securities held in each investor's portfolio is con? strained. Although Levy's resultant asset pricing model is somewhat dif? ferent in appearance than the asset pricing model proposed by Mao [81 in 1971, it can be shown that both models are not only quite comparable in content but that both result in some very promising theoretical and empirical implications. Thus, the purpose of this paper is twofold. First, these two important contributions to the literature on asset pricing in imperfect markets will be compared and contrasted. Second, it will be shown that both models can yield a clinical form of the traditional CAPM, which appears to be more desirable for empirical testing purposes. This paper is organized into four sections. In Section I, the paper by Mao [81 is reviewed. The similarities and differences of the asset pric? ing models proposed by Mao [8] and Levy [5] are discussed in Section II. In Section III, the implications of the clinical forms of the traditional CAPM proposed by Mao and Levy are examined with particular reference to Roll's [93 recent criticisms of the validity of past empirical tests of the traditional CAPM. In the fourth and final section, some concluding remarks are presented._