A generalized two-moment asset pricing model

Lim Kian Guan (Singapore Management University)
Monday, April 29, 2013 - 2:00pm
Spandauer Strasse 1, Room 23

In this paper we propose a generalized two-moment CAPM that subsumes rather naturally the Sharpe-Lintner CAPM as a special case. While there are other developed models that also subsume the latter as a special case, such as the three-moment CAPM or the lower partial moment model, the generalized model in this paper embodies all the advantages and prized classical results of easy computation of optimal portfolio weights and thus establishment of uniqueness and existence of a maximum expected utility, attainment of aggregation across heterogeneous agents with different risk aversions to a representative agent, and other properties. These properties are often not available in the other models. The generalized model in this paper decomposes portfolio variance into two parts, a desirable part comprising positive variability, and the remaining part that is not desirable. Minimization is taken with respect not to variance as in the Sharpe-Lintner CAPM, but to the subvariance, or the total variance less the desirable positive variability. We provide a range of discussion on motivations for the development of this original idea of positive variability and of the associated positive covariability. Positive covariability reduces risk premium, and has a similar effect compared to positive skewness or upper partial moment. The empirical results indicate a clear case of superior statistical performance over the more restrictive Sharpe-Lintner CAPM, and more robust and stable result versus the Kraus-Litzenberger (1976) three-moment CAPM. While somewhat similar in performance with the lower partial moment models of Hogan and Warren (1974), and of Bawa and Lindenberg (1977), our generalized two moment model nevertheless facilitates easy intuition, and fast computation of a unique optimal portfolio set of weights.