Multiple Criteria Portfolio Choice with Variance Decomposition onto Half Spaces

In this paper we propose a multiple criteria framework (MCF) for generalizing the traditional two-moment CAPM. It includes the Sharpe-Lintner CAPM as a special case. The model decomposes effective portfolio variance into two parts, an undesirable total variance part and a desirable positive variability part. Minimization is taken with respect not to total variance as in the Sharpe-Lintner CAPM, but to the total variance less the positive variability. Positive covariability reduces risk premium, and has a similar effect compared to positive skewness or upper partial moment. The empirical results in our MCF model indicate good performance of the model. Most importantly, the model produces computable portfolio showing analytical tradeoffs between the MCF skewness and idiosyncratic volatility that could explain the negative premium of the latter in the literature.