This paper analyzes the portfolio selection problems with multivariate skew-normally distributed risky returns. We obtain a partial elliptic cone-shaped mean-variance-skewness (MVS) frontier and a closed-form MVS portfolio strategy for investors with a cubic utility. We empirically show that the utility increase of our MVS strategy over the traditional mean-variance strategy depends on the investors' prudence and risk-aversion levels. We define an asymmetry-variance efficient portfolio whose mean and variance also affect the utility difference. In addition, we obtain a three-moment capital asset pricing model which could be easily implemented for asset pricing tests.

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