Unique closed-form solutions of portfolio selection subject to mean-skewness-normalization constraints - Xin Lu; Qiong Liu; Fengxin Xue (Operations Research Perspectives, 2019)
This paper originally proposes two unique closed-form solutions, respectively to risky assets only and a risk-free asset existing situations, of the mean-variance-skewness (MVS) optimization model subject to mean-sknewness-normalization constraints for portfolio selection. The efficient frontier and capital allocation surface (CAS) respectively derived from the two solutions are two hyperboloids, and tangent to each other at one hyperbola referred to as the market portfolio curve. Moreover, this curve intersects the mean-skewness plane of the portfolio return wtih zero-variance (zero-risk) at a line. Calculating the distance between a point on the coincident curve with the vertex of the CAS, we present a novel ratio to measure the performance of the risk-adjusted returns of market portfolio. The ratio is similar to the Sharpe ratio, moreover, under the more realistic assumption that portfolio returns follow a skew-normal distribution, the novel ratio can quantify the degree (or absence) of market portfolio exuberance.
Keywords: G11; C61; 330; Portfolio selection; Mean-variance-skewness optimization model; Skew-normal distribution; Unique closed-form solution; Efficient frontier; Tangency portfolio; Ratio of return versus risk