This paper proposes a new way to measure and deal with risk within the portfolio selection problem using a skewness/semivariance biobjective optimization framework. The solutions of this biobjective optimization problem allow the investor to analyse the efficient trade-off between skewness and semivariance. Due to the endogeneity of the cosemivariance matrix, the biobjective problem is solved using a derivative-free algorithm based on direct multisearch. For four datasets, collected from the Fama/French benchmark collection, the direct multisearch was able to determine the in-sample Pareto frontier. The out-of-sample performance of the skewness/semivariance model was assessed by choosing three portfolios (the portfolio that maximizes a skewness per semivariance ratio, the portfolio that maximizes the Sharpe ratio and the portfolio that maximizes the Sortino ratio) at each in-sample Pareto frontier and measuring their performance in terms of skewness per semivariance ratio, Sharpe ratio, Sortino ratio and turnover. The results show that the efficient skewness/semivariance portfolios are consistently competitive, and often superior, comparatively to the benchmark portfolios considered. Both in-sample and the out-of-sample performance analysis were conducted using three different benchmark returns for the semivariance computations.
JEL Classification: C44; C58; C61; C63; C88; G11.
Keywords: portfolio selection, semivariance, skewness, multiobjective optimization, derivative-free optimization, direct multisearch.