Multinational Portfolio Construction Using Polynomial Goal Programming and Lower Partial Moments

Abstract

This study is based on the earlier argument that downside risk measures are more appropriate than variance for constructing portfolios when the return rates of securities tend to be asymmetrically distributed. The purpose of this study is threefold. First, the return distributions of six Asian stock markets are tested for normality using the Wilk-Shapiro test. Second, a new portfolio selection model that considers expected rates of return, skewness and lower partial moments using polynomial goal programming is proposed. Six Asian stock market indexes are used as empirical data. Finally, optimal portfolios constructed by goal programming models based on variance and lower partial moments are compared. The empirical evidence showed that replacing variance by lower partial moments for portfolio selection decisions significantly changes the construction of the optimal portfolio. Moreover, the portfolio selection model based on lower partial moments created portfolios with higher expected returns than that based on variance for the same downside risks in all scenarios.