Mean–Variance–Skewness–Kurtosis Approach to Portfolio Optimization: An Application in Istanbul Stock Exchange

Portfolio optimization, the construction of the best combination of investment instruments that will meet the investors’ basic expectati-ons under certain limitations, has an important place in the finance world. In the portfolio optimization, the Mean Variance model of Markowitz (1952) that expresses a tradeoff between return and risk for a set of portfolios, has played a critical role and affected other studies in this area. In the Mean Variance model, only the covariances between securities are considered in determining the risk of portfolios. The model is based on the assumptions that investors have a quadratic utility function and the return of the securities is distributed normally. Various studies that investigate the validity of these assumptions find evidence against them. Asset returns have significant skewness and kurtosis. In the light of these findings, it is seen that in recent years researchers use higher order of moments in the portfolio selection (Konno et al, 1993; Chunhachinda et al, 1997; Liu et al, 2003; Harvey et al, 2004; Jondeau and Rockinger, 2006; Lai et al, 2006; Jana et al,2007; Maringer and Parpas, 2009; Briec et al, 2007; Taylan and Tatlidil, 2010).In this study, in the mean- variance- skewness- kurtosis framework, multiple conflicting and competing portfolio objectives such as maximizing expected return and skewness and minimizing risk and kurtosis simultaneously, will be addressed by construction of a poly-nomial goal programming (PGP) model. The PGP model will be tested on Istanbul Stock Exchange (ISE) 30 stocks. Previous empirical results indicate that for all investor preferences and stock indices, the PGP approach is highly effective in order to solve the multi conflicting portfolio goals in the mean – variance - skewness – kurtosis frame-work. In this study, portfolios will be formed in accordance with the investor preferences over incorporation of higher moments. The effects of preferences both on the combination of stocks in the portfolios and descriptive statistics of portfolio returns will be analyzed. Another aim of this study is to investigate the impacts of the incorporation of skewness and kurtosis of asset returns into the portfolio optimization on portfolios’ returns descriptive statistics.