Multiobjective Optimization of Mean–Variance-Downside-Risk Portfolio Selection Models

In this research paper we experimentally investigate the out-of-sample performance of three multiobjective portfolio optimization models, namely Mean–Variance-VaR, Mean–Variance-LPSD (LPSD: Lower Partial Standard Deviation) and Mean–Variance-Skewness. For solving the optimization problems, we apply a very popular efficient and effective Multiobjective Evolutionary Algorithm, SPEA2 (SPEA: Strength Pareto Evolutionary Algorithm) since the problems are not solved using existing mathematical programming techniques at least in reasonable computational time. The models are tested on real data drawn from the S&P 100 and S&P 500 indexes. Out-of-sample results show that the efficient portfolios generated by SPEA2 for the Mean–Variance-LPSD portfolio selection model outperform the market portfolio measured by S&P 500 index considering three performance measures; final wealth, Sharpe ratio, Sortino ratio. The efficient portfolios generated by SPEA2 for the Mean–Variance-VaR comes next and it also beat the S&P 500 index for all performance measures. The efficient portfolios generated by SPEA2 for the Mean–Variance-Skewness portfolio optimization model does not provide satisfactory results and fail to beat the market. Furthermore, comparison against competing portfolios, that have shown good out-of-sample performance in past studies, like the global minimum variance portfolio and the second order stochastic dominance portfolio shows that the portfolios of the proposed models except Mean–Variance-Skewness provide competing results.