Portfolio optimization based on downside risk: a mean-semivariance ef¿cient frontier from Dow Jones blue chips

To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks when the investor is especially interested in the constrained minimization of downside risk measured by the portfolio semivariance. Concerning the opportunity set and observation period, the mean-semivariance efficient frontier model is applied to an actual case of portfolio choice from Dow Jones stocks with daily prices observed over the period 2005¿2009. From these daily prices, time series of returns (capital gains weekly computed) are obtained as a piece of basic information. Diversification constraints are established so that each portfolio weight cannot exceed 5 per cent. The results show significant differences between the portfolios obtained by mean-semivariance efficient frontier model and those portfolios of equal expected returns obtained by classical Markowitz mean-variance efficient frontier model. Precise comparisons between them are made, leading to the conclusion that the results are consistent with the objective of reflecting downside risk Pla Santamaría, D.; Bravo Selles, M. (2013). Portfolio optimization based on downside risk: a mean-semivariance ef¿cient frontier from Dow Jones blue chips. Annals of Operations Research. 205(1):189-201. doi:10.1007/s10479-012-1243-x Aouni, B. (2009). Multi-attribute portfolio selection: new perspectives. INFOR. Information Systems and Operational Research, 47(1), 1–4. Arenas, M., Bilbao, A., & Rodríguez, M. V. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133, 287–297. Arrow, K. J. (1965). Aspects of the theory of risk-bearing. Helsinki: Academic Bookstore. Ballestero, E. (2005). Mean-semivariance efficient frontier: a downside risk model for portfolio selection. Applied Mathematical Finance, 12(1), 1–15. Ballestero, E., & Pla-Santamaria, D. (2004). Selecting portfolios for mutual funds. Omega, 32, 385–394. Ballestero, E., & Pla-Santamaria, D. (2005). Grading the performance of market indicators with utility benchmarks selected from Footsie: a 2000 case study. Applied Economics, 37, 2147–2160. Ballestero, E., Pérez-Gladish, B., Arenas-Parra, M., & Bilbao