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

Abstract

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.

Análise da eficácia da variância e de medidas Downside Risk para formação de carteiras

“…Entre as medidas de risco consideradas sob a abordagem de downside risk estão: Semivariância (MARKOWITZ, 1959), Lower Partial Variance (BAWA, 1975), Lower Partial Moment (BAWA; LINDENBERG, 1977), Valueat-Risk (RISKMETRICS, 1996) Bawa (1975Bawa ( , 1978, Bawa e Lindenberg (1977) e Fishburn (1977 BRAVO, 2013;GAO et al, 2014). Ademais, há uma crescente atenção para medidas de downside risk devido a fatores macroeconômicos, como crises financeiras, acordos da Basileia I e II, aumento do uso de derivativos na formação de carteiras e problemas de "caudas pesadas" nas distribuições de probabilidade de ativos de renda fixa (JARROW; ZHAO, 2006).…”

“…Os problemas relacionados aos modelos média-LPM envolvem, sobretudo, o fato da matriz de semivariância-cosemivariância ser assimétrica e endógena. Alguns dos pesquisados que têm proposto metodologias são: Hogan e Warren (1972,1974), Ang (1975), Elton, Gruber e Padberg (1976), Nawrocki (1983) e Nawrocki e Staples (1989), Harlow (1991), Markowitz et al (1993), Gilli e Këllezi (2000), Athayde (2001) CHUA, 1979;BOND;SATCHELL, 2002;BERTSIMAS;LAUPRETE;SAMAROV, 2004;BOASSON;BOASSON;ZHOU, 2011;HAMRIN, 2011;DITRAGLIA;GERLACH, 2013;PLA-SANTAMARIA;BRAVO, 2013;GAO et al, 2014), o que também ocorreu para estudos no Brasil (ANDRADE, 2006;MONTINI, 2011MONTINI, , 2012.…”

Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

“…Within a single objective framework, one suitable method to solve this problem is dynamic programming, which was initially proposed by Eppen and Fama (1969) and Neave (1970), and more recently followed by Penttinen (1991), Chen and Simchi-Levi (2009), and Melo and Bilich (2013). On the other hand, compromise programming (CP) and goal programming (GP) (Zeleny, 1982;Yu, 2013;Ballestero and Romero, 1998;Ballestero and Pla-Santamaria, 2004;Bravo, Ballestero, and Pla-Santamaria, 2012;Pla-Santamaria and Bravo, 2013) are possible approaches to deal with multiple objectives. When the CMP is formulated as a linear/quadratic program, we can benefit from state-of-the-art mathematical programming solvers to obtain optimal solutions.…”

“…A common criticism to the use of variances points out that it makes no distinction between positive and negative deviations. Although this fact is only a problem when the cost distribution is asymmetric, it can be solved by using semi-variances or upside/downside deviations as in Ballestero (2005) and Pla-Santamaria and Bravo (2013).…”

“…Common criticism to the use of variance points out that it makes no distinction between positive and negative deviations. However, this drawback can be easily solved by using semivariance or upside/downside deviation as in Ballestero (2005) and Pla-Santamaria and Bravo (2013). In the context of cash management, we propose to calculate the risk of a policy X by computing the variance of daily costs as follows:…”