Portfolio Optimization with Second-Order Stochastic Dominance Constraints and Portfolios Dominating Indices

Portfolio optimization models are usually based on several distribution characteristics, such as mean, variance or Conditional Value-at-Risk (CVaR). For instance, the mean-variance approach uses mean and covariance matrix of return of instruments of a portfolio. However this conventional approach ignores tails of return distribution, which may be quite important for the portfolio evaluation. This chapter considers the portfolio optimization problems with the Stochastic Dominance constraints. As a distribution-free decision rule, Stochastic Dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. We implemented efficient numerical algorithms for solving the optimization problems with the Second-Order Stochastic Dominance (SSD) constraints and found portfolios of stocks dominating Dow Jones and DAX indices. We also compared portfolio optimization with SSD constraints with the Minimum Variance and Mean-Variance portfolio optimization.

[1]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[2]  Josef Hadar,et al.  Stochastic dominance and diversification , 1971 .

[3]  M. Chapman Findlay,et al.  Stochastic dominance : an approach to decision-making under risk , 1978 .

[4]  Wlodzimierz Ogryczak,et al.  From stochastic dominance to mean-risk models: Semideviations as risk measures , 1999, Eur. J. Oper. Res..

[5]  ANTONIO MONTANÉS,et al.  Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH , 2000 .

[6]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[7]  Timo Kuosmanen,et al.  Efficient Diversification According to Stochastic Dominance Criteria , 2004, Manag. Sci..

[8]  Gautam Mitra,et al.  Portfolio construction based on stochastic dominance and target return distributions , 2006, Math. Program..

[9]  A. Ruszczynski,et al.  Portfolio optimization with stochastic dominance constraints , 2006 .

[10]  Milos Kopa,et al.  A second-order stochastic dominance portfolio efficiency measure , 2008, Kybernetika.

[11]  Gábor Rudolf,et al.  Optimization Problems with Second Order Stochastic Dominance Constraints: Duality, Compact Formulations, and Cut Generation Methods , 2008, SIAM J. Optim..

[12]  H. Levy.  Stochastic Dominance: Investment Decision Making under Uncertainty , 2010 .

[13]  Csaba I. Fábián,et al.  An enhanced model for portfolio choice with SSD criteria: a constructive approach , 2011 .

[14]  Gautam Mitra,et al.  Processing second-order stochastic dominance models using cutting-plane representations , 2011, Math. Program..