An enhanced model for portfolio choice with SSD criteria: a constructive approach

Abstract

We formulate a portfolio planning model that is based on second-order stochastic dominance as the choice criterion. This model is an enhanced version of the multi-objective model proposed by Roman et al. [Math. Progr. Ser. B, 2006, 108, 541–569]; the model compares the scaled values of the different objectives, representing tails at different confidence levels of the resulting distribution. The proposed model can be formulated as a risk minimization model where the objective function is a convex risk measure; we characterize this risk measure and the resulting optimization problem. Moreover, our formulation offers a natural generalization of the SSD-constrained model of Dentcheva and Ruszczyński [J. Bank. Finance, 2006, 30, 433–451]. A cutting plane-based solution method for the proposed model is outlined. We present a computational study showing: (a) the effectiveness of the solution methods and (b) the improved modeling capabilities: the resulting portfolios have superior return distributions.

Keywords:

• Computational finance
• Asset allocation
• Downside risk
• Choice models
• Financial modelling
• Portfolio optimization
• Risk measures

Acknowledgements

The authors would like to acknowledge the support for this research from several sources. Professor Csaba Fábián's research was partly supported by OTKA, the Hungarian National Fund for Scientific Research, project 47340, and by Mobile Innovation Centre, Budapest University of Technology, project 2.2. His visiting academic position to CARISMA was supported by OptiRisk Systems, Uxbridge, UK, and by BRIEF (Brunel University Research Innovation and Enterprise Fund). Dr. Diana Roman's contribution to this work was supported by BRIEF (Brunel University Research Innovation and Enterprise Fund). The PhD studies of Victor Zverovich were supported by OptiRisk Systems. These sources of support are gratefully acknowledged.