Robust optimization and portfolio selection: The cost of robustness

• Published in: European journal of operational research Vol. 212; no. 2; pp. 417 - 428
• Main Authors: Gregory, Christine, Darby-Dowman, Ken, Mitra, Gautam
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16-07-2011; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Exact sciences and technology; Mathematical models; Mathematical programming; Operational research; Operational research and scientific management; Operational research. Management science; Optimization; Optimization techniques; Portfolio diversification; Portfolio selection; Portfolio theory; Programming; Rates of return; Robust optimization; Robustness; Stochasticity; Studies; Uncertainty; Uncertainty modelling; Uncertainty modelling Robust optimization Portfolio selection; Uncertainty modelling; Robust optimization; Portfolio selection; Costs; Modeling; Optimization; Stochastic programming; Polyhedron; Uncertain system; Stock exchange; Robustness; Ellipsoid; Portfolio management
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.02.015

Robust optimization is a tractable alternative to stochastic programming particularly suited for problems in which parameter values are unknown, variable and their distributions are uncertain. We evaluate the cost of robustness for the robust counterpart to the maximum return portfolio optimization problem. The uncertainty of asset returns is modelled by polyhedral uncertainty sets as opposed to the earlier proposed ellipsoidal sets. We derive the robust model from a min-regret perspective and examine the properties of robust models with respect to portfolio composition. We investigate the effect of different definitions of the bounds on the uncertainty sets and show that robust models yield well diversified portfolios, in terms of the number of assets and asset weights.