A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set

The “separable” uncertainty sets have beenwidely used in robust portfolio selection models [e.g., see Erdoğan et al. (Robust portfolio management. manuscript, Department of Industrial Engineering and Operations Research, Columbia University, New York, 2004), Goldfarb and Iyengar (Math Oper Res 28:1–38, 2003), Tütüncü and Koenig (Ann Oper Res 132:157–187, 2004)]. For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in Lu (A new cone programming approach for robust portfolio selection, technical report, Department ofMathematics, Simon Fraser University, Burnaby, 2006; Robust portfolio selection based on a joint ellipsoidal uncertainty set, manuscript, Department of Mathematics, Simon Fraser University, Burnaby, 2008), these “separable” uncertainty sets typically share two common properties: (i) their actual confidence level, namely, the probability of uncertain parameters falling within the uncertainty set is unknown, and it can be much higher than the desired one; and (ii) they are fully or partially box-type. The associated consequences are that the resulting robust portfolios can be too conservative, and moreover, they are usually highly non-diversified as observed in the computational experiments conducted in this paper and Tütüncü and Koenig (Ann Oper Res 132:157–187, 2004). To combat these drawbacks, the author of this paper introduced a “joint” ellipsoidal uncertainty set (Lu in A new cone programming approach for robust portfolio selection, technical report, Department of Mathematics, Simon Fraser University, Burnaby, 2006; Robust portfolio selection based on a joint ellipsoidal uncertainty set, manuscript, Department of Mathematics, Simon Fraser University, Burnaby, 2008) and showed that it can be Z. Lu was supported in part by SFU President’s Research Grant and NSERC Discovery Grant. Z. Lu (B) Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada e-mail: [email protected]