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**A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set.**
*(English)*
Zbl 1208.91136

Summary: The “separable” uncertainty sets have been widely used in robust portfolio selection models [e.g., see D. Goldfarb and G. Iyengar, Math. Oper. Res. 28, No. 1, 1–38 (2003; Zbl 1082.90082)]. For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [Z. Lu, “A new cone programming approach for robust portfolio selection”, technical report, Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada (2006); “Robust portfolio selection based on a joint ellipsoidal uncertainty set”, Optim. Methods Softw. 26, No. 1, 89–104 (2009)], 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 [R. H. Tütüncü and M. Koenig, Ann. Oper. Res. 132, 157–187 (2004; Zbl 1090.90125)]. To combat these drawbacks, the author of this paper introduced a “joint” ellipsoidal uncertainty set [Lu, loc. cit.] and showed that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters. For this uncertainty set, the author showed in [Lu, loc. cit.] that the corresponding robust maximum risk-adjusted return (RMRAR) model can be reformulated and solved as a cone programming problem. In this paper, we conduct computational experiments to compare the performance of the robust portfolios determined by the RMRAR models with our “joint” uncertainty set [Lu, loc. cit.] and Goldfarb and Iyengar’s “separable” uncertainty set proposed in the seminal paper [Goldfarb, loc. cit.]. Our computational results demonstrate that our robust portfolio outperforms Goldfarb and Iyengar’s in terms of wealth growth rate and transaction cost, and moreover, ours is fairly diversified, but Goldfarb and Iyengar’s is surprisingly highly non-diversified.

### MSC:

91G10 | Portfolio theory |

91G60 | Numerical methods (including Monte Carlo methods) |

90C20 | Quadratic programming |

90C22 | Semidefinite programming |

### Software:

SeDuMi
Full Text:
DOI

### References:

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[5] | Lu, Z.: A new cone programming approach for robust portfolio selection. technical report, Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada, December (2006) |

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[11] | Zhu, S., Fukushima, M.: Worst-case conditional value-at-risk with application to robust portfolio management, technical report 2005–2006, Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan, July (2005). (Accepted in Operations Research) |

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