Dynamic Mean-Risk Portfolio Selection with Multiple Risk Measures in Continuous-Time

36 Pages Posted: 21 Jan 2014 Last revised: 9 Feb 2014

See all articles by Jianjun Gao

Jianjun Gao

Shanghai University of Finance and Economics; Shanghai Jiao Tong University

Yan Xiong

Shanghai Jiao Tong University

Duan Li

Chinese University of Hong Kong; City University of Hong Kong

Date Written: January 20, 2014

Abstract

Different risk measures emphasize different aspects of a random loss. If we examine the investment performance according to different spectra of the risk measures, any policy generated from a mean-risk portfolio model with a sole risk measure may not be a good choice. We study in this paper the dynamic portfolio selection problem with multiple risk measures in a continuous-time setting. More specifically, we investigate the dynamic mean-variance-CVaR (Conditional value at Risk) formulation and the dynamic mean-variance-SFP (Safety-First-Principle) formulation, and derive analytical solutions for both problems, when all the market parameters are deterministic. Combining a downside risk measure with the variance (the second order central moment) in a dynamic mean-risk portfolio selection model helps investors control both the symmetric central risk measure and the asymmetric downside risk at the tail part of the loss. We find that the optimal portfolio policy derived from our mean-multiple risk portfolio optimization model exhibits a feature of two-side threshold type, i.e., when the current wealth level is either below or above certain threshold, the optimal policy would dictate an increase in the allocation of the risky assets. Our numerical experiments using real market data further demonstrate that our dynamic mean-multiple risk portfolio models reduce significantly both the variance and the downside risk, when compared with the static buy-and-hold portfolio policy.

Keywords: Dynamic Portfolio Optimization, Mean-Risk Model, Mean-CVaR, Mean-Variance

JEL Classification: G11, C61

Suggested Citation

Gao, Jianjun and Xiong, Yan and Li, Duan, Dynamic Mean-Risk Portfolio Selection with Multiple Risk Measures in Continuous-Time (January 20, 2014). Available at SSRN: https://ssrn.com/abstract=2382343 or http://dx.doi.org/10.2139/ssrn.2382343

Jianjun Gao

Shanghai University of Finance and Economics ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Shanghai Jiao Tong University ( email )

800 Dongchuan Road
Shanghai
China
+86-18201925139 (Phone)
+86 34205004 (Fax)

Yan Xiong

Shanghai Jiao Tong University ( email )

KoGuan Law School
Shanghai 200030, Shanghai 200052
China

Duan Li (Contact Author)

Chinese University of Hong Kong ( email )

Shatin, New Territories
Hong Kong

City University of Hong Kong

Tat Chee Avenue
Kowloon Tong
Kowloon
Hong Kong
852 3442 8591 (Phone)

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