Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk

Xu GUO; Raymond H. CHAN; Wing Keung WONG; Lixing ZHU

doi:10.1057/s41283-018-0043-2

Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk

Xu GUO, Raymond H. CHAN, Wing Keung WONG^*, Lixing ZHU

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

50 Citations (Scopus)

Abstract

This paper extends (Jiang et al. in J Bank Finance 34:3055–3060, 2010; Guo in Risk Manag 20(1):77–94, 2018) and others by investigating the impact of background risk on an investor’s portfolio choice in the mean–VaR, mean–CVaR, and mean–variance framework, and analyzes the characterization of the mean–variance, mean–VaR, and mean–CVaR boundaries and efficient frontiers in the presence of background risk. We derive the conditions that the portfolios lie on the mean–variance, mean–VaR, and mean–CVaR boundaries with and without background risk. We show that the MV, VaR, and CVaR boundaries depend on the covariance vector between the returns of the risky assets and that of the background asset and also the variance of the return of the background asset. We develop properties on MV, mean–VaR, and mean–CVaR efficient frontiers. In addition, we establish some new properties for the case with a risk-free security, extend our work to the non-normality situation, and examine the economic implication of the mean–VaR/CVaR model.

Original language	English
Pages (from-to)	73-98
Number of pages	26
Journal	Risk Management
Volume	21
Issue number	2
Early online date	27 Aug 2018
DOIs	https://doi.org/10.1057/s41283-018-0043-2
Publication status	Published - 1 Jun 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Limited.

Funding

Acknowledgements The authors are grateful to the Editor, Igor Lončarski, and the anonymous referee for constructive comments and suggestions that led to a significant improvement of an early manuscript. The third author would like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. The research is partially supported by the National Natural Science Foundation of China (No. 11601227), The Chinese University of Hong Kong, Asia University, China Medical University Hospital, Hang Seng Management College, Lingnan University, the China Postdoctoral Science Foundation (2017M610058), Ministry of Science and Technology (MOST), Taiwan, and the Research Grants Council (RGC) of Hong Kong (Project Number 12500915).

Keywords

Background risk
CVaR
Mean–variance model
Portfolio selection
VaR

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10.1057/s41283-018-0043-2

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title = "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk",

abstract = "This paper extends (Jiang et al. in J Bank Finance 34:3055–3060, 2010; Guo in Risk Manag 20(1):77–94, 2018) and others by investigating the impact of background risk on an investor{\textquoteright}s portfolio choice in the mean–VaR, mean–CVaR, and mean–variance framework, and analyzes the characterization of the mean–variance, mean–VaR, and mean–CVaR boundaries and efficient frontiers in the presence of background risk. We derive the conditions that the portfolios lie on the mean–variance, mean–VaR, and mean–CVaR boundaries with and without background risk. We show that the MV, VaR, and CVaR boundaries depend on the covariance vector between the returns of the risky assets and that of the background asset and also the variance of the return of the background asset. We develop properties on MV, mean–VaR, and mean–CVaR efficient frontiers. In addition, we establish some new properties for the case with a risk-free security, extend our work to the non-normality situation, and examine the economic implication of the mean–VaR/CVaR model.",

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Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk

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