TY - JOUR
T1 - Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk
AU - Guo, Xu
AU - Chan, Raymond H.
AU - Wong, Wing Keung
AU - Zhu, Lixing
N1 - Funding Information:
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).
Publisher Copyright:
© 2018, Springer Nature Limited.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
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U2 - 10.1057/s41283-018-0043-2
DO - 10.1057/s41283-018-0043-2
M3 - Article
AN - SCOPUS:85052957347
SN - 1460-3799
VL - 21
SP - 73
EP - 98
JO - Risk Management
JF - Risk Management
IS - 2
ER -