How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk

Abstract This paper explores how background risk affects individual investment decisions under the framework of uncertainty theory. We propose an uncertain mean-variance model with background risk and give its optimal solution when the returns of stocks and background asset obey normal uncertainty distributions. On this basis, we study the characteristic of the mean-variance efficient frontier of the stock portfolio in the presence of background risk. Furthermore, we compare the proposed model with the uncertain mean-variance model without background risk and discuss the efficiency difference between the two models and further give the condition where the two models select the same stocks. Based on the comparison, we analyze how background risk affects individual portfolio choice. Finally, we give some numerical examples as illustrations.

[1]  João F. Cocco,et al.  Portfolio Choice in the Presence of Housing , 2000 .

[2]  A. Tversky,et al.  Rational choice and the framing of decisions , 1990 .

[3]  Xiaoxia Huang,et al.  A risk index model for portfolio selection with returns subject to experts’ estimations , 2012, Fuzzy Optim. Decis. Mak..

[4]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[5]  Andreas Wagener,et al.  Multiple Risks and Mean-Variance Preferences , 2009, Oper. Res..

[6]  Lixing Zhu,et al.  Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk , 2018, Risk Management.

[7]  John Hicks,et al.  Causality in Economics , 1980 .

[8]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[9]  Alexandre M. Baptista.  Optimal delegated portfolio management with background risk , 2008 .

[10]  J. Heaton,et al.  Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk , 2000 .

[11]  Takao Asano,et al.  Portfolio Inertia Under Ambiguity , 2004, Math. Soc. Sci..

[12]  C. Gollier.  The economics of risk and time , 2001 .

[13]  V. Atella,et al.  Household portfolio choices, health status and health care systems: A cross-country analysis based on SHARE. , 2012, Journal of banking & finance.

[14]  Hao Di,et al.  Uncertain portfolio selection with background risk , 2016, Appl. Math. Comput..

[15]  Lixing Zhu,et al.  The two-moment decision model with additive risks , 2017 .

[16]  Deborah Lucas,et al.  Portfolio Choice in the Presence of Background Risk , 2000 .

[17]  Roger Wilkins,et al.  The determinants of household risky asset holdings: Australian evidence on background risk and other factors , 2009 .

[18]  Xiaoxia Huang,et al.  Mean-variance models for portfolio selection subject to experts' estimations , 2012, Expert Syst. Appl..

[19]  Robert B. Litterman,et al.  Global Portfolio Optimization , 1992 .

[20]  Chiaki Hara,et al.  Effects of background risks on cautiousness with an application to a portfolio choice problem , 2011, J. Econ. Theory.

[21]  Jia Zhai,et al.  Mean-risk model for uncertain portfolio selection with background risk , 2018, J. Comput. Appl. Math..

[22]  F. Knight.  The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[23]  Xiaoxia Huang,et al.  Mean-risk model for uncertain portfolio selection , 2011, Fuzzy Optim. Decis. Mak..

[24]  Terje Lensberg,et al.  Investment behavior under Knightian uncertainty – An evolutionary approach , 1999 .

[25]  Xiaoxia Huang,et al.  Mean-chance model for portfolio selection based on uncertain measure , 2014 .

[26]  Xiaoxia Huang,et al.  Portfolio Analysis - From Probabilistic to Credibilistic and Uncertain Approaches , 2012, Studies in Fuzziness and Soft Computing.

[27]  Alexandre M. Baptista.  Portfolio selection with mental accounts and background risk , 2012 .

[28]  Kai Yao,et al.  A formula to calculate the variance of uncertain variable , 2015, Soft Comput..

[29]  Yongkai Ma,et al.  An Analysis of Portfolio Selection with Background Risk , 2009 .