Abstract
This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain mean-variance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented.
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References
Beaud, M., & Willinger, M. (2014). Are people risk vulnerable? Management Science, 61(3), 624–636.
Chipman, J. S. (1973). The ordering of portfolios in terms of mean and variance. The Review of Economic Studies, 40(2), 167–190.
Eichner, T., & Wagener, A. (2003). Variance vulnerability, background risks, and mean-variance preferences. The Geneva Papers on Risk and Insurance Theory, 28(2), 173–184.
Eichner, T., & Wagener, A. (2009). Multiple risks and mean-variance preferences. Operations Research, 57(5), 1142–1154.
Guo, X., Wagener, A., Wong, W. K., & Zhu, L. (2018). The two-moment decision model with additive risks. Risk Management, 20(1), 77–94.
Huang, X. (2010). Portfolio analysis: From probabilistic to credibilistic and uncertain approaches. Berlin: Springer.
Huang, X. (2011). Mean-risk model for uncertain portfolio selection. Fuzzy Optimization and Decision Making, 10(1), 71–89.
Huang, X. (2012). Mean-variance models for portfolio selection subject to experts’ estimations. Expert Systems with Applications, 39(5), 5887–5893.
Huang, X. (2017). A review of uncertain portfolio selection. Journal of Intelligent & Fuzzy Systems, 32(6), 4453–4465.
Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284–296.
Lajeri-Chaherli, F. (2003). Partial derivatives, comparative risk behavior and concavity of utility functions. Mathematical Social Sciences, 46(1), 81–99.
Li, X., Wang, Y., Yan, Q., & Zhao, X. (2019). Uncertain mean-variance model for dynamic project portfolio selection problem with divisibility. Fuzzy Optimization and Decision Making, 18(1), 37–56.
Liu, B. (2007). Uncertainty theory. Berlin: Springer.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2010). Uncertaint theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.
Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.
Meyer, J., et al. (1987). Two-moment decision models and expected utility maximization. American Economic Review, 77(3), 421–430.
Ormiston, M. B., & Schlee, E. E. (2001). Mean-variance preferences and investor behaviour. The Economic Journal, 111(474), 849–861.
Qin, Z., Kar, S., & Zheng, H. (2016). Uncertain portfolio adjusting model using semiabsolute deviation. Soft Computing, 20(2), 717–725.
Saha, A. (1997). Risk preference estimation in the nonlinear mean standard deviation approach. Economic Inquiry, 35(4), 770–782.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The Review of Economic Studies, 25(2), 65–86.
Xue, L., Di, H., Zhao, X., & Zhang, Z. (2019). Uncertain portfolio selection with mental accounts and realistic constraints. Journal of Computational and Applied Mathematics, 346, 42–52.
Yao, K. (2015). A formula to calculate the variance of uncertain variable. Soft Computing, 19(10), 2947–2953.
Yao, K., & Ji, X. (2014). Uncertain decision making and its application to portfolio selection problem. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(01), 113–123.
Zhai, J., & Bai, M. (2018). Mean-risk model for uncertain portfolio selection with background risk. Journal of Computational and Applied Mathematics, 330, 59–69.
Acknowledgements
This work is supported by National Social Science Foundation of China No. 17BGL052, USTBNTUT Joint Research Program No. TW201709 and Fundamental Research Funds for the Central Universities No. FRF-MP-20-12.
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Huang, X., Jiang, G. Portfolio management with background risk under uncertain mean-variance utility. Fuzzy Optim Decis Making 20, 315–330 (2021). https://doi.org/10.1007/s10700-020-09345-6
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DOI: https://doi.org/10.1007/s10700-020-09345-6