动态均值-方差资产组合的有效性:时变风险容忍度视角

doi:10.16381/j.cnki.issn1003-207x.2021.01.001

摘要/Abstract

摘要： 尽管均值-方差模型在静态资产组合优化过程中得到广泛运用并证明是有效的，但在动态情景下，均值-方差模型运用于动态资产组合优化过程中的有效性问题引起人们的质疑：一是常风险规避系数的设定不符合事实；二是投资者偏好设定不符合动态情景下的主流效用函数族。鉴于此，本文假设投资者风险容忍度是资产组合投资期与投资者期望收益率的函数，研究动态均值-方差资产组合的有效性问题。基于均值-方差分析框架构建时变风险容忍度下的动态资产组合模型；运用伊藤定理和拉格朗日乘子法获得最优资产组合封闭解；基于二次效用偏好下的动态资产组合，从资产组合策略、夏普率、确定性等价收益率和有效前沿等视角验证动态均值-方差资产组合策略和业绩，并予以实证。结果表明：动态均值-方差资产组合不但具有同等业绩而且体现了其灵活性和风险对冲价值；尽管动态均值-方差资产组合表现出高杠杆性，但其确定性等价收益率较高，且随投资期的增加呈现倒U型趋势；动态均值-方差资产组合的投资期效应显著，强于投资者期望收益率。研究指出，时变风险容忍度下的动态均值-方差资产组合管理和优化策略有效，但在短投资期（低于12个月）和（或）低期望收益率下并不适用。研究不但拓展了均值-方差模型在动态情境下的应用，而且体现了投资者源于心理和（或）其财富变化的投资行为调整。

关键词: 动态均值-方差资产组合, 时变风险容忍度, 有效性, 策略与业绩

Abstract: Although the mean variance model has been widely used and proved to be effective in the process of static portfolio optimization, the effectiveness of the mean variance model in the process of dynamic portfolio optimization in the dynamic scenario has aroused people's doubts: One is that the setting of constant risk aversion coefficient does not conform to the fact, and the other is that the investor preferences do not fit the mainstream utility function family under the dynamic situation. In view of this, the effectiveness of dynamic mean-variance portfolio is studied by assuming that the investor's risk tolerance is a function of portfolio's investment horizon and investor's expected return rate.Based on mean-variance framework, the model of dynamic portfolio under time-varying risk tolerance is constructed; it uses the Ito theorem and Lagrange multiplier method to obtain the closed-form solution of optimal portfolio; comparing with the dynamic portfolio under quadratic utility preference, it tests the strategy and performance of dynamic mean-variance portfolio from the aspects of portfolio strategy, Sharpe ratio, certainty equivalent rate of return, and efficient frontier, and does an empirical study.The results show, the dynamic mean-variance portfolio not only has the same performance, but also embodies its flexibility and risk hedging value; although the dynamic mean-variance portfolio shows high leverage, the certainty equivalent rate of return is higher, and presents the trend of inverted U shape with the increasing of investment horizon; the dynamic mean-variance portfolio has a significant effect of investment horizon, which is stronger than that of expected return rate. It is pointed out that the strategy of dynamic mean-variance portfolio management and optimization under time-varying risk tolerance is effective, but is not suit for short investment horizon (less than 12 months) and(or) low expected yield. The study not only extends the application of mean-variance model under the dynamic situation, but also reflects the adjustment of investment behavior due to the changing of investor's psychology and (or) his wealth.

Key words: dynamic mean-variance portfolio, time-varying risk tolerance, effectiveness, strategy and performance

中图分类号:

F830.91

何朝林, 涂蓓, 王鹏. 动态均值-方差资产组合的有效性:时变风险容忍度视角[J]. 中国管理科学, 2021, 29(1): 1-11.

HE Chao-lin, TU Bei, WANG Peng. The Effectiveness of Dynamic Mean-variance Portfolio: An Aspect of Time-varying Risk Tolerance[J]. Chinese Journal of Management Science, 2021, 29(1): 1-11.

参考文献

[1] Cochrane J.A mean variance benchmark for intertemporal portfolio theory[J]. The Journal of Finance, 2014,69(1):1-49.
[2] Markowitz H. Mean-variance approximations to expected utility[J]. European Journal of Operational Research, 2014, 234(2):346-355.
[3] Li D, Ng W L. Optimal dynamic portfolio selection:Multiperiod mean-variance formulation[J]. Mathematical Finance, 2000, 10(3):387-406.
[4] Zhou X Y, Li D. Continuous-time mean-variance portfolio selection:Astochastic LQ framework[J]. Applied Mathematics & Optimization, 2000, 42(1):19-33.
[5] Basak S, Chabakauri G. Dynamic mean-variance asset allocation[J]. Social Science Electronic Publishing, 2010, 23(8):2970-3016.
[6] 李仲飞,袁子甲.参数不确定性下资产配置的动态均值-方差模型[J].管理科学学报,2010,13(12):1-9.
[7] Yao Haixiang, Zeng Yan, Chen Shumin. Multi-period mean-variance asset-liability management with uncontrolled cash flow and uncertain time-horizon[J]. Economic Modelling, 2013, 30(1):492-500.
[8] 王秀国,王义东. 基于随机基准的动态均值-方差投资组合选择[J]. 控制与决策,2014,29(3):499-505.
[9] 何朝林.均值-方差模型具有一般不确定性下的最优资产组合选择[J].中国管理科学,2015,23(12):63-70.
[10] Qin Zhongfeng. Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns[J]. European Journal of Operational Research, 2015, 245(2):480-488.
[11] Yao Haixiang,Li Zhongfei, Li Duan. Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability[J]. European Journal of Operational Research,2016,252(3):837-851.
[12] Bellante D, Green C A. Relative risk aversion among the elderly[J]. Review of Financial Economics, 2004, 13(3):269-281.
[13] Ho H. An Experimental Study of Risk Aversion in Decision-making Under Uncertainty[J]. International Advances in Economic Research, 2009, 15(4):369-377.
[14] 易祯,朱超.人口结构与金融市场风险结构:风险厌恶的生命周期时变特征[J].经济研究,2017,52(9):150-164.
[15] Björk T,Murgoci A,Xun Y. mean-varianceportfoliooptimizationwithstate-dependentriskaversion[J]. An International Journal of Mathematics,Statistics and Financial Economics,2014,24(1):1-24.
[16] Cui Xiangyu, Xu Lu, Zeng Yan. Continuous time mean-variance portfolio optimization with piecewise state-dependent risk aversion[J]. Optimization Letters, 2015, 10(8):1-11.
[17] 迟国泰,段翀.基于时变跳跃次数的基准利率风险测算研究[J].管理科学学报,2017,20(7):86-103.
[18] 贺志芳,文凤华,黄创霞,等.投资者情绪与时变风险补偿系数[J].管理科学学报,2017,20(12):29-38.
[19] 李仲飞,陈峥.带有随机收入与时变风险厌恶系数的最优投资-消费问题[J].系统工程理论与实践,2017,37(7):1665-1678.
[20] 常浩,荣喜民,赵慧.不完全金融市场下基于二次效用函数的动态资产分配[J].系统工程理论与实践,2011,31(2):205-213.
[21] Kim T S, Omberg E. Dynamic nonmyopic portfolio behavior[J]. Review of Financial Studies, 1996, 9(1):141-161.
[22] Wachter J A. Portfolio and consumption decisions under mean-reverting returns:An exact solution for complete markets[J]. Journal of Financial & Quantitative Analysis, 2002, 37(1):63-91.
[23] Brennan M J, Xia Y. Persistence, predictability, and portfolio planning[M]. Handbook of Quantitative Finance and Risk Management. Springer US, 2010:289-318.
[24] Xia Yihong. Learning about predictability:The effects of parameter uncertainty on dynamic asset allocation[J]. Journal of Finance, 2001, 56(1):205-246.
[25] Lioui A, Poncet P. Understanding dynamic mean variance asset allocation[J]. European Journal of Operational Research, 2016, 254(1):320-337.
[26] Patrick B. Brownian equilibria under Knightian uncertainty[J]. Mathematics and Financial Economics, 2015, 9(1):39-56.