状态依赖和损失厌恶下的鲁棒投资组合模型及实证

Empirical study on robust portfolio model under regime-dependent and loss aversion

金融实证研究表明,资产的收益和风险随市场状态而变化,利用单一状态刻画资产的收益特征不能满足实际的投资需要。本文从资产收益分布随市场状态转换的角度出发,利用前景理论刻画投资者损失厌恶的心理特征,并同时考虑投资组合的调整费用,构建状态依赖下的损失厌恶投资组合模型。然后,考虑模型对参数的敏感性问题,将资产的收益率看成区间随机变量,并结合鲁棒优化理论构建状态依赖和损失厌恶下的鲁棒投资组合模型。在此基础上,采用对偶理论,将投资组合模型转换为线性规划问题,进而降低了模型的求解难度。进一步地,为了直观地控制模型的保守程度,在模型中引入了最大违反概率。最后,利用实证的方法,研究在不同市场状态下资产的收益特征以及投资组合模型的有效性。

Since Markowitz(1952)firstly formulated the mean-variance model,the portfolio optimization as an effective risk management tool has attracted a lot of attention.However,there are several well-known documented limitations in the mean-variance model.Black et al.’s study(1992)showed that the model is highly sensitive to the expected returns.A small perturbation in expected returns may lead to a large variation in the optimum portfolio allocation.To address the issue of sensitivity,many scholars proposed robust portfolio models by taking the parameter uncertainty into consideration.From the current researches,most of robust portfolios are proposed under the hypothesis that investors are perfectly rational beings,which does not always hold in real life.Furthermore,many empirical studies indicated that the return and risk of financial assets vary with regimes.Thus,the portfolio model that employs a single state to describe the return distribution cannot meet practical demands any more.In this study,the robust portfolio model under regime-dependent and loss aversion is proposed.The model considers the features of the regime-switching,loss aversion,and parameter uncertainty.The process of researching this study is given as follows.Firstly,we assume that return distributions are dynamic with respect to different regimes because the return and risk of financial assets vary with market regimes.The prospect theory is used to describe investors’loss aversion characteristics,which means that people are more sensitive to losses than to gains.Furthermore,the loss aversion utility function proposed by Fortin et al.(2011)is used to measure the portfolio’s utility.After considering the transaction cost of portfolio adjustment,the loss aversion portfolio model under regime-dependent is presented.Secondly,we regard the asset return as an interval random variable after considering the parameter uncertainty.Based on the robust framework of Bertsimas et al.(2004),the robust portfolio model under regime-dependent and loss aversion is proposed.Following the duality theory,the proposed model can be transformed as a linear programming problem,which reduces computational complexity.Moreover,to adjust the conservatism of the proposed model and reflect investors’safety requirement intuitively,a concept of the most violated probability is introduced to determine the value of the robust parameter.Thirdly,based on the Markov regime-switching model,we use the real data to study the regime-switching in Chinese stock market and the effectiveness of the portfolio model.The results show that:(1)the expected return and standard deviation are significant different under various regimes;(2)the regime-switching is important in the portfolio decision-making,especially for the portfolios with the increasing degree of conservation;(3)compared with the nominal portfolio model,the robust portfolio model exhibits robustness against the expected return and meets investors’safety requirement;and(4)under the condition of meeting the investors’safety requirement,the return of the portfolio model outperforms the index investment,and the investment return is robust for the value of the most violated probability.Thus,the proposed portfolio model is viable in real investment.