最优组合选择中的风险容忍参数选择

Optimal Portfolio Selection Based on Risk Tolerance Parameters

文中提出了一种新的评价资产管理者能力的指标-跟踪比率(Tracking Ratio;TR)法,它很好地克服了夏普比率(SR)和信息比率(IR)在评价管理者能力上的不足。与此同时首次讨论了期望效用函数中的风险容忍参数选择,结果表明风险容忍参数的选取并不是全部正实数,而是由历史数据的期望收益率、方差-协方差矩阵和大盘收益共同确定的正实数区间,由此区间确定的最低要求收益同时也是判别投资组合是否为有效组合的必备条件。实证得到了结合TR曲线、效用函数曲线和组合有效前沿曲线选择出的最佳风险容忍参数以及相应的最优组合权重。

An increasing number of investors and asset managers are concerned with optimal portfolio selection.In 1952,Markowitz developed the Mean-Variance Model （EV）,which turns portfolio selection into quantitative analysis.Since then,many scholars have proposed restricted optimal portfolio models,such as tracking error volatility,transaction cost,drop constraints,VaR and CVaR,based on EV model.Meanwhile,other scholars used Sharpe Ratio （SR） and Information Ratio （IR） to evaluate different effective frontiers.With portfolio models continuously proposed,the researchers found effective frontier explicit expressions based on return maximization.Risk minimization could not be achieved when constraints increase （more than equal to three）.Besides,SR can only evaluate asset managers＇ total investment ability,but can＇ t measure managers＇ investment capacity other than using indices for different markets （bull or bear）.Although IR can accurately measure asset managers＇ investment ability beyond index,it cannot measure total investment ability.This paper discusses effective frontier selection under utility function maximization by introducing risk tolerance parameters.This model can overcome ineffective frontier expressions of traditional models.This paper proposes a new evaluation index of asset managers＇ ability——namely Tracking Ratio （TR） on that basis.TR overcomes the lack of manager capacity evaluation of Sharpe Ratio （SR） and Information Ratio （IR）.First of all,this paper uses corresponding expect utility function maximization models when considering risk-free asset.Then,we calculate the optimal portfolio weights of the proposed models and their corresponding expressions of tracking ratios by using the Lagrange multiplier method.Meanwhile,this paper deduces obtaining risk tolerance parameter selection range by combining tracking ratio with expect utility maximization.The results show a real interval determined by the expected return rate,variance-covariance matrix of history data and grail return,Besides,the minimum requirement return determined by the interval is also the necessary condition which determines whether the portfolio is effective.This finding further proves that effective frontier curve is not the hyperbolic curve in （σ,v） space that proposed by Merton.Finally,we conduct an empirical analysis of historical price data of Shanghai composite index,ShenZheng component index,SSE 180,Hushen 300 Index and Small and medium plate index in Chinese stock market.The empirical result verifies the feasibility and effectiveness of selecting optimal portfolio weight based on our proposed model.The finding also proves the importance of risk tolerance parameters in the course of portfolio selection.