基于损失厌恶的基金管理者的投资决策模型

The Investment Decision Model for a Fund Manager with Loss Aversion

本文从风险约束的视角研究基金管理者呈损失厌恶的投资决策问题。用行为金融学的前景理论刻画损失厌恶,构建了以CVaR为风险约束的最大化管理者期望价值的投资决策理论模型。利用辅助函数得到了与原模型具有相同最优解的等价模型,并利用Monte Carlo模拟方法将等价模型转化为线性规划问题,通过求解等价模型得到了管理者的最优投资策略和努力水平。为了说明本文提出的模型和方法的有效性,用我国股市的数据进行了数值实例。本文的研究成果为基金管理者提供了投资决策的理论依据和方法。

Security investment funds are a type of professionally managed investment vehicles that pool money from many investors to purchase securities.With the development of security fund companies,this industry plays an important role in the financial system.There is a principal-agent relationship between a fund manager and his/her investors who do not know the investment behavior of the manager.The manager may be in a moral hazard situation because the information known by the manager and investors are asymmetric.Thus,it is important to examine a manager＇s investment behaviors.The aim of this paper is to study the optimal investment policy of the manager and its impact on the performance of fund from the perspectives of behavioral finance and risk management.The process of researching this problem is given as follows.First,we consider the loss aversion of the manager who is responsible for implementing investment strategy,managing trading portfolio,and receiving management fees as compensation.Furthermore,the performance of the fund is related to the investment ability of the manager,such as stock selection ability and market timing ability.Moreover,the manager＇s behavioral characteristics about the risks of investing securities are the most important factors impacting investment strategies.The manager is assumed to be rational and risk-averse in the literatures.However,the manager is not always risk-averse but can also be loss-averse with the change of the return and risk of the portfolio according to the research of behavioral finance.Therefore,we consider the loss aversion of the manager in order to analyze the impact of manager＇s risk preferences on the performance of fund and optimal investment policies.Second,conditional value at risk （CVaR） is used as a risk measure to control the risk of portfolio.Mathematically speaking,CVaR is derived by taking a weighted average between the value at risk （VaR） and losses exceeding VaR,which allows the manager to limit the likelihood of incurring losses caused by certain types of risk-but not all risks.The income of the manager is part of fund management fees which are included in the return of the portfolio.The manager can select more risky assets with a higher return so that the manager can receive management fees.The manager has risk-taking behaviors which are not beneficial to the investors.Thus,we use CVaR to control the risk-taking behavior of the manger in order to protect investors.This paper studies investment decision making problems in a single investment period with the manager being loss averse.The prospect theory in behavioral finance is used to describe the loss aversion of the manager.The investment decision theory model with CVaR as a risk constraint and maximizing the expected value of the manager are proposed.The equivalent model with the same optimal solution as the original model is derived by constructing an auxiliary function.Using the Monte Carlo simulation method,the equivalent model is transformed into a linear programming model which is computed to obtain the optimal investment policies and the effort level of the manager.Some numerical examples are given using stock data in China＇s stock market in order to demonstrate the effectiveness of the model and method proposed in the paper.Fund managers can use the findings of this study to assist in their investment decision making process.