Investor's Portfolio Trading Behavior Under The Knightian Uncertainty

Markowitz studied the asset portfolio and its trading behavior through the mean-variance model,which attracted wide attention from scholars.The mean-variance model provides a concise and effective analysis framework for the problem of portfolio trading behavior based on the balance between returns and risks,inspiring a series of abundant research in the fields of asset portfolio,asset pricing and asset trading behavior,etc.Markowitz also fully supplemented the applicable conditions and limitations of the mean-variance model:firstly,objectively speaking,assuming that the distribution characteristics of asset returns are known,the results of the study of the behavior of asset portfolio transactions in a deterministic environment is not in consistent with facts;secondly,the "Ellsbregy paradox" clearly points out that the investors show characteristic of uncertainty avoidance,which is a risk avoidance type,and which is more obvious in the worst scenario.At this time,the uncertainty significantly affects the asset portfolio restructuring,trading behavior and its performance.Therefore,it is necessary to further study the issue of investor portfolio trading behavior under Knightian uncertainty.This article assumed that investors were risk aversion type,based on the mean-variance asset portfolio framework,using relative entropy to measure the degree of Knightian uncertainty of the model parameters,construct a portfolio model under Knightian uncertainty,and analyze investors' trading behavior of the asset portfolio in the worst scenario and its relationship with the performance of the asset portfolio.By listing the risk premium and its covariance separately from the model parameters,relative entropy was introduced to measure the degree of Knightian's uncertainty of the model,establishing a minimum-maximum portfolio model,and obtaining the optimal analytical solution of the model by using Lagrange method.Analysis of the impact of model parameter's Knightian uncertainty on portfolio performance and the adjustment of trading behavior were conducted.Three different types of asset portfolio sample data of macro characteristics,industrial characteristics and industrial chain characteristics were selected for comparative experimental research.The results showed that:(1)Knightian's uncertainty significantly affected the portfolio trading behavior.In the worst scenario,with the increase in the degree of uncertainty of the model parameter's Knightian uncertainty,although investors increased investment in risk assets in portfolio trading,their portfolio performance was declining;(2)The risk premium uncertainty had significant impact on portfolio performance.As the risk premium uncertainty increased,investors increased their investment in risk assets,the variance of the asset portfolio also increased,and the increase in the variance was greater than the increase in the risk premium,explaining that the uncertainty of the risk premium in the financial market has a "cost effect" problem;(3)The uncertainty of asset risk premium on asset portfolio transactions was stronger than on the uncertainty of risk premium covariance.As the uncertainty of the risk premium increased,the variance of the asset portfolio also increased and the increase was greater than the degree of uncertainty;when the uncertainty of the risk premium and its covariance all coexist,the uncertainty of the risk premium covariance appeared a trend of increasing at first and then decreasing,but the variance of the asset portfolio continued to increase as the uncertainty increased.(4)Substitution investment helped hedging asset portfolio risks and improving asset portfolio performance.As the model parameter's degree of uncertainty increased,the performance of asset portfolios with alternative characteristics will change more than those with complementary characteristics.The study elaborated on the impact of Knightian uncertainty on the trading behavior of the asset portfolio,gained insight into the economic phenomena in the financial market,and based on this,put forward suggestions to optimize the trading behavior of the asset portfolio under the Knightian uncertainty.Therefore,the innovations of this paper are mainly reflected in three points:the first is introducing the relative entropy method to measure the Knightian uncertainty of the model parameters,and optimizing the portfolio model under the Knightian uncertainty;the second is proposing the concept of maximum effective relative entropy based on the risk neutral measurement,from the perspective of the Knightian uncertainty,providing an analytical framework for the study of portfolio trading behavior under the worst scenario and explaining the phenomenon of "non-market participation";the third is,based on comparative empirical analysis,pointing out that alternative investment would help to improve the performance of the asset portfolio under the worst scenario and help to optimize the trading behavior of the asset portfolio.However,there are limitations in this research.The actual portfolio trading process is usually dynamic.Further in-depth research is required on How to introduce Knightian uncertainty into the dynamic portfolio trading model.