Uncertain Portfolio Models With Multiplicative Background Risks

In reality,investors face not only financial risk but also background risk,that is,the risk brought by other exogenous uncertainties.Multiplicative background risk is a major category of background risk,which refers to the risk that affects on final wealth in a multiplicative way,such as inflation risk and exchange risk,and has a significant impact on investment.So far,most existing portfolio studies with multiplicative background risk are based on probability theory and assume security returns and background risk are random variables.In fact,due to the fast-changing environment or occurrence of unexpected events,historical data often do not reflect the real frequency effectively.Then people have to rely on expert estimates to help make investment decisions.Since people usually overestimate the possibility of the real occurrence of uncertain events,the use of probability theory will amplify the artificial estimation deviation.In view of the above situation,this paper uses uncertainty theory and regards securities return and multiplicative background risk as uncertain variables,to study the uncertain portfolio problem with multiplicative background risk.The main research contents and results of this paper are as follows:(1)This paper uses variance to measure investment risk,to study the uncertain portfolio problem considering inflation.This paper builds an uncertain meanvariance portfolio model considering inflation,and proves the impact of inflation uncertainty on portfolio through theoretical analysis on the basis of equivalent form of model.Based on the optimal solution of the model when the returns of risky asset and inflation obey linear uncertain distributions,the influence of the change of inflation on the investment choice is analyzed.It is found that the uncertainty of inflation increases the investment risk and leads investors to reduce the investment in risky asset.The investment proportion in risky asset increases with the mean of inflation rate and decreases with the increase of the width of inflation rate.(2)Using chance to measure investment risk,the uncertain portfolio problem considering inflation is studied.Firstly,this paper constructs the uncertain meanchance portfolio model considering inflation,gives the equivalent form of the model,and compares it with the model without considering inflation and the model that does not allow borrowing.Then,the optimal solution is given,and the influence of inflation on investment decision is analyzed when the returns of risky asset and inflation obey the linear uncertain distributions.The results show that ignoring inflation leads investors to choose portfolios with nominal wealth that exceeds their risk tolerance.Limiting borrowing for investment can restrict the potential for higher returns.When the mean of inflation rate increases or the width increases,the investment in risky assets decreases.And inflation makes the investors change the investment proportion in risky asset more gently when the stock market changes.(3)Using risk index to measure investment risk,the uncertain portfolio problem considering exchange risk is studied.This paper constructs an uncertain mean-risk index portfolio model considering exchange risk,and gives equivalent forms and the optimal solution of the model.Then the influence of changes in exchange rate on investment decision is analyzed when both risk asset returns and exchange rate obey linear or normal uncertain distributions.The analysis and experimental results show that the increase of the mean of exchange rate will lead the risky asset investment and expected wealth increase,while the increase of standard deviation of exchange rate will lead to the risky asset investment decrease.In face of exchange risk,investors with lower risk tolerance should hedge exchange risk through forward contracts,while investors with higher risk tolerance should choose portfolios without forward contracts.Compared with the uncertain meanchance model,the mean-risk index model is more comprehensive in measuring risk.(4)This paper uses variance to measure investment risk and entropy to measure the degree of investment diversification,takes the international portfolio problem affected by two multiplicative background risks,i.e.,exchange and tax risk,as an example,to study the uncertain portfolio problem considering multiple multiplicative background risks.This paper constructs an uncertain mean-varianceentropy international portfolio model,analyzes the relationship between the model considering multiple multiplicative background risks and the model considering single multiplicative background risk,and gives the deterministic equivalent forms.Then the paper analyzes the portfolio decision by using the data of NASDAQ and New York Stock Exchange.The results show that when investors’ risk tolerance level is low,they should hedge exchange risk through forward contracts,and when making investment decisions,uncertain tax rate cannot be ignored and more accurate tax rate distribution should be given as far as possible.Compared with equal-weight portfolio,the optimal portfolio based on mean-variance-entropy model performs better.