Research On Possibilistic Portfolio Selection Model With Background Risk

The fundamental objective of investment decisions is to select the optimal investmentportfolio from a large number of financial assets. The classical portfolio selection modelsassume that investors are risk aversion and they could allocate their wealth among risky assetswith the purpose of dispersing the risk and making profit. In the classical models, they onlyconsider financial risk. However, in real world, there exist some background risks which areresulted from risky non-financial assets such as the risks resulted from labor income, healthstatus, real estate and so on. These background risks will greatly affect the investmentbehavior and make portfolio selection more complicated with the reason that background riskscannot be dispersed by adjustment in financial markets. Up to now, some researchers haveinvestigated the influence of background risks on portfolio selection. These literatures areproposed under the framework of probability theory, in which the return of risky asset isviewed as a random variable.However, there exist many non-random factors in real financial market. Especially, in afuzzy uncertain economic environment, the return of risky assets is represented by a fuzzynumber. Therefore, how to select the optimal investment portfolio in a fuzzy uncertaintyenvironment has become an important research field.Taking the above-mentioned two aspects into consideration, we aim to systematicallystudy the problem of portfolio selection with background risk factors based on possibilitytheory and propose some possibilistic portfolio selection models with background risk undervarious environments. In order to make it better understood, we will analysis the porposedpossibilistic portfolio selection models and their efficient frontiers. The main work andcontributions of this thesis can be summarized as the following four aspects:First, we present a possibilitic mean-variance model on the basis of the preferencedegree of background risk and formulate a two-objective possibilistic portfolio model withliquidity constraint. We also discuss the influence of the different appetite degrees ofbackground risk and their efficient frontiers. We analyze the existing researches aboutbackground risk and regard the returns of risky assets and background assets as fuzzyvariables. Then, we propose a possibilitic mean-variance model based on the preferencedegree of background risk and a two-objective possibilistic portfolio model with liquidityconstraint, respectively. Assume that the returns of risk assets and background assets obeyLR-type possibility distribution, we propose two specific portfolio selection models based onfuzzy set theory. After that, we compare the efficient frontiers of the above-mentioned possibilistic portfolio model with various appetite degrees of background risk and analyze theinfluence of the liquidity constraint on the allocation of possibilistic portfolio withbackground risk. Empirical results indicate that the appetite degree of background risk affectthe portfolio risk and efficient frontiers. Suppose that the given expected return levels areidentical, as the value of background risk appetite degree approximates to1, the investors willprefer market risk. In this case, the investors will suffer less portfolio risk and thecorresponding efficient frontier of the portfolio will move to the upper left.Second, we propose two fuzzy portfolio selection models, namely, a fuzzy portfolioselection model with VaR constraint and a fuzzy portfolio selection model with backgroundrisk and value at risk (VaR). In the proposed two models, we discuss the influence of theconfidence level and the intercept of the straight line of VaR on the optimal investmentstrategy. Furthermore, we study the influence of the background assets mean and variance onthe efficient frontier. Then, we extend the classical VaR risk measure by credibility measureand define a fuzzy VaR risk measure. Consider the defined fuzzy VaR risk measure, wedevelop a fuzzy portfolio selection model with VaR constraints. At the same time, weincorporate the transaction cost and background risk into above-mentioned model and presenta fuzzy portfolio selection model with background risk and transaction cost. Then, under theassumption that the expected returns of risky assets and background assets are bell-shapefuzzy variables, we analyze the influence of confidence level and the intercept of the straightline of VaR on the optimal investment strategy. Meanwhile, we demonstrate the effect of thevariations of background assets mean and variance on its efficient frontier. Keep the otherparameters in the model invariant, when the means of background assets increase, the efficientfrontier moves to the upper left and the investment risk decreases. On the other hand, when thevariance of returns on background asset decreases and the other parameters in the model areinvariant, the efficient frontier moves to the left and the investment risk decreases.Third, we give the possibilistic mean, variance and covariance of the multiplication oftwo fuzzy numbers. Meanwhile, we formulate an international portfolio selection model withbackground risk. Based on possibilistic theory, we compute the possibilistic mean value,variance and covariance of the multiplication of two fuzzy numbers. On the basis ofafore-mentioned factors, we integrate both background risk and exchange rate risk intoportfolio selection model. Consider the variability and uncertainty of exchange rate, we viewboth the value of unit investment on risky asset and exchange rate as fuzzy numbers. Then, wepropose a possibilistic portfolio selection model with background risk and exchange rate risk.We comparatively analyze the influence of two risk abvoe on portfolio decision-making. Empirical results demonstrate that, when the given expected value is a invariant, the portfoliorisk with exchange rate risk and background risk is higher than the one without them. It meansthat if we neglect background risk and exchange rate risk, the investors will underestimateportfolio risk and suffer greater losses.Finally, we propose a possibilistic portfolio adjusting model with background risk. Inmost existing literatures, they only consider the investment risk. However, they ignore thebackground risk generated by many factors such as labor income, proprietary income,investments in real estate, etc. Based on this fact, we further study a possibilistic portfolioadjusted model with background risk under the framework of possibility theory. We discussthe influence of the appetite degrees of background risk on the portfolio adjusting strategies.Empirical results indicate that the preference degree of background risk affects the optimaladjusting strategy. When the investors’ appetite degree about background risk decreases, theportfolio risk will increase and the corresponding efficient frontier moves to the lower right.