Uncertain Portfolio Selection Model And Decision Making Considering Options,Forward Contracts

Portfolio selection is to obtain as much profit as possible by optimal investment of one's capital to various financial assets under risk management.In 1952,Markowitz proposed the famed mean-variance portfolio model,which opened the door to modern portfolio theory.In real life,there are often situations where there are no historical data(such as newly issued stocks)or historical data cannot effectively reflect the future financial markets(such as the continuous meltdown of the US stock market in 2020).Then people have to use humans'estimates to help investment decision.The humans' estimates may deviate from the future real situation.Using probability theory may amplify the human estimation deviation.So this paper applies uncertainty theory to solve portfolio selection problem.In the field of uncertain portfolio,no scholar considers the investment of financial derivatives.Therefore,this article studies the portfolio selection problem considering financial derivatives under uncertain circumstance'The detailed research contents and innovations are as follows.(1)We discuss a mean-chance portfolio model with options under uncertain environment where stock index price is treated as an uncertain variable.Then we compare the optimal expected returns of portfolio with options and that without options.An important conclusion is reached:The portfolio investment with options produces a no less expected return than that without options.In addition,we make sensitivity analysis.As an illustration,a numerical example is presented as well.The numerical results reveal that the options should be considered in portfolio investment.And the call option with maximum exercise price is most valuable per premium cost with the same exercise date.(2)We model the portfolio investment with options by using risk index,which is defined as the average loss below the risk-free interest rate.Both analytical computation and empirical analysis reveal that the uncertain mean-risk index and the mean-chance portfolio have the same conclusion:Considering options generates a better return for portfolio;the options can effectively hedge the risk;and the call option with a higher exercise price offers higher return per unit of premium.Furthermore,we find that the mean-risk index model produces higher expected return in most cases than the mean-chance model.(3)Domestic portfolio selection is expanded to international portfolio selection issue.When stock prices and foreign exchange rates are uncertain variables,this paper discusses the uncertain mean-variance international portfolio selection with forward contracts.The study shows that the return on international portfolio is greater than or equal to that on domestic investment.And currency forwards have a good performance in improving return and reducing investment risk measured by variance when security prices and foreign exchange rates are lognormal variables,meanwhile considering forwards moves the efficient frontier of the portfolio to upper left.Further,if the log-security-price and log-exchange-rate have the same belief degrees at their respective expected values,currency forwards can effectively reduce investment risk.However,the study also confirms that currency forwards are not always advantageous.(4)For the same international portfolio problem,an uncertain mean-chance model is proposed.Then the analytical solution of the model is given.Furthermore,the impact of forwards hedging on uncertain international portfolio investment is discussed.At small risk tolerable level,forward contracts have a good performance in hedging risk and bringing high return.But,when the risk tolerable level becomes large,the risk reduction caused by the forward contracts also eliminates the potential high return.Moreover,considering forwards in international portfolio can bring more stable and relatively high return than that no forwards are considered.