Analysis Of Optimal Investment Portfolio Construction Based On Utility Indifferent Price

How to evaluate the risk of stock portfolio has always been the focus of research in finance.If the risk caused by the change of stock price in the portfolio cannot be accurately measured,investors will face huge financial risks.The traditional risk assessment index value at risk does not consider the impact of the amount of each stock in the portfolio and the investor’s personal risk aversion on the portfolio risk assessment,but in fact,with the increase of the stock holdings,the individual’s risk assessment increases exponentially.So there are certain defects in the actual operation of the value of risk.In this paper,the nonlinear relationship between portfolio size and risk and the degree of investors’ individual risk aversion are included in the risk assessment of portfolio,and based on this,the price risk assessment index of portfolio utility indifference is proposed.This article investigates the properties of utility indifference price in evaluating portfolio risk and its performance in constructing the optimal investment portfolio.For individual investors,due to their limited energy and ability,there are fewer types of stocks in the portfolio when choosing an investment portfolio.Therefore,in empirical analysis,this article constructs an investment portfolio of eight stocks,allowing investors to freely choose the number of stocks held in each stock in the portfolio.Using the weekly closing price data of stocks from January 2019 to August 2022,calculate the utility indifference price of the investment portfolio and construct an investment portfolio that maximizes the utility indifference price.Then,compare the portfolio with the optimal investment portfolio based on value at risk and the equivalent investment portfolio through Sharpe values,and measure the advantages and disadvantages of the three investment portfolios from a cost-benefit perspective.This paper shows how to calculate the utility indifference price of the portfolio through the discrete mixed normal distribution GARCH model(MN-GARCH model),and how to estimate the parameters of the discrete mixed normal distribution GARCH model through the characteristic function method to solve the problem that the likelihood function parameter space is unbounded when estimating the model,and the estimation deviation is large when the real value is extreme.Finally,Monte Carlo simulation is used to verify the consistency and asymptotic normality of the feature function estimator.The results show that the utility indifference price takes into account the nonlinear relationship between portfolio size and risk and the degree of risk aversion of investors.Its assessment of portfolio risk increases exponentially with the increase of stock holdings,and can reflect the difference of risk aversion of investors in risk assessment of the same portfolio.In this empirical study,the investment portfolio based on utility indifference price performs better on the Sharpe value than the optimal investment portfolio based on value at risk and equal value investment portfolio.At the same time,the discrete mixed normal distribution GARCH model can effectively capture the "peak fat tail" and asymmetric characteristics of stock returns,and can also describe time-varying volatility well.The feature function estimation method also solves the shortcomings of the maximum likelihood method in this model.