Research On Nonlinear Programming Stock Portfolio Based On Factor Analysis And Fuzzy Optimization

After 40 years of reform and opening up,China’s financial industry has developed rapidly,while venture capital is an important part of the financial industry.Nowadays,with the rapid development of China’s economy,the national wealth and disposable income are getting higher and higher.In the case of the real interest rate gradually turning negative,the Chinese people who have always been conservative are gradually trying to "embrace risk".At present,the risk investment of general investors in China is still dominated by securities.People’s risk investment is essentially a trade-off between income and risk.For the asset allocation of risk investment portfolio,rational investors will choose the portfolio that can obtain the highest expected return under the same risk,or the portfolio that has the lowest risk under the same expected return.Therefore,how to measure and allocate the risk and return of portfolio is of great practical significance for the management of their own investment.In the early 1860s,Markowitz put forward the classical mean-variance model,which first tried to solve the core problem of portfolio investment,that is,how to evaluate the expected return and risk of risk assets,and how to balance the expected return and risk in the portfolio allocation of risk assets,which laid the foundation for future research in this field Basics.One of the core parts of this paper is to improve and optimize the model.In addition,Markowitz’s mean-variance model solves the problem of how to determine the allocation proportion of assets after determining the alternative assets of the portfolio,but does not give the corresponding explanation for how to determine the assets.Therefore,the portfolio research of this paper will also combine with the previous research results,introduce a method of using financial indicators to evaluate the company’s comprehensive operating performance to assist in the selection of alternative investment assets,and combine it with the portfolio model,so as to form a complete set of methods of establishing alternative stocks to asset allocation.This paper first introduces a method based on factor analysis to evaluate and compare the comprehensive operating performance of listed companies,in order to help screen out the candidate stocks as the candidate assets of the portfolio model,and then combine them with the portfolio model.In the research of portfolio,we introduce market friction and other factors to improve the Markowitz mean variance model,relax its constraints,and make the model closer to the reality.Then,the objective function of the model is further optimized,and the original single objective portfolio model is transformed into a dual objective nonlinear programming model with unknown return and risk.In the process of solving the problem,the fuzzy linear programming model will be used to optimize the portfolio,and the income and risk of the portfolio will be dynamically balanced,and the optimal portfolio scheme will be given.In order to further explain and demonstrate the method and model discussed in this paper,this paper takes the component listed companies of CSI 300 food and beverage industry index as an example,gives the calculation steps and results of the improved model before and after the improvement,and compares and analyzes the results of the portfolio model by calculating the Sharpe ratio and the Treynor index of the portfolio.By comparison,it is found that compared with the single objective model which only considers return or risk,the model which considers both return and risk after fuzzy optimization has higher Sharpe ratio and treynold index,which means that more excess return can be obtained for each unit of risk,Therefore,the portfolio given by the optimized model is a better asset allocation scheme.