Fuzzy Portfolio Selection Model With Cardinality Constraints

To obtain the high-yield and low-risk investment strategies is the focus of the modern portfolio research.Scholars carried out a lot of research on the framework of Markowitz mean-variance model and the probability theory.In actual investment practice,on the one hand,due to the uncertainty of the securities sample data,it is difficult for investors to obtain accurate probability distribution of yield.At the same time,the subjective factors of investors also have an impact on investment strategies,which makes investment management becomes more complicated.In this paper,we uses fuzzy theory and optimization theory to study the portfolio selection problem under uncertainty environment.On the other hand,the transaction cost in the securities transaction process directly affects the revenue,it is unrealistic to contain a large amount of securities in a portfolio,but the number of securities is too small,the risk of the entire portfolio will also become larger.Therefore,this paper refer to the existing research,focusing on the impact of cardinality constraint on portfolio strategies and returns.Firstly,based on the possibility theory and the classic investment model,we studied the influence of cardinality constraints,and for more realistic,we consider various constraints such as transaction costs and threshold constraints to construct a mean-semivariance fuzzy portfolio selection model with cardinal constraints.Then we validate the validity and effectiveness of the model by using the securities data from Shanghai Stock Exchange from April 2012 to April 2017,and analyze the impacts of the cardinality constraint on portfolio strategy and earnings.Next we construct the interval mean-variance-liquidity fuzzy portfolio selection model with cardinal constraints based on the mean-variance model,the interval theory and possibility definition,which also considered the securities liquidity.Finally the date of Shanghai Securities Exchange from February 2014 to March 2017 was used to empirically analyze the investment strategy with cardinality constraints of the proposed model.The results show that the cardinality constraints affects the investor's investment strategy and the final return,however,the impact of the cardinality constraint is limited to a certain extent.Investors choose a reasonable amount of securities to form a portfolio based on the characteristics of different securities can obtain the best investment income.