Study of Portfolio Optimization Model Based on Design-Free Estimation

With the continuous advancement of the financial field, Markowitz portfolio model has become more mature, and covariance matrix estimation stands out in the application of the portfolio model. The covariance matrix estimation deviation problem in the portfolio model has great influence on the optimal solution. In order to correct the deviation of the covariance matrix and reduce the influence of the dimension curse and time-varying problems on the results, in this paper, the Design -Free estimation method is applied for the first time in the portfolio optimization model. Specifically, the portfolio optimization model is built on the basis of Design-Free estimation. The advantage of Design-Free estimation method is that it has no limit condition for the sample randomness and the parameter structure of covariance matrix, and can ensure that the estimated covariance matrix is a non-singular matrix, which effectively improves the accuracy of estimation. The empirical results show that compared with the traditional model and the stochastic matrix M-P distribution estimation portfolio model, the portfolio model based on design-free estimation has higher return-risk ratio.