Study On LASSO Penalized Quantile Regression Of Optimal Portfolio

Portfolio plays an important role in the financial field,and one of the most classic models is the mean-variance model proposed by Markowitz.To measure expected return by mean and to measure investment risk by variance marks the beginning of optimal investment portfolio.The mean-variance portfolio has the problem of parameter uncertainty.On this basis,the estimation of the inverse matrix and the mean are gradually carried out.With the development of modern technology,the available financial data has higher dimensions and its structure is complex.As a result,many estimates are no longer applicable.Due to the sparsity of high-dimensional data,the method of penalty regression is applied in many fields to solve the high-dimensional problem.Meanwhile,in the process of investment,investors not only pay attention to the impact of conditional mean on returns,but also pay more attention to judging risks through extreme values to improve expected returns,that is,studying conditional quantiles to measure risks and get the optimal portfolio.Therefore,it has certain practical significance and value to study the high-dimensional penalty quantile regression optimal portfolio.Under the background of mean-variance portfolio model,this dissertation proposes LASSO penalty quantile regression method to study the optimal portfolio based on the two cases that the sample size of n is greater than the dimension of p and the dimension of p is greater than the sample size of n.Under some regularity conditions,the proposed method can control the risk and attain the maximum expected return asymptotically.Based on risk and Sharpe ratio,in sample and out of sample simulation studies compare with the existing methods and the proposed method has a good effect.Selecting SP500 index data in empirical research,the real application carried out to assess the performance of the proposed method.When the sample size of n is greater than the dimension of p,this dissertation considers whether there are transaction costs or not.When the dimension p is larger than the sample size n,this dissertation considers whether there are two cases in the period of economic recession.The results illustrate the robustness and effectiveness.It further shows its practical value and has good guidance for investment management practice.