Portfolio Decision And Performance Evaluation Based On Quantile Regression

Since Markowitz propose analysis framework of mean-variance model, marks the beginning of modern portfolio theory. On this basis, the portfolio investment decision theory and the method of research made great progress, and provide the theory basis and decision support for diversification to reduce financial risk. In this paper, we carry out two aspects of research work on the portfolio investment decision problem.Proposed the mean-VaR model based on quantile regression and given the algorithm. Demonstrated the equivalence relation between VaR and quantile regression, when the confidence level is 100(1-α)%, the VaR is the opposite of the α quantile of the return sequence distribution function. The mean-VaR model solving process can be converted to a quantile regression problems, so as to avoied complex convex programming. In order to verify the validity of the model, we select 60 component stocks from the CSI 300 index, to compare the VaR risk portfolio investment model based on quantile regression with the variance risk portfolio investment model based on mean regression, performance, characteristics, the efficient frontier and the tail risk value of kernel density estimation. The empirical results show that the VaR risk portfolio investment model based on quantile regression can make investors for small tail risks, and better able to disperse the VaR risk, suitable for the tail risk management, and has more practical significance.Give portfolio investment decision plan which based on the LASSO quantile regression and solved the problem of performance evaluation. LASSO quantile regression is a combination of LASSO method and quantile regression which have two aspects of advantages. On one hand, through LASSO variable selection function, it can identify the important influence factors at different quantiles. On the other hand, through the quantile regression, it can carefully reveal the relationship between the explanatory variables and response variable at different quantiles. To applied LASSO quantile regression to portfolio decision, we select the hedge fund strategies index, Fama-French factors, the style and bond index to portfolio analysis. We then compare the style portfolio with some classical methods for portfolio choice, such as mean regression portfolio, equal-weighted portfolio, Markowitz portfolio. The empirical results show that the portfolio performance evaluation method which based on LASSO quantile regression is the most effective, and can get the best risk adjusted returns.This paper’s research work is mainly combining portfolio investment theory with risk measure based on quantile regression, and the performance evaluation method. It provides new thinking to the portfolio investment decision analysis that helps to the further development of the portfolio investment research. At the same time, this article embarks from the investors’ investment preferences, in order to obtain a optimal risk management and performance evaluation results, which for investment management practice has good guidance.