Assets Allocation Strategy Based On Sparse Group LASSO Penalized Quantile Regression

With the rapid development of domestic financial market,quantitative investment methods have been widely used.However,China's economic and financial markets are at a new stage of development,and various unstable factors have exacerbated the fluctuations of financial markets.Therefore,while ensuring the maximum return on investment,it is particularly necessary to carry out reasonable and effective investment strategy research and method of risk measurement.Portfolio investment is a common method of asset allocation.The existing research on portfolio investment is based on the Markowitz mean-variance portfolio theory.However,due to the large estimation error,we usually only minimize the global variance of a portfolio.In the process of optimization,in order to solve the problem that a large number of elements of the covariance matrix need to be estimated,some scholars have proposed an effective method to impose penalty term in the objective function.It can also construct a sparse portfolio,which effectively reduces transaction costs.In changing risk measurement,the "pessimistic asset allocation strategy" with the quantile regression model as the objective function has received widespread attention.This strategy minimizes extreme tail risk called in the portfolio.However,in order to make the quantitative investment model more consistent with the "top-down" investment behavior of investors,and as the stock market usually has a plate effect,some scholars have suggested that investment portfolios that consider industry factors are more effective.To sum up,this article selects the sparse group LASSO,a regularization term that can divide assets into groups in advance,combines it with quantile regression model,and applies and penalty terms into global minimum portfolio strategy simultaneously.It can reduce transaction costs and investment risks,and enable the model to achieve the goals of "sparsity" and "risk diversification" at the same time.For this reason,this paper uses the Alternating Direction Multiplier Method(ADMM)to solve the model,and combines numerical simulation and empirical analysis to compare the performance indicators with some portfolio strategies in the existing research.The following three conclusions are drawn: First,this article allows investors to classify the stock industries in advance,improving the interpretability of the quantitative investment model;Second,this strategy can be effective by achieving sparse selection of industries and diversifying extrem risks of the investment portfolio;Third,by introducing penalties,the number of assets in the investment portfolio can be effectively reduced to control transaction costs.