Portfolio Analysis Based On Sparse Algorithm And Risk Measurement Method

For a long time,the relationship between risk and return of investment portfolio and the source of risk premium have been the main issues concerned by investors and the interest of scholars all over the world.At present,there are many models for the study of excess risk premium of stocks,and the most familiar one is the multi-factor model.This model establishes an effective screening mechanism to select stock portfolio by selecting factors related to stock price,such as corporate fundamental information,market information and macroeconomic information.However,with the advent of the information age,the number of factors is increasing.How to reduce the dimensionality of high-dimensional factor data,select risk factors that can effectively reflect excess returns,and conduct investment analysis based on this factor has become a research topic of many scholars.Principal component analysis is one of the most widely used dimensionality reduction methods in the market.The basic principle is to maximize the variance of selected factors,extract the principal components that can represent all factors to the greatest extent,and use the principal components to select stocks.Although the method can effectively reduce the factor dimension and correlation and reduce the systemic risk,in the process of constructing the principal component,the premise that the investor does not invest is considered to obtain more excess returns.That is to say,the selection of principal component does not reflect the risk premium information of stocks,and the stock portfolio selected by using principal component factor has a low or even negative correlation with the market excess return,which leads to the fact that many pca stock selections are not very effective.Lasso regression is also a commonly used method of dimensionality reduction.Its principle is to add a L1 penalty term on the basis of least square regression.By adjusting the penalty coefficient to control variable selection and at the same time to realize the estimation of variable coefficient,Lasso regression can be used to deal with the situation that the number of variables exceeds the number of samples.Compared with the more commonly used ridge regression,the results of Lasso regression are more sparse,which can realize the selection of variables,as well as the robustness of ridge regression.However,although Lasso regression can effectively reduce the data dimension,it can accurately track the risk premium.It has advantages in time series regression and variable screening,but it does not optimize the risk-return relationship,and it does not represent all factors to the greatest extent.Make the portfolio face a greater systemic risk.Therefore,this paper combines the advantages of Lasso regression in time series regression and variable selection,as well as the advantages of principal component analysis in sectional data,to explore a sparse model that can reflect the relationship between stock risk premium and risk factors.In the process of research,Fama-MacBeth's two-step regression method was used for reference.In the first step,Lasso regression was used to select risk factors in time series,and the contribution of each factor to risk premium was quantified.Second,the cross-section regression was used to calculate the price of each factor coefficient and test the explanatory power of the selected factor for risk premium.Finally,the coefficients obtained in the first and second steps are applied to the original risk factor data to make the factors with strong explanatory ability of risk premium have greater weight,and the principal component analysis model with additional weight information is established.This method can achieve the following two points at the same time.first,it can maximize the variance of risk factors on the sectional data,Second,the additional weight preserves the change trend of each factor in the time series relative to the stock risk premium,which solves the problem that the ordinary principal component analysis only ACTS on the factor itself and cannot reflect the stock risk premium,Finally,this paper analyzes the results and the meaning of this risk factor in the real economic environment,and explains the source of stock risk premium,its causes and effects.