Research On Factor Covariance Estimation In Stock Market Structured Risk Models

With the rapid development of China's capital market,the focus of financial investors and researchers has shifted from indexed investment to quantitative investment.In fact,quantitative investment strategy is a kind of active portfolio management strategy with the aid of quantitative tools.The expected return and risk are the two protagonists of active investment management.The application of quantitative technology to active investment management is to find a balance between the two.However,a majority of modern financial models are about the expected return than the risk,so it will be an important research direction to establish the quantitative model from the risk angle.Based on the Barra models,which are widely used in the field of risk management,this paper chooses risk factors and industry factors with the explanatory ability and predictive ability to set up a structured risk model which is suitable for A share market.Factor returns are obtained by cross-section regression and their influences on portfolio income are analyzed.On this basis,the key to establish an effective risk model is to find an optimal estimation method of factor covariance matrix.The traditional method of sample covariance estimation lacks accuracy and robustness.The commonly used covariance estimation models can be divided into two categories: structured models and high frequency time series models.In this paper,for practical application,the sample covariance is eigen-adjusted as a “real” matrix,factor incomes are generated by multiple simulations,and derive factor covariance estimators from some structured models like random matrix model and combined estimation model.Then the evaluating indicator of the risk distance between the estimators and the “real” matrix is established,so as to compare the estimated effect and prediction effect of different estimators.The experiments of historical data and simulated data show that the estimators of complex structure obtained by combining different estimators are better than those of simple structure.They are closer to the “real” factor covariance matrix than estimator derived from average correlation model,and are more robust.At the same time,the combined estimator also shows a relatively better prediction effect.