Application Of High-dimensional Covariance Matrix Estimation Methods In Industry Configuration

This article is an empirical article on how to build a portfolio based on risk planning in industry configuration.In the question of "industry allocation",the main is the "inter-industry correlation",which includes two aspects:cross-sectional(simultaneous)correlation and time series(cross-period)correlation.There are usually two perspectives(method categories)to study the correlation between industries:"economic logic" and "statistical logic".The first research question of this article is:how to estimate(predict)the covariance matrix more accurately.From the perspective of machine learning,prediction can be roughly divided into two steps:select the appropriate data in the sample and because of financial time series problems often face sample The problem of inconsistent distribution of internal and external data,so the use of short window width data can better capture the current market structure,but the sampling error is larger(Variance),and the use of long window width data can be better To reduce the sampling error,but can't reflect the current market situation,so the deviation is large(Error).In order to keep the distribution of data within and outside the sample as uniform as possible and choose to use short window width data,it is necessary to reduce the sampling error as much as possible from the perspective of the model.The high-dimensional covariance matrix estimation method used in this paper mainly includes two categories:one is the sampling error is reduced when estimating the cross-sectional correlation.The other is When estimating the cross-sectional correlation,it better reflects the current market structure and the simultaneous estimation of the cross-sectional correlation.In terms of evaluation indicators,this paper uses the out-of-sample variance of the minimum variance combination,combined with the MCS(Model confidence set)method,as a measure of the accuracy of the covariance matrix estimation.It is found through empirical research that the compressed estimation method is more suitable for the domestic industry allocation problem and the DCCGARCH model is used to capture the intertemporal rotation effect between industries,thereby improving the accuracy of the estimation.Since covariance matrix estimation is only a link in combination construction,the relationship between covariance matrix estimation,combination constraint conditions and combination construction method(risk planning method)needs to be further studied.Further discussions in this session are also minor innovations in this article compared to other related literature.As for the discussion on the relationship between covariance matrix estimation method and combination construction method,the combination construction method used in the empirical research is based on risk planning From the perspective,the essence is to explore how to choose the objective function in the sample to obtain the risk dispersion outside the sample(without considering the income term).Therefore,in this paper,based on the derivative index calculated by the combined net value sequence,combined with the MCS(Model confidence set)method,the relevant evaluation index is constructed.Through empirical research,it is found that:in the domestic industry allocation problem,the combination construction from the perspective of risk planning Among the methods,the risk parity method under the soft threshold rule is relatively good,but in a statistical sense,it is not significantly better than other portfolio construction methods,possibly because the domestic industry is mainly driven by market factors,and various industries The risk exposure is relatively close,and it is difficult to form an independent market,so it is difficult for various risk planning methods to better disperse the risks outside the sample.