Risk Estimation And Portfolio Optimization In The A-share Marke

In this article,we have completed the covariance estimation of the A-share market.The estimate at the end of June 2019 has 3,500 dimensions.The starting point for estimating covariance in this paper is a factor model.Using the approach of Barra risk model,the covariance matrix is decomposed into system risk and trait risk and estimated separately.In estimating system risk,this article selected 32 industry factors and 10 Barra risk factors.We first tested these factors and found that none of the 10 risk factors has the ability to predict returns,that is,they are not Alpha factors.They have the ability to explain returns,but the ability to explain is not all stable.Four of the ten risk factors have better explanatory power,namely market value,beta,momentum,and residual fluctuations.Industry factors have a better ability to explain returns,and they are more stable.The Barra model framework referenced in this article is from CNE5 and a series of literature published by Morgan Stanley in 2012.Therefore,we tested the adaptability of the Barra model in the A-share market today.We found that near 2012,the Barra model can explain the degree of return to 40%,and then gradually declined,and now maintained at the level of 15-20%.The main reason for the decline in explanatory ability is that when mining risk factors within a sample,it is often impossible to guarantee continued validity outside the sample.The focus of this article is to explore methods rather than determine factors,and not to look for other risk factors.The first improvement we tried was to reduce the number of risk factors.It is found that,similar to some research conclusions,we also found that after retaining all industry factors,it does not seem to need too many risk factors.When the average absolute deviation of the covariance estimator is used as a standard,we find 10 risk factors The performance is similar to retaining the best 4 or even retaining only the best 1.The second improvement we tried was to make the risk factor matrix symmetrically orthogonal so that the new risk factor matrix would no longer have collinearity problems.It is true that orthogonal rotation does not improve the ability of factors to explain returns.However,after rotation,the estimation of factor returns will be more stable.In the author’s limited literature reading range,no studies have found orthogonal transformations to be used for covariance estimation.Under the criterion of mean absolute deviation,we see that symmetric orthogonal improves the Barra estimator.We also examined the impact of the Newey West adjustment and found that before and after the adjustment,the Newey West adjustment was not able to improve the estimates,either under the average absolute deviation or under the criterion of minimizing the out-of-sample performance of the combination of variances.The third improvement we tried was based on the phenomenon that the covariance estimator biases found in the study continue in the same direction,and a compression estimator aimed at correcting the previous period bias was constructed.The quantity is very different,and we give its derivation in the text.As one of the most important innovations in this article,we find that this compression estimation method greatly improves the Barra estimator under both standards.From 2011 to2019,its compression multiple of the Barra estimator is between 0.6 and Between 4.We extended this compression estimation method to the sample covariance,the covariance estimator,and the risk matrix based on the Fama French three-factor model.We found that the compression estimation method under the standard of average absolute bias greatly improved the sample covariance.Variance and the performance of the Fama French three-factor model estimator.There is no improvement in the risk matrix.We believe that this compression method is advanced in that the information that the variance is accumulative is passed to the original estimator.The risk matrix is one of the few estimators in high-dimensional covariance estimation,which reflects the clustering characteristics of variance.In the end,we determined a better estimation method for the A-share covariance,that is,based on the Barra risk model,to separately estimate the system risk and the trait risk.When the system risk was estimated,the risk factors were symmetrically orthogonal to each other.Compression estimation.This method is one of the best on the average absolute bias standard,and the out-of-sample performance of the minimum variance combination is the best.This article believes that the compression method that can convey the information of variance aggregation is very compatible with the factor model.The outstanding advantage of the factor model is the dimensionality reduction.Since the common factor values are relatively stable over time,the factor model can hardly reflect the information of the aggregation of variance.On the Fama French three-factor model,we verified this view again.After combining it with the compression method in the paper,the estimators under both standards have improved significantly.In the combinatorial optimization part,this paper introduces realistic constraints into the mean variance model and proposes a combinatorial optimization scheme that approximates the maximum information ratio.The combined optimization scheme has three advantages: First,the constraints of the scheme include industry constraints and market value style constraints.The selection of these two constraints is based on the characteristics of the A-share market: the degree of interpretation of returns by industry factors and market value factors High,the weight distribution of constraint combinations in different industries and different market value tiers can effectively spread risk.The second point is that the constraints of the income equation are added to the constraints,and the objective function is to minimize the risk.By traversing the constraint value on the benefits,and then solving,comparing the expected information ratios,the solution with the highest expected information ratio is found.This is one of the innovations of this article.Third,the corresponding relationship between the expected risk before optimization and the actual risk after optimization is designed as a risk adjustment function.This function is used to reform the traversal optimization process,and then the solution with the highest risk-adjusted expected information ratio is found.This point is also an important innovation of this article.In the empirical part,we show that the risk-adjusted search for the highest expected information ratio is significantly enhanced on the CSI 500 Index,and also shows a significant improvement over the benchmark solution.Many studies have shown that the mean-variance model systematically underestimates risk.The research in this paper finds that the combined optimization model under the mean-variance framework after the introduction of realistic constraints does not systematically underestimate risk.Under the optimization framework in this paper,the predicted tracking error has a beautiful monotonic relationship with the actual tracking error.When the predicted annual tracking error is higher than 6%,the actual tracking error often fails to reach the predicted value,and the predicted annual tracking error is less than 6 At%,the actual tracking error is often higher than the predicted value.The relationship between pre-forecast risk and ex-post actual risk depends to some extent on the constraints used,and the industry constraints and market value style constraints used in the article are adapted to the A-share market.In any case,it is important to study the relationship between predicted risk before optimization and actual risk after optimization,which will help improve the optimization model.