Portfolio Optimization With Shrinkage Covariance Matrix And Sparse Method

This paper focuses on several issues in portfolio optimization.First,a sparse factors portfolio is constructed based on a shrinkage covariance matrix and a sparseization method.Secondly,a new portfolio optimization algorithm combining shrinkage covariance matrix and resampling method is proposed.Thirdly,the single factor is taken as an example to illustrate the shortcomings of IC,and the weighted IC is derived.The weighted IC can better reflect the relationship between the factor and the returns,and then derive the weighted composite factor based on the weighted IC.The factors portfolio is constructed with the composite factor optimal weight as the target exposure of the corresponding factors.The first part of this paper studied how to construct a sparse factors portoflio.We first discuss the two methods of constructing a factors portfolio.One is to construct a factors portfolio using cross-sectional regression of a multi-factor model.However,this method is not flexible enough to meet the individual needs and constraints of investors.The other is to construct a factors portfolio using the Markowitz meanvariance framework.This approach is very flexible and can meet the requirements of investors to join individual restrictions.Therefore,in order to obtain the sparse factors portfolio,we choose to add the l1 regularization condition to the weight under the Markowitz mean-variance framework,and threshold the covariance matrix to achieve the sparse purpose.The second part of the paper proposes a new algorithm for building optimal portfolios.First,we analyze the drawbacks of the Markowitz mean-variance framework.Some solutions to the problem of dealing with asset allocation vectors that are very sensitive to model input have been reviewed.There are two main methods,one is to improve the estimation accuracy of the model input,such as the prediction of better expected return and the more accurate estimation of the covariance matrix;the second is the resampling method proposed by Michaud.In the method of improving the estimation accuracy of the model input,the compression covariance matrix method has been proved by a large number of experiments that it can actually reduce the influence of the error on the model.But the effect of Michaud's resampling method on some data sets is still controversial.In order to further reduce the impact of estimation error on the model results,we propose a new algorithm that combines these two methods for asset allocation.The third part of this paper explores the construction of composite factors portfolio.We first explored how to construct an optimal factor weight that maximizes the composite factor IR.Then,a single factor is taken as an example to illustrate the shortcomings of IC,and the weighted IC is derived.The weighted IC is more reactive than the IC.Then,based on the weighted IC,we derive the optimal factor weight of the weighted composite factor.Finally,we use the optimal weight of the composite factor as the target exposure of the corresponding factor to construct a composite factors portfolio.And use the actual data to compare the weighted composite factors portfolio,the composite factors portfolio,and the original factors portfolio.