The Research On Multi-factor Higher-order Comoments Shrinkage Estimation And Its Application In Portfolio Selection

The mean-variance model proposed by Markowitz assumes that the distribution of asset returns is a normal distribution or the utility function has a quadratic form.Numerous financial literature studies have shown that the distribution of return on assets has obvious sharp peaks,thick tails and asymmetric characteristics.These typical characteristics(Stylized Facts)have had a large impact on the mean-variance model established by Markowitz.In fact,with the improvement of financial measurement modeling technology and the continuous development of financial practice,the typical characteristics of the distribution of return on assets and the non-quadratic of the utility function have gradually become closely related to higher-order comoments.Therefore,the research on portfolio modeling and optimization based on higher-order comoments has begun to attract the attention of many scholars at home and abroad.The research on higher-order comoments usually adopts the direct method and the indirect method.The direct method is to directly optimize the function composed of the moments of the portfolio return as the objective function,thereby forming the mean-variance-skewness or mean-variance-skewness-kurtosis portfolio problem.The indirect method is to indirectly solve the expected utility function through the third-order or fourth-order Taylor expansion of the expected utility function.The above two methods,no matter which method is adopted,it is difficult to avoid the estimation of the added higher-order moment matrix.When the number of assets is large,the covariance matrix,coskewness matrix and cokurtosis matrix will be affected by the assets.The increase in the number leads to a significant increase in the parameters to be estimated,resulting in the "curse of dimensionality".A more effective method is to impose certain constraints on the elements in the moment matrix of each order,so as to structure it to reduce the dimensionality of the parameter space.This method aims to reduce the estimation error by increasing the model setting error,and then reduce the dimensionality of the high-dimensional matrix problem.Based on previous studies,this dissertation proposes a multi-factor higher-order comoment shrinkage estimation method based on the multi-factor model and moment estimation method to improve the estimation accuracy of the higher-order comoment matrix,thereby further improving the higher-order comoment portfolio which performed.Further,we select the number of factors of the higher-order comoment matrix obtained by the multi-factor higher-order comoment shrinkage estimation,and extract the common factors that can reflect the higher-order comoment information with a smaller number of factors to achieve the purpose of dimensional reduction.Specifically,the main research contents of this dissertation are as follows:First,this dissertation first proposes a multi-factor shrinkage higher-order comoment estimation method based on a multi-factor model.Based on the singlefactor shrinkage higher-order comoment matrix,we extend the single-factor shrinkage method to the multi-factor shrinkage method based on the multi-factor model.In order to obtain the multi-factor shrinkage estimator,we first obtain the multi-factor shrinkage estimation intensity,and the multi-factor shrinkage intensity is essentially an estimator,so we derive it mathematically and obtain its asymptotic consistency,and then obtain the multi-factor shrinkage estimator asymptotic consistency.Next,we use Monte Carlo simulation technology to test the large sample property of the proposed multi-factor shrinkage estimator.In order to reflect the effectiveness of the estimation method proposed in this dissertation,we also compare with the existing higher-order comoment estimation methods.In the empirical analysis,we combined the real data of some stocks in the Shanghai and Shenzhen 300 constituent stocks to further test the effectiveness of the multi-factor shrinkage estimation method,and compare it with the existing higher-order comoment estimation methods,which is a potential basis for further higher-order comoment portfolio analysis.Second,this dissertation selects the optimal number of factors for the higherorder comoment matrix estimated by multi-factor higher-order comoment shrinkage.The traditional principal component analysis method can only extract the information of asset return in the covariance matrix,and many studies have shown that the distribution of asset return has higher-order moment characteristics,so the method based on principal component analysis cannot effectively extract assets higher-order moment information in the asset return.We use the method of moment component analysis to extract the number of common factors from the multi-factor higher-order moment shrinkage estimation matrix.Under the assumption that asset return follows the multi-factor model,the moment component analysis of each order moment matrix constructed is carried out,and then the number of common factors is extracted.In the empirical analysis,we take the stocks selected from the Shanghai and Shenzhen 300 constituent stocks as an example.Through in-sample and out-ofsample analysis,we select the number of factors of the multi-factor higher-order moment shrinkage matrix,and extract the higher-order moment information based on the real return.Thirdly,using the real data of China's Shanghai and Shenzhen 300 listed companies,the multi-factor shrinkage higher-order moment method and the existing higher-order moment estimation method constructed higher-order moment investment portfolio strategies are compared and analyzed.Under the assumption that investors have utility functions with constant relative risk aversion coefficients,the expected utility function is expanded by Taylor series,and the global optimization algorithm is used to obtain the optimal portfolio weights obtained under each estimation method.We construct mean-variance-skewness higher-order moment portfolio strategies and mean-variance-skewness-kurtosis higher-order moment portfolio strategies respectively,and perform out-of-sample forecasting performance analysis based on equal-weight higher-order moment portfolios.In order to reflect the robustness of each estimation method,we further verify it by adjusting the risk aversion coefficient,the number of assets and the length of the rolling window.In addition,we compared the similarities and differences between the two higher-order moment portfolio strategies.At the same time,it also compares the out-of-sample forecasting performance of the higher-order moment portfolio strategy and the portfolio strategy based on the mean-variance model.Finally,we analyze from the sample,construct a higher-order moment portfolio strategy,and further test the advantages and disadvantages of the multi-factor shrinkage estimation method and the existing estimation methods.The main innovations of this dissertation are mainly reflected in the following three aspects:(1)Aiming at the problem that the number of parameters to be estimated increases geometrically due to the increase in dimension in the estimation of highorder moment matrix,this dissertation provides an estimation method that can effectively reduce the sampling error.By weighing the error caused by the multifactor model setting and the estimation error produced by the sample estimation method,a high-order moment estimation method based on multi-factor shrinkage is proposed.This method can well balance the error problems caused by the two methods,which means that when using this method to estimate the high-order moment matrix,the accuracy of the estimation can be improved,which lays the foundation for further construction of high-order moment portfolios.(2)This dissertation selects the optimal number of factors for the multi-factor higher-order moment shrinkage estimation matrix.The classical principal component analysis method is generally suitable for extracting the information of the return on assets from the covariance matrix,and a large number of studies have shown that the distribution of return on assets has sharp peaks,thick tails and asymmetry,so the method based on principal component analysis cannot fully extract the higher-order moment information in the return on assets.Through the moment component analysis of the multi-factor higher-order moment shrinkage estimation matrix,a small number of factors that can better explain the asset return are extracted.(3)This dissertation introduces the higher-order moment matrix estimated by the multi-factor higher-order moment shrinkage estimation method into the higherorder moment portfolio through the higher-order Taylor approximation expansion based on the expected utility function,thereby constructing the higher-order moment portfolio strategy.On the one hand,by constructing the mean-varianceskewness and mean-variance-skewness-kurtosis higher-order moment portfolio strategies respectively,it is analyzed and compared in many aspects with the higherorder moment portfolio strategies constructed by existing estimation methods.It is found that the investment portfolio strategy constructed by the method proposed in the dissertation performs better on the out-of-sample forecast metrics.Further tests on the robustness of the proposed method show that the investment portfolio strategy constructed by the proposed method still performs well after adjusting various parameters and experimental environment.On the other hand,compared with the traditional mean-variance portfolio model,it is found that the higher-order moment portfolio strategy constructed by the multi-factor higher-order moment shrinkage estimation method can not only fully absorb the historical information of stock returns and perform the higher-order moments modeling can also improve the investment welfare of investors and has very good economic value in the capital market.