The Research On The Estimation Of Multivariate Time-varying Higher Order Co-moments And Its Application In Portfolio

The modern portfolio theory initiated by Markowitz mainly focuses on the first two moments of assets' return,that is,it is assumed that the first two moments of return can fully describe the characteristics of the distribution of return.However,as advanced technology are applied to the capital market,investors can obtain more and more information by obtaining higher frequent data of return.High-frequency data often make the asset return rate have the characteristics of sharp peak,thick tail and skewness.These characteristics prompt investors to pay attention to the higher order moments of return rate,such as the third and fourth order moments,when carrying out portfolio.Therefore,scholars proposed to introduce higher-order moments into the portfolio model and put forward the portfolio model based on higher-order moments.In recent years,some scholars have found that the high-order moments of assets' return are time-varying in the financial market,and the introduction of time-varying high-order moments into the portfolio model can bring more returns and less risks to investors.The estimation of the time-varying co-moments of assets' return is very difficult because of the lack of information of higher order moments in the distribution and the curse of dimensionality.In addition,scholars calculate the optimal weight by taking the weight as the variable and maximizing the investor's expected utility function after estimating all order moments of return when carrying out the portfolio based on high-order moments.However,few scholars have studied the sensitivity of the optimal weight to the moment of return.If the optimal weight is not sensitive to the higher order moments,then we only need to pay more attention to the mean and variance-covariance matrix rather than higher order moments.Based on the above problems,this paper firstly systematically review and summarizes the existing literature on the portfolio based on the higher order moment.In view of the problems existing in the existing literature,the following problems are studied:(1)This paper firstly studies the sensitivity of the optimal weight of mean-variance-skewness model and mean-variance-skewness-kurtosis model to the selection of utility function and the selection of risk measure in the utility function under the investment strategy of maximizing the investor's expected utility function.Next,this paper studies the sensitivity of the optimal weight to each moment of assets' return.We find that for these two models,the optimal weight shows different characteristics on the selection of utility function,the selection of risk measure and the sensitivity of each moment of return.For the mean-variance-skewness model,there may be no solution problem for the optimal weight,while for the mean-variance-skewness-kurtosis model,there always exists an solution for the optimal weight.In addition,the sensitivity of the optimal weights of these two models to the higher order moments is higher than that of the mean and variance.(2)In this paper,an estimation method for multivariate time-varying higher order moments is proposed by using the constant correlation coefficient among higher order moments and the idea of shrinkage estimation.For this estimation method,we just estimate the time-varying higher order moment for each asset return,then use the correlation among higher order moments to estimation time-varying comoments.In order to obtain more precise estimation for the time-varying higher order comoments,we use the idea of the shrinkage estimation to shrink the sample comoments and the time-varying higher order comoments estimated by the above procedure and the shrinkage estimation for time-varying higher order comoments.(3)By means of the factor model,this paper proposes another estimation method for time-varying higher order comoment.We assume the characteristics of assets' return can be decomposed into two parts,the common component and heterogeneous component.Some observable factors can characterize the common component of assets' return.The heterogeneous components are mutual independent.We firstly build the linear regressive model for factor and estimate the factor loading.Next,we assume the distribution of factor follows skewed student t distribution with time-varying parameters and obtain the time-varying higher order moment for single asset by the time-varying distribution parameters.Similarly,we assume the distribution of each heterogeneous component follows skewed student t distribution with time-varying parameters and obtain time-varying higher order moment for each heterogeneous component.Lastly,we use the expressions of higher order comoments among assets' return,factors and heterogeneous component to obtain the time-varying higher order comoment of assets' return.The innovation of this paper is mainly reflected in the following three aspects:(1)This paper analyze the sensitive of the optimal weight to the selection of utility function,the selection of risk measure in utility function and each order moment of asset return.(2)This paper proposes an estimation method for multivariate time-varying higher order comoments of assets' return based on the constant correlation coefficient among higher order moments and the idea of shrinkage estimation.(3)This paper proposes another estimation method for multivariate time-varying higher order comoments of assets' return based observation factors.The main idea is to set the distribution of factors as a distribution with the characteristics of time-varying distribution parameters,then use the time-varying distribution parameters to obtain the time-varying cohigher order moment of factors,and finally use the time-varying higher order comoment of factors to obtain the time-varying higher order comoment of assets' return.