The Research On Modeling Multivariate Time-varying Higher Order Moments And Its Application In Portfolio Selection

Markowitz's mean-variance portfolio model is the cornerstone of modern portfolio theory,which pioneered the theory and method of portfolio investment for rational investors under uncertainty,and it has revolutionary impact on academic research and industry practice in the field of finance.However,with the improvement of financial econometrics modeling and the development of financial practice,the shortcomings of this model gradually emerge.The mean-variance portfolio model can involve a severe welfare loss in the presence of non-normally distribution asset returns and non-quadratic preferences.At the same time,many studies have indicated that the non-normally distribution asset returns and non-quadratic preferences are intrinsically related to their higher order moments.Implementing portfolio selection with higher order moments is an inevitable trend to overcome the defects of the mean-variance portfolio model.Furthermore,it is also found that asset returns have asymmetric and fat tail features and these features also change with time,which is characterized by time-varying skewness and kurtosis.Therefore,it is necessary to focus on the time-variation characteristics of higher order co-moments of asset returns in the portfolio research based on higher order moments.And it requires dynamic modeling method for the higher order co-moment matrix of asset returns.However,the current research on dynamic portfolio is mainly based on the time-variation of the first two order moments,and the portfolio research based on the time-varying higher order moments is very rare.Although the estimation of the conditional expectation vector and the conditional covariance matrix is mature,the estimation of the higher order conditional co-moment matrix is very difficult due to the curse of dimensionality.In this paper,we propose a suitable method for modeling multivariate time-varying higher order moments to solve the estimation problem of the higher order conditional co-moment matrix,and study the dynamic portfolio based on higher order moments.This paper summarizes the current research modeling on the higher order moments and its application.To overcome deficiencies of existing researches,we study the identification test of time-varying higher order moments and the dynamic modeling multivariate time-varying higher order moments and its application.Specific research contents obtained are as follows:(1)In this paper,we introduce the autoregressive conditional density(ARCD)model which is suitable for dynamic modeling higher order moments of the individual asset return.Considering that the asset return has asymmetric and fat-tailed properties,we use the inverse scale factor method to introduce asymmetry into the student T distribution and generalized error distribution,and obtain the skewed student T(SST)distribution and skewed generalized error(SGE)distribution.Then,the ARCD-SST model and the ARCD-SGE model are established based on the SST distribution and the SGE distribution respectively,and the parameters estimation,the identification test of time-varying higher order moments and model diagnosis test are discussed.In view of the shortcomings of existing identification tests of time-varying higher order moments,we propose a regression-based test.The Monte Carlo simulation is used to study the finite sample properties of the regression-based test,and the empirical size and empirical power under finite samples are obtained.(2)The multivariate time-varying higher order moments model based on dynamic conditional correlation is proposed by combining the dynamic conditional correlation modeling and the autoregressive conditional density model,which is also called the dynamic equicorrelation-autoregressive conditional density(DECO-ARCD)model.This model is based on the DCC-GARCH model,which takes into further consideration of the time-varying characteristics of the higher order moments.Thus,this model is an extension of the DCC-GARCH model,and it can be expressed as the nonlinear combinations of the autoregressive conditional density models.Then,we obtain the estimation of the higher order conditional co-moment matrix based on the model,and use the new impact surface to describe the effect of shocks on the higher order co-moments matrix.Finally,we use this model to study the higher order moments of the stock returns of the five components from the SSE 50 index,and use the prediction of the higher order conditional co-moment matrix to construct the dynamic portfolio.(3)The multivariate time-varying higher order moments model based on generalized orthogonal transform is obtained by combining the generalized orthogonal transform and autocorrelation conditional density model,which is also called the generalized orthogonal-autoregressive conditional density(GO-ARCD)model.This model is based on the GO-GARCH model,which further considers the time-varying characteristics of the higher order moments.Therefore,this model is an extension of the GO-GARCH model,and it can be expressed as the linear combination of the autoregressive conditional density models.In the process of model estimation,the independent component analysis is introduced to simplify the estimation into two steps,that is,the estimation of the mixed matrix and the estimation of the multiple autoregressive conditional density models.Then,we obtain the estimation of the higher order conditional co-moment matrix,and use the new impact surface to describe the effect of shocks on the higher order co-moments matrix.Finally,we use this model to study the higher order moments of the stock index returns of 15 countries participating in the Belt and Road,and use the prediction of the higher order conditional co-moment matrix to construct the dynamic portfolio.The main innovation of this paper is mainly reflected in the following three aspects:(1)In this paper,we propose two feasible methods to avoid the curse of dimensionality caused by the fact that a large number of parameters need to be estimated.These two methods impose some structural constraints on the higher order conditional co-moment matrix to reduce the number of parameters to be estimated and obtain two kinds of multivariate time-varying higher order moments models,which are also called dynamic equicorrelation-autoregressive conditional density(DECO-ARCD)model and generalized orthogonal-autoregressive conditional density(GO-ARCD)model.On the one hand,we can use these two models to describe the non-normal and time-varying characteristics of the asset returns.On the other hand,we can also easily obtain the estimation of the higher order conditional co-moment matrix.(2)In this paper,we propose a regression-based test to solve the shortcomings of existing identification tests of time-varying higher order moments.This test uses the standardized residual obtained by fitting the GARCH model to construct the test statistic.On one hand,it uses the probability integral transformation to avoid the constraints on the existence of the higher order moments of the time series.On the other hand,it considers the impact of the parameter estimation uncertainty on the statistical properties of this test,which makes it have good asymptotic statistical properties.The subsequent simulation study further indicates that the regression-based test has a good finite sample property and has a suitable empirical size and a high empirical power.(3)In this paper,we use the fourth-order Taylor series expansion of the expected utility function to introduce the higher order co-moment matrix into the portfolio and construct a dynamic portfolio strategy based on the higher order moments.Then,we compare it with different portfolio strategies.On the one hand,it can investigates the economic value of the portfolio strategies based on volatility timing and distribution timing.On the other hand,it can also investigate the impact of different utility function and different risk aversion on dynamic portfolio strategy based on higher order moments.The empirical studies of 5 stock returns and 15 national index returns show that: Firstly,the static mean variance portfolio strategy is not always dominant compared to the equal weight portfolio strategy,and its performance is related to the selected data set;Secondly,compared to the static mean-variance portfolio strategy,the dynamic portfolio strategy can obtain higher returns and smaller variance.And investors are more inclined to dynamic investment portfolio;Thirdly,the economic value of the dynamic portfolio with the higher order co-moment matrix is higher than that of the dynamic portfolio with the covariance matrix;Finally,with the increasing of risk aversion coefficient,the economic value of the static portfolio and dynamic portfolio has a significant decline.