Application Of Modified MHAR Model In Volatility Timing Strategy

With the increasing scale of quantitative funds and ETFs in the global market,the quantitative management of large-scale portfolios has gradually become a hot topic in academic research.Among them,the most important research is the volatility timing strategy.The core idea is to adjust the portfolio weight according to the covariance matrix.So it is important to estimate and predict the covariance matrix.On the other hand,with the increasing availability of high-frequency data,modeling with high-frequency data has become a hot topic in academic research.When predict the covariance matrices,the model which most commonly used is the multivariate heterogeneous autoregressive model(MHAR)extended by one-dimensional heterogeneous autoregressive(HAR)model,which can effectively capture the long memories of the volatility.However,it uses the same coefficients for all elements in the covariance matrix,and cannot describe the different properties of diagonal and non-diagonal elements.Secondly,a lot of research shows that the return of assets has asymmetry effect on the volatility,and the MHAR model cannot capture this trait.Based on these two considerations,this paper expands on the basis of the MHAR model.Firstly,this paper proposes a MHAR-D model that can separately model diagonal and off-diagonal elements,and compares it with the existing DRD model..Secondly,the paper introduces linear threshold model,logical smooth transfer model and semi-covariance model to describe the information asymmetry effect in the above three models,and compares them.For the covariance matrix estimator,KEM,MRK and MRC estimators that can satisfy the robustness of the noise and the asynchronous transaction and ensure the positive definiteness are selected.Further,these three covariance matrix estimators are used in the above model for out-of-sample prediction,and the economic value under three kinds of volatility timing strategies,such as equal risk contribution,minimum variance and most diversified portfolio,are compared.In addition,the MCS test is used.In order to verify whether the optimal model is applicable under different market conditions,this paper divides the out-of-sample prediction interval into low-volatility and high-volatility intervals to test the robustness.The empirical data are 1-second high-frequency data of 20 constituents in the SSE 50 Index that have different liquidity.Empirical studies have found that in the Chinese market:(1)The proposed MHAR-D model for constructing different structures of diagonal and non-diagonal elements is superior to the traditional MHAR model,while the DRD model is not necessarily better than the MHAR model.(2)Introducing leverage model in the above three benchmark MHAR models can improve the economic efficiency of investors.(3)After introducing the leverage,the global optimal result appears in the MRC-MHAR-D-ST model,which further illustrates the superiority of MHAR-D model.Secondly,the combination of ST leverage and MHAR-D model proposed in this paper is more suitable for China market.(4)The above results are robust in various market environments.In the study of the volatility strategy,it is found that the most diversified portfolio is more applicable in the low volatility market,and the minimun variance portfolio is more applicable in the high volatility market.