A Study Of Stock Volatility Forecasting And Portfolios Based On MHAR Model

Volatility is a measure of the level of risk of financial assets,and the estimation and forecasting of multivariate volatility is of great value in the construction of optimal investment portfolios.With the development of China’s modern capital market system,the size and role of China’s stock market has gradually increased.Over the past decade,the market capitalization of China’s stock market has increased from nearly twenty-plus trillion to over ninety trillion RMB.Companies are able to raise funds quickly by Initial Public Offering,while stock investors are able to construct portfolios to obtain stable returns while diversifying risk.High-frequency data of assets contain richer market information compared with low-frequency data.This paper estimates and forecasts the multivariate volatility of stocks based on high-frequency data and applies it to construct dynamic portfolios,which helps investors to allocate stock market assets and manage changes in portfolio risk more effectively and obtain expected returns from the perspective of wealth management.In this paper,10 constituent stocks belonging to different sectors in China’s SSE 50 index are selected according to liquidity indicators as research subjects,and five-minute high-frequency data from August 12,2019 to December 31,2021 are used to construct three multivariate volatility estimators of realized covariance(RC),modulated realized covariance(MRC),and threshold realized covariance(TRC),where MRC and TRC estimators are designed to address the market microstructure noise and jumps that exist in high frequency data.In this paper,a multivariate heterogeneous autoregressive(MHAR)model is constructed based on the idea of the heterogeneous market hypothesis,and the MHAR-D model is constructed by adding the diagonal elements of the covariance matrix alone as lagged variables in the MHAR model.Considering that the daily volume data of stocks may contain additional valid information,this paper then introduces individual stock daily volume indicators into the MHAR model and its extended form of MHAR-D model respectively,and proposes the improved MHAR-V and MHAR-D-V models.In order to facilitate the evaluation of the advantages and disadvantages of different multivariate volatility estimators and forecasting models,this paper applies the forecasting results of four models under three estimators to the minimum variance portfolio and evaluates the portfolio performance using the portfolio mean,portfolio standard deviation and Sharpe ratio indicators to explore the most appropriate estimator and model.Through this paper,we find that(1)the multivariate volatility of stocks has significant long memory characteristics,and the realized variance of individual stocks exhibits stronger long memory compared to the realized covariance of different stocks.Compared with short-term investors whose trading frequency is daily,the trading behavior of medium and long-term investors whose trading frequency is weekly and monthly has a greater impact on the diversified volatility of stocks,that is,there is heterogeneity among Chinese stock market investors.(2)Compared to the RC estimator,both the MRC estimator,which attenuates the effect of market microstructure noise,and the TRC estimator,which removes the jump component,improve the goodness of in-sample fit of the multivariate volatility models,resulting in smaller loss function values for each model’s out-of-sample forcasting.The model forcasting results based on the MRC estimator applied to the minimum variance portfolio obtain lower portfolio risk and higher portfolio return.(3)Under the three estimators of RC,MRC and TRC,the MHAR-V and MHAR-D-V models with the introduction of daily stock volume indicators significantly improve the in-sample fit and out-of-sample forcasting performance of the original models,and the model forcasting results obtained higher portfolio mean and Sharpe ratio when applied to the minimum variance portfolio.This indicates that making full use of the additional information in the individual stock daily volume data can effectively enhance the forecasting ability of the multivariate volatility model and thus improve the economic performance of the portfolio.(4)After adjusting the sample for robustness testing,the MHAR-V model with the MRC estimator still has the highest portfolio performance,which is the optimal model for this paper,and the forcasting results of this model can obtain at least 1.68% more annualized return when applied to the minimum variance portfolio than the benchmark MHAR model with the MRC estimator.