Stock Return Forecast And Portfolio Performance Research Based On VAR

In modem portfolio theory,one(covariance matrix)and two parameters(covariance matrix and mean vector)need to be considered when seeking the optimal solution of the minimum variance and mean?variance portfolio models.In fact,these parameters are unknown.However,these input parameters are unknown,and in the process of finding the optimal solution,it is necessary to consider the problems of error accumulation and model instability.Therefore,in order to correctly calculate the risk of optimizing portfolio,the key to the problem is how to accurately estimate the expected return and covariance matrix,which has important theoretical and practical significance for portfolio performance research.The main research work of this paper is carried out in the following three aspects.One is to show that a vector-autoregressive(VAR)model captures stock return serial dependence in a statistically significant manner;the other is to replace the covariance matrix in the min-V portfolio model with 1-norm constraint by the covariance matrix estimator obtained from the VAR model to obtain the optimal solution of the portfolio;the third is to replace the covariance matrix obtained from M-V portfolio model with 1-norm constraint by the covariance matrix estimator obtained from the VAR model to obtain the optimal solution for the portfolio.The main work and conclusions are as follows:1.Using a VAR model to capture serial dependence in stock returns.We show that a vector-autoregressive(VAR)model captures stock return serial dependence in a statistically significant manner.We verify the validity of the VAR model for stock returns by performing extensive statistical tests on five empirical datasets and conclude that the VAR model is significant for all datasets.therefore,it is general enough to capture any linear relation between stock returns in consecutive periods,regardless of whether its origin can be traced back to cross-covariances,autocovariances,or both.And we find autocorrelation of portfolio and individual stock returns.We also find lead-lag relations between:big-stock portfolios and small-stock portfolios,growth-stock portfolios and value-stock portfolios also exists in China's stock market.2.Replacing the covariance matrix in the min-V portfolio model with 1-norm constraint by the covariance matrix estimator obtained from the VAR model,and the covariance matrix in the min-V portfolio model with 1-norm constraint improved by the nonparametric autoregressive(NAR)model.We used some software,such as MATLAB?R?EXCEL,to studied and analysed.Empirical analysis includes two parts.Part one,testing the statistical significance of the VAR model;second,we calculated the optimal solution?Sharpe ratio and turnover rate of the minV?VAR-min-V?NAR-min-V portfolio model,and built effective frontier.The results show that the VAR-min-V portfolio model predicts a higher portfolio yield.3.Replacing the covariance matrix in the M-V portfolio model with 1-norm constraint by the covariance matrix estimator obtained from the VAR model.And the covariance matrix in the M-V portfolio model with 1-norm constraint improved by the nonparametric autoregressive(NAR)model.The empirical analysis mainly includes two parts:First,we calculated the optimal solution?Sharpe ratio and turmover rate of the M-V,VAR.M-V and NAR-M-V portfolio model,and built effective frontier.The results show that the VAR-M-V and NAR-M-V portfolio models are less risky than M-V,VAR-M-V is slightly better than the NAR-MV portfolio model.Second,we predicted portfolio returns by using the optimal solution calculated from part one.The results show that the VAR-M-V portfolio model predicts a higher portfolio yield.