Factor Allocation Strategy Based On GARCH-Copula Method

As modern finance developing,more and more investment tools have been created and appeared in the financial market.Among them,factor investment is one of the most important methods that many investors and researchers pay attention to.They try to find the common risk factors which impact on different stocks,so using them to measure the expected return and volatility of equities.Most using factor models like CAPM,three factors,and five factors et al have made significant returns for investors and laid the foundation for subsequent extensive researches.When selecting factors,often they should be linear uncorrelation,so we can use them to realize diversification across factors.But recent researches have given some new evidence that although factors have low linear correlation,there seems some non-linear correlation,high dimension correlation,or asymmetry correlation among them,and these correlations may be time-varying.These correlations could cause the factors to become more covariant at certain market conditions,such as financial crisis.Without considering these correlations,portfolio returns could be less than we expected.Besides,complicated correlations may cause the distribution of the factors we use against the assumption of multinormal distribution.So,knowing the complicated correlations,it's worth setting up suitable models to analysis the impact of them,and finding if the correlation will affect our portfolio returns.To accomplish the purpose above,we will use the GARCH-Copula model,which is often used for multivariable correlation problems.We will use this method to consider the time-varying correlations among factors,taking them in the decision of asset allocation,and finally,test whether the time-varying correlations will bring higher returns.The benefit of using GARCH-Copula is we can separate the factors'distribution themselves and the correlation among them.With GARCH models,we can model each factor's autocorrelation,heteroscedasticity et al,and with the Copula model,we can measure the interaction among factors.Besides,this system is flexible.The selecting of single dimension distribution functions has no dependence on the multivariant distribution function,and each single distribution function can be different.First,we will use the ARMA-GARCH model for each factor return,and assuming the standard deviation is skew-t distributed.After removing autocorrelation and heteroscedasticity,use the distribution function to fit a Copula model.We have selected four types of Copula functions,constant normal Copula,constant t Copula,DCC normal Copula,and DCC t Copula.The DCC model could dynamically model the relationship between the correlation matrix at each time among multiple factors.By connecting the lag of the correlation matrix and the factor shocks,it will output a dynamic correlation matrix for each time.We fit the model with the five factors in the Chinese stock market,and finally examed using DCC t Copula will have the best performance and the correlations are time-varied.Besides,we also tried to find if the factors have asymmetry correlations,but there's no enough evidence to confirm that.To further explore the economic value of time-varying correlations,we used the Copula models above in the rolling investment with the historical data.By using the predicted variance matrix,combining the predicted returns,we maximize the mean-variance utility function of an investor and get the optimal factor weights.For the control group,use a fixed correlation matrix instead of a dynamic one.It turns out that after considering the time-varying correlation,investors could get a higher annualized average return.So there's the economic value of time-varying correlations.In short,we use the GARCH-Copula model to confirm the time-varying correlations among five factors of the Chinese stock market,and these correlations could bring higher returns for investors,the method could be used when investors encounter such problems.