Model 3

We have already pointed out that the J. P. Morgan RiskMetrics process is a non-stationary GARCH(1,1) process. The generally poor performance of this process which is fully multivariate in the sense of being based on the construction of a covariance matrix and which does also attempt to capture the autocorrelation of volatility is rather surprising. The main drawback of this process is possibly the en-masse assignment of the same parameter set for all financial series. In defense of the en-masse RiskMetrics setting of $\beta_1 = 0.94$ we would like to point out that the parameters for tail emphasized GARCH(1,1) in table 1 may very well be approximated by an en-masse setting of $\beta_1 \approx 0.96$but with non-zero and diverse minimum variance $\alpha_0$. It would seem that adding a minimum variance ($\alpha_0 \neq 0$) to the RiskMetrics variance prediction might go a long way in improving its performance. We believe that the difference in values for $\beta_1$ may arise simply out of our portfolio choice which does not have the variations in instrument class which are attempted to be captured by the RiskMetrics settings.