Models 4 and 5

Table 1 shows the comparison between the parameters fit for GARCH(1,1) and tail emphasized GARCH(1,1). The main observation is that $\alpha_0$ for tail emphasised GARCH(1,1) - which represents a minimal variance - is considerably larger than regular GARCH(1,1). Also, by and large, $\beta_1$ is comparatively smaller for the individual series but comparatively larger for the sum series for tail emphasised GARCH(1,1). This opposing movement of $\beta_1$on the individual and sum series as a consequence of tail emphasis may point to possible volatility conditional effects on covariance to be discussed in paper [31].

While increasing the size of the minimal variance $\alpha_0$ may appear as a panacea for bad performance from the regulatory perspective - it should be noted that the mean log-likelihood will begin to deteriorate rapidly - if $\alpha_0$ is increased further - causing the model to predominantly over-estimate risk. Thus, in our view, the mean log-likelihood function achieves the right balance for penalizing risk underestimation and risk overestimation. In the beginning of this section we had commented that figures 1u and 1m make model 5 appear too conservative. Through figure 5u and 5m we can appreciate however that model 5 is reasonable and particularly so in the context of large movements. This highlights the deficiency of digital measures like exceedence count as the sole criteria for comparative evaluation of model performance in the context of risk management.