Assessment of VaR Performance

As mentioned earlier, the GARCH models are widely used for the management of risk. It is thus important to assess their quality through the various VaR measures discussed below. We begin with the assumption of conditional normal distribution in the return series and the results of the coverage tests for the thirteen modelling approaches and the RiskMetrics model. We then report the results of the coverage tests for the Student t distribution assumption, with 4 and 24 degrees of freedom.

A

5.3.4.1 Test for “Correct Unconditional Coverage” Ho: / = a

99% VaR Forecast

A

The main criterion is to achieve a probability of failure / equal to the desired level, i.e. a =0.01. The results of backtesting the VaR models for the 100-day out-of- sample forecasting period assuming normal distribution are shown in Table 5.8. The Christoffersen (1998) test rejects all the volatility modelling approaches except Tl. The likelihood ratio statistics for approaches T2 to T13, and the RiskMetrics, are all highly significant at the 1% level. This suggests that approaches T2-T13, and the

RiskMetrics, do not have the correct unconditional coverage property. However, the

likelihood ratio statistics for Tl is not statistically significant at the 1% level of significance, and therefore appears to satisfy the required coverage.

We next look at the results for the Student t distribution with 4 degrees of freedom assumption, which are shown in Table 5.14. It is clear that all results are statistically significant at the 1% level. Therefore, the results suggest that all modelling approaches (inclusive of the RiskMetrics), fail the correct unconditional coverage tests. However, more favourable results are obtained when we consider the

results of the Student t distribution with 24 degrees of freedom assumption, which are reported in Table 5.20. With the exception of the T3, T4, T5, T13 and the RiskMetrics approaches, the results of the coverage test for the other nine modelling approaches are not significant at the 1% level. Therefore, it appears that the nine modelling approaches satisfy the correct unconditional coverage property.

95% VaR Forecast

We turn to the results for the normal distribution assumption, which are presented in Table 5.9. The likelihood ratio statistics for the T4, T8, T i l , T12 and T13 volatility modelling approaches are statistically insignificant at the 5% level. Therefore, it appears that only these five approaches have the correct unconditional coverage. The rest, including the RiskMetrics approach, fail the correct unconditional test.

Similarly, the results of the coverage tests for the Student t distribution with assumptions of 4 degrees of freedom and 24 degrees of freedom are presented in Table 5.15 and Table 5.21, respectively. All results with the exceptions of the T4 and T5 approaches (for the 24 degrees of freedom) are statistically significant at the 5% level. All the modelling approaches fail the coverage test, and therefore, none of the modelling approaches appears to have the necessary coverage.

5.3.4.2 Test for “Independence”

First, we focus on the results for the normal distribution assumption for the 99% and 95% VaR models, which are presented in Table 5.10 and Table 5.11, respectively. For the 99% VaR coverage, we find that all approaches T1-T13 and the

RiskMetrics fail the independence test. The F-statistics obtained for these approaches

the required coverage property. For the 95% VaR coverage, only the T l, T2 and the T10 approaches pass the independence test. The F-statistics of all other approaches are significant at the 5% level. Therefore, we conclude that only the T l, T2 and T10 approaches satisfy the independence coverage criteria.

Next, we turn to the results of the 99% and 95% VaR independence tests for the Student t distribution, assuming 4 degrees of freedom, which are presented in Table 5.16 and Table 5.17, respectively. For the 99% VaR coverage, we find that with the exception of the T4, T6 and the RiskMetrics approaches, all the modelling approaches pass the independence test. The F-statistics for these approaches are not statistically significant at the 1% level, and therefore, they appear to have the required coverage property. For the 95% VaR coverage, we find that with the exceptions of the T4, T7, T9 and Tl 1 approaches, all the other approaches including the RiskMetrics approach appear to have the necessary coverage. The F-statistics for these approaches are not significant at the 5% level.

Next, we look at the results of the 99% and 95% VaR independence tests for the Student t distribution, assuming 24 degrees of freedom, which are reported in Table 5.22 and Table 5.23, respectively. For the 99% VaR coverage, we find that only approach T6 passes the independence tests. The F-statistics is insignificant at the 1% level. The rest of the modelling approaches do not appear to have the independence property. For the 95% VaR coverage, we find that only the T l, T2, T7, T10 and the T12 approaches have the independence property. The results for the rest of the modelling approaches are statistically significant at the 5% level, and therefore, they fail the independence test

5.3.4.3 Test for “Correct Conditional Coverage”

We analyse the results of both the 99% and 95% VaR measures for the normal distribution assumption, which are presented in Table 5.12 and Table 5.13, respectively. For the 99% VaR coverage, we find that the regression-based tests reject the adequacy of all models conclusively, with all F-statistics obtained showing significance at the 1% level. The results exhibit the existence of significant lagged dependence in the failure process. Given these results, we conclude that none of the VaR models are appropriate for the KLCI returns. The results are similar when we focus on the 95% VaR coverage. We find that all approaches produce results that are statistically significant at the 5% level. Therefore, these approaches do not have the correct conditional property.

Next, we turn to the results of the 99% and 95% coverage for the Student t distribution with 4 degrees of freedom. The results are reported in Tables 5.18 and 5.19 respectively. The results obtained for both the 99% and 95% VaR coverage indicate that all modelling approaches fail the correct conditional test. The results are statistically significant at the 1% level. Therefore, none of the modelling approaches has the required VaR coverage.

Finally, we analyse the results of the 99% and 95% coverage for Student t distribution with 24 degrees of freedom, which are reported in Tables 5.24 and 5.25 respectively. For the 99% VaR coverage, we find that all approaches do not have the required correct conditional coverage property. The results for all approaches are significant at the 1% level. The results for the 95% VaR coverage indicate that all the approaches again fail the correct conditional coverage test. All results are highly statistically significant at the 1% level. Therefore, none of the modelling approaches has the correct conditional coverage property.