Introduction:

This measure is inspired by the BIS Green, Yellow and Red zone designations associated with a risk model defined as follows:

Green zone: A risk model is stated to be in this zone on day t if there are 4 or fewer events of losses beyond the 99% confidence level in the last 250 days - which is precisely the set X_t^(k,P) defined in expression .

Yellow zone: A risk model is stated to be in this zone on day t if there are between 5 and 8 events of losses beyond the 99% confidence level in set X_t^(k,P).

Red zone: A risk model is stated to be in this zone on day t if there are 9 or more events of losses beyond the 99% confidence level in set X_t^(k,P).

The BIS uses the above zones as the basis for assessing the reliability of VaR models.

To construct our measure we first allow the prescribed confidence (99%) to become a variable c and then determine the frequency of the red and green zone designations associated with the model in the out-of-sample period as a function of c. Since our out-of-sample has 1000 prediction-realization pairs, we have 4 non-overlapping periods of 250 days but 751 distinct but overlapping moving samples, X_t^(k,P), $t\in[251,1001]$,in which to determine the frequency of the BIS colour designations. (We omit the yellow frequency from the presentation since the frequency of this middle designation leads to no clarity in the comparison of models.)