PRMIA Exam 8010 Topic 1 Question 40 Discussion

The current Basel rules for the basic VaR based charge for market risk capital set market risk capital requirements as the maximum of the following two amounts:

1. 99%/10-day VaR,

2. Regulatory Multiplier x Average 99%/10-day VaR of the past 60 days

The 'regulatory multiplier' is a number between 3 and 4 (inclusive) calculated based on the number of 1% VaR exceedances in the previous 250 days, as determined by backtesting.

- If the number of exceedances is <= 4, then the regulatory multiplier is 3.

- If the number of exceedances is between 5 and 9, then the multiplier = 3 + 0.2*(N-4), where N is the number of exceedances.

- If the number of exceedances is >=10, then the multiplier is 4.

So you can see that in most normal situations the risk capital requirement will be dictated by the multiplier and the prior 60-day average VaR, because the product of these two will almost often be greater than the current 99% VaR.

The correct answer therefore is = max(200mm, 3*250mm) = $750mm.

Interestingly, also note that a 99% VaR should statistically be exceeded 1%*250 days = 2.5 times, which means if the bank's VaR model is performing as it should, it will still need to use a reg multiplier of 3.