The PRMIA Operational Risk Manager (ORM) Exam (8010) exam is a good choice and if the candidate manages to pass PRMIA Operational Risk Manager (ORM) Exam, he/she will earn PRMIA ORM Certification. Below are some essential facts for PRMIA 8010 exam candidates:
Which of the following techniques is used to generate multivariate normal random numbers that are correlated?
Correct : C
A PRNG (pseudo random number generators of the kind included in statistical packages and Excel) is used to generate random numbers that are not correlated with each other, ie they are random. A Markov process is a stochastic model that depends only upon its current state. Simulation underlies many financial calculations. None of these directly relate to generating correlated multivariate normal random numbers. That job is done utilizing a Cholesky decomposition of the correlation matrix.
Specifically, a Cholesky decomposition involves the factorization of the correlation matrix into a lower triangular matrix (a square matrix all of whose entries above the diagonal are zero) and its transpose. This can then be combined with random numbers to generate a set of correlated normal random numbers. This technique is used for calculating Monte Carlo VaR.
The 99% 10-day VaR for a bank is $200mm. The average VaR for the past 60 days is $250mm, and the bank specific regulatory multiplier is 3. What is the bank's basic VaR based market risk capital charge?
Correct : C
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.
