Pass the PRMIA PRM Certification 8008 Questions and answers with CertsForce

When modeling for operational risk, we are generally concerned with tail losses - this is because the horizon for operational risk is 1 year at the 99.9th percentile. Since the 99.9th percentile is in the tail region, we would like to ensure that the tails are modeled as accurately as possible. Operational risk distributions are modeled using heavy tailed distributions.

Heavy tailed parametric distributions such as log-normal, pareto and others are therefore a good choice for modeling risk severity, therefore statement I is correct.

Body-tail distributions are combinations of parametric distributions, with different types of distributions being used to model the body and the tail - this provides flexibility because small and medium losses upto a threshold can be modeled using one distribution, and losses beyond the threshold can be modeled using a different distribution that is a better estimate of the tail. Statement II is therefore correct.

A log-likelihood function simplifies the optimization of a regular likelihood function. We generally maximize (or minimize the risk functional) a likelihood function with a view to estimating the parameters of the underlying distribution. If the likelihood function is complex, it may sometimes make it mathematically easier to optimize the log of the function - as that changes exponents and multiplications to additions, while behaving in the same way as the underlying function. Therefore statement III is correct, log-likelihood is a means to estimate parameters for a distribution.

Statement IV is correct as body-tail distributions allow modeling different parts of the distribution differently from each other.

Rating agencies target both accuracy and stability when they assign ratings. These two objectives can sometimes conflict, so a balance needs to be struck between the two. Rating agencies do not target any particular 'accuracy ratio' or rankings. Therefore Choice 'c' is the correct answer.

Statement I is true. If a Monte Carlo simulation is based upon the same parameters as used for analytical VaR, and enough number of simulations are carried out, we would get the same results as with analytical VaR.

Statement II is false. We cannot use Monte Carlo simulations using parameters based upon a normal assumption when the underlying distribution is not normal. For example, if a return stream is based upon say a uniform distribution, we cannot use a simulation based upon drawings from a normal distribution even though we use the same mean and standard deviation.

Statement III is true. This is the advantage of historical simulations - no assumptions are necessary. (Historical simulations however often suffer from the great disadvantage of the paucity of data that would cover all possibilities.)

Statement IV is true. The results of historical simulations are limited to the data they are based upon.

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

Therefore any losses from poor strategic planning will not be a part of operational risk. Choice 'd' is the correct answer.

Note that floods, earthquakes and the like are covered under the definition of operational risk as losses arising from loss or damage to physical assets from natural disaster or other events.

The term 'group risk' has been defined in the FSA document 08/24 on stress testing as the risk that a firm may be adversely affected by an occurrence (financial or non-financial) in another group entity or an occurrence that affects ther group as a whole. These risks may occur through:

- reputational contagion,

- financial contagion,

- leveraging,

- double or multiple gearing,

- concentrations and large exposures (particularly intra-group).

Thus, the insurance sector may be considered a group, and a firm may suffer just because another group firm has had losses or reputational issues.

The FSA statement goes on to identify some elements of group risk as follows:

- intra-group exposures (credit or operational exposures through outsourcing or service arrangements, as well as more standard business exposures);

- concentration risks (from credit, market or insurance risks which could put a strain on capital resources across entities simultaneously);

- contagion (reputational damage, operational or financial pressures); and

- complex group structures (with dependencies, complex split of responsibilities and accountabilities).

Therefore Choice 'a' is the correct answer and the rest of the choices are incorrect.

Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice 'd' is the correct answer.

Note that Basel II defines operational risk as follows:

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

If VaR is calculated based upon historical simulations, and these simulations are designed as to include all stress scenarios of interest, then VaR and stress tests can be a part of an integrated risk measurement system. Therefore it is not correct to say that stress tests are always separately modeled from VaR and II is false. I and III are true, and therefore Choice 'd' is the correct answer.

Statement I is true, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models.

Statement II is correct, the number of data points from which model parameters are estimated must be greater than the number of parameters. So if a distribution, say Poisson, has one parameter, we need at least two data points to estimate the parameter. Other complex distributions may have multiple parameters for shape, scale and other things, and the minimum number of observations required will be greater than the number of parameters.

Statement III is true, if the ILD data and scenarios cover the same risk, they are essentially different perspectives on the same risk, and therefore should be combined as weighted averages.

But if they cover completely different risks, the models will need to be added together, not averaged - which is why Statement IV is true.

According to ISDA standard definitions, the legal claim for OTC derivatives is the current replacement value of the contract. Therefore Choice 'c' is the correct answer. None of the other choices are correct.

For EVT, we use the block maxima or the peaks-over-threshold methods. These provide us the data points that can be fitted to a GEV distribution.

Least squares and maximum likelihood are methods that are used for curve fitting, and they have a variety of applications across risk management.