Free Practice Questions for PRMIA 8010 Exam

Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income.Therefore Choice 'd' is the correct answer.

Assuming time invariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period andn the number of time periods that we need to compute the new transition matrix for.

However, when the new time period is less than the time period the matrix is available for, the only way to deriving a transition matrix for a partial period is to numerically calculate a matrix M such that M^n = P. Therefore Choice 'b' is the correct answer. Taking cube roots of a matrix is not a possible operation, dividing by 3 gives a matrix meaningless in this context, and P x P x P will give us the transition matrix for 3 years, not 1/3rd of a year.

The easiest way to answer this question is to ignore the joint probability of default as thatis irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it is to think of asset portfolios, where diversification reduces risk (ie standard deviation) butthe expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% = $250,000.

This can also be seen from the lens of a joint probability distribution as follows:

There are four possibilities for this portfolio:

- Only loan A defaults: loss of $1m: 9% probability

- Only loan B defaults: loss of $1m: 14% probability

- Both loan A and B default: loss of $2m: 1% probability

- Neither A nor B default: loss of $0m: 76% probability

Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) = $250,000.

(Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A & B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

High frequency and low severity risks, for example the risks of fraud losses for a credit card issuer, may have high expected losses, but low unexpected losses. In other words, we can generally expect these losses to stay within a small expected and known range. The capital requirement will be the worst case losses at a given confidence level less expected losses, and in such cases this can be expected to below.

On the other hand, medium severity medium frequency risks, such as the risks of unexpected legal claims, 'fat-finger' trading errors, will have low expected losses but a high level of unexpected losses. Thus the capital requirement for suchrisks will be high.

It is also worthwhile mentioning high severity and low frequency risks - for example a rogue trader circumventing all controls and bringing the bank down, or a terrorist strike or natural disaster creating other losses - will probably have zero expected losses & high unexpected losses but only at very high levels of confidence. In other words, operational risk capital is unlikely to provide for such events and these would lie in the part of the tail that is not covered by most levels ofconfidence when calculating operational risk capital.

Note that risk capital is required for only unexpected losses as expected losses are to be borne by P&L reserves. Therefore the operational risk capital requirements for a low severity high frequency risk is likely to be low when compared to other risks that are lower frequency but higher severity.

Thus Choice 'c' is the correct answer.

This question relates to fitting a distribution to the true severity of the operational risk loss we are trying to model. The quality of the fit, or the precision of the fit, has two elements to the difference between the severity as represented by our model and the true severity. To understand this, consider the three data points below:

a. The true severity,

b. The best approximation of the true severity in the model space, and

c. The fit based on the dataset.

- True severity is what we are trying to model.

- The model space refers to the collection of analytical distributions (log-normal, burr etc) that we are considering to arrive at the estimate of the severity.

- The 'best approximation of the true severity in the model space' is reached byestimating the parameters of the distribution that optimizes the risk functional.

- The 'fit' is the actual parameter estimates we settle for with the distribution we have determined best fits the true estimate of our severity. When estimating parameters,we have various methods available for estimation - the least squares method, the maximum likelihood method, for example, and we can get different estimates depending upon the method we choose to use.

Our severity model will be different from the true severity, and the total difference can be split into two types of errors:

1. Fitting error, represented by 'c - b' above: The difference between the fit based on the dataset and the best approximation of the true severity is called 'fitting error', ie, a measure of the extent to which we could have estimated the parameters better.

2. Approximation error, represented by 'b - a' above: Approximation error is the difference between the true severity, and the best approximation of the true severity that can be achieved within the model space is called 'approximation error'.

One can reduce the approximation error by expanding the model space by adding more distributions. This will reduce the approximation error, but generally has the effect of increasing the fittingerror because the complexity of the model space increases, and there are more ways to fit to the true severity.

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 GEVdistribution.

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

The ISDA MA provides a template that can be used by market participants to document derivativetransactions. It has a core section that applies always, and various schedules that can be agreed to by the parties. The ISDA MA considerably facilitates closing transactions once the ISDA MA has been has been negotiated, without requiring a renegotiationeach time.

A key feature of the ISDA MA is that it binds all transactions into a single net obligation. The ISDA Master 2002 states that "All transactions are entered into in reliance on the fact that this Master Agreement and all Confirmations form a single agreement between the parties ... and the parties would not otherwise enter into any Transactions." Therefore transactions under the ISDA MA are not considered separate obligations.

The ISDA MA does indeed define close out processes, default and termination events, and the CSA is one of the parts of the MA that describes the collateral related agreement.

Other than Choice 'c', all others represent valid approaches to allocate economic capital to underlying business units. There is no such thing as 'fixed ratioeconomic capital contribution'

The capital adequacy ratio, also called the minimum capital requirement for credit risk per Basel II is 8% of riskweighted assets. The other choices are incorrect.

By assuming the assets to be independent, we are reducing the correlation from a positive number to zero. Reducing asset correlations reduces the combined standard deviation of the assets, and therefore reduces economic capital. Therefore Choice 'b' is the correct answer.

Note that this question could also be phrased in terms of the impact on VaR estimates, and the answer would still be the same. Both VaR and economic capital are a multiple of standard deviation, and if standard deviation goes down, both VaR and economic capital estimates will reduce.