PRMIA 8008 - PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition

Note that events of default under the ISDA MA are caused by one of the parties that is considered 'at fault'. In contrast, "termination events" are events for which no one is at fault, for example changes in legislation, illegality etc that still justify termination of the transactions under the contract.

The ISDA MA describes the following 8 types of events of default:

1. failure of pay or deliver

2. breach of agreement

credit support default

4. misrepresentation

5. default under specified transaction

6. cross default

7. bankruptcy

8. merger without assumption

All of the options presented in the question are events of default.

Stress events rarely play out in a well defined period of time, and looking back it is always difficult to put exact start and end dates on historical stress events. Even after that is done, the question arises as to what magnitude of a change in a particular risk factor (for example interest rates, spreads, or exchange rates) are reasonable to consider for the purposes of the stress test.

Statements I and III correctly identify the two approaches that are acceptable and used in practice - the risk manager can either take the maximum adverse move - from peak to trough - in the risk factor, or alternatively he or she could consider the change in the risk factor from the start of the event to the end as defined for the purposes of the stress test. Between the two, the approach mentioned in statement III is considered slightly superior as it produces more believable shocks.

Statement II is incorrect because we never want to consider the minimum, and statement IV is not correct as it is likely to generate a shock of a magnitude that is not plausible. Therefore Choice 'b' is the correct answer.

Choice 'b' is the correct answer. When two securities have a correlation of +1, they are effectively the same security. In such cases, the standard deviations of the two securities are additive, which means the VaRs can simply be added together to get the combined VaR. All the other choices are incorrect.

Choice 'c' in particular would have been correct if the securities were completely uncorrelated, ie if they had a correlation of zero.

Choice 'a' would have been correct if their correlation were -1.

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.

Stress testing provides an independent and complementary perspective to other risk management tools such as value-at-risk and economic capital. Both are tools that serve similar purposes but are not interchangeable. Stress testing, no matter how exhaustively done, can not replace other tools such as those based on analytical or historical models. It can provide a useful sense check to validate models and assumptions, but is not a replacement for traditional techniques. Therefore statement I is false.

Stress testing can certainly help identify risks with new products for which historical data may be limited, and analytical models may be based upon many unproven assumptions. It can help challenge the risk characteristics of new products where stress situations have not been observed in the past. Therefore statement II is correct.

ICAAP stands for the 'internal capital adequacy assessment process' performed by a bank (remember the acronym and its expansion). Stress testing is an integral part of a firm's ICAAP, and not distinct. It is one of the elements of the internal process. Therefore statement III is false.

Statement IV is correct as stress testing is indeed a powerful tool that can communicate risks throughout the organization as the stress scenarios are easier to comprehend than arcane statistical models. They are also easier to explain to regulators, and are a powerful communication tool.

Thus Choice 'c' is the correct answer.

All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI - ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management's desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.

A computation of Altman's Z-score considers the following ratios:

- Working capital to total assets

- Retained earnings to total assets

- EBIT to total assets

- Market cap to debt

- Sales to total assets

It does not consider Net Income to total assets, therefore Choice 'c' is the correct answer. This makes sense as net income is after interest and taxes, both of which are not relevant for considering the cash flows for debt servicing.

The minimum multiplication factor specified under Basel II is 3. Therefore the correct answer is Choice 'a'. The exact requirements are laid down below.

Each bank must meet, on a daily basis, a capital requirement expressed as the higher of (i) its previous day’s value-at-risk number measured according to the parameters specified in this section and (ii) an average of the daily value-at-risk measures on each of the preceding sixty business days, multiplied by a multiplication factor.

The multiplication factor will be set by individual supervisory authorities on the basis of their assessment of the quality of the bank’s risk management system, subject to an absolute minimum of 3. Banks will be required to add to this factor a “plus” directly related to the ex-post performance of the model, thereby introducing a built in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 1 based on the outcome of so-called “backtesting.”

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.

According to Basel II, where marking-to-market is not possible, banks may mark-to-model, where this can be demonstrated to be prudent. Marking-to-model is defined as any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input. When marking to model, an extra degree of conservatism is appropriate. Supervisory authorities will consider the following in assessing whether a mark-to-model valuation is prudent:

• Senior management should be aware of the elements of the trading book which are subject to mark to model and should understand the materiality of the uncertainty this creates in the reporting of the risk/performance of the business.

• Market inputs should be sourced, to the extent possible, in line with market prices. The appropriateness of the market inputs for the particular position being valued should be reviewed regularly.

• Where available, generally accepted valuation methodologies for particular products should be used as far as possible.

• Where the model is developed by the institution itself, it should be based on appropriate assumptions, which have been assessed and challenged by suitably qualified parties independent of the development process. The model should be developed or approved independently of the front office. It should be independently tested. This includes validating the mathematics, the assumptions and the software implementation.

• There should be formal change control procedures in place and a secure copy of the model should be held and periodically used to check valuations.

• Risk management should be aware of the weaknesses of the models used and how best to reflect those in the valuation output.

• The model should be subject to periodic review to determine the accuracy of its performance (e.g. assessing continued appropriateness of the assumptions, analysis of P&L versus risk factors, comparison of actual close out values to model outputs).

• Valuation adjustments should be made as appropriate, for example, to cover the uncertainty of the model valuation.

The model should be created independent of the front office, and not by it. Therefore statement III does not represent an appropriate choice. Choice 'a' is the correct answer.