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

Stress tests can cover known events, but since the future is unknown, and new events may be entirely different from what has happened in the past, they provide no assurance that an institution's worst case losses would be covered. Hence II is false.

Stress testing is required to be performed as part of Basel II, and therefore III is false.

Historical events do not have sharply defined start and end dates. Often, even after a crises ends, its after effects may continue to affect the markets for a long time. In such cases, it may be difficult to define the start and end of the crises. In many cases, the crises may persist for months or even years, making it difficult for the risk manager to identify a time period that covers the essence of the crises, and yet is focused enough to constitute a plausible scenario. Therefore IV is false too. Only I is true, and the correct answer is Choice 'b'.

The first two formulae describe component VaR. The last formula is the formula for Marginal VaR. Therefore I and II is the correct answer.

Component VaR is a VaR decomposition technique that allows the total VaR for a portfolio to be broken down and attributed to the components of a portfolio. The total of the component VaR for each constituent of a portfolio is equal to the VaR for the portfolio. This property is extremely useful as opposed to the standalone VaR for each constituent taken alone as it can be used for allocating trading budgets.

The correct answer is choice 'a'

A long position in a credit sensitive bond is equivalent to earning the risk free rate and the spread on the bond. The risk free rate can be earned through a long position in a treasury bond, and the spread can be earned in the form of premiums on a CDS, which are received by the protection seller, ie the party short a CDS contract. Therefore we can get the same results as a long bond position using a combination of a long treasury bond and a short position in a CDS. Choice 'a' 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.

Altman's Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the 'distance to default model', and therefore Choice 'a' is the correct answer.

A fat tailed distribution has more weight in the tails, and therefore at a high level of confidence the VaR estimate will be higher for a distribution with heavier tails. At relatively lower levels of confidence however, the situation is reversed as the heavier tailed distribution will have a VaR estimate lower than a thinner tailed distribution.

A higher level of kurtosis implies a 'peaked' distribution with fatter tails. Among the given choices, a distribution with kurtosis equal to 8 will have the heaviest tails, and therefore a higher VaR estimate. Choice 'a' is therefore the correct answer. Also refer to the tutorial about VaR and fat tails.

When calculating volatility weighted VaR, returns are adjusted by a factor equal to the current volatility divided by the historical volatility, ie the volatility that existed during the time period the returns were earned. If the current volatility is greater than the historical volatility (also called contemporary volatility), then it has the effect of increasing the magnitude of any past returns (whether positive or negative). This in turn increases the VaR.

Consider an example: if the current volatility is 2%, and a return of -5% was earned at a time when the volatility was 0.8%, then the volatility weighted return would be 12.5% (=-5% x 2%/0.8%). Clearly, this has the effect of increasing the VaR.

Choice 'd' is therefore the correct answer.

Any good risk measure has the property that it is sub-additive, which means the whole is less than the sum of the parts. In the case of VaR, sub-additivity arises due to the diversification effect, or said differently, due to the correlation between different assets being less than one. Therefore Choice 'd' is the correct answer.

Super-additivity is just the opposite of sub-additivity, ie, the whole is greater than the sum of the parts. Good risk measures do not have super-additivity. Therefore Choice 'b' is incorrect.

Choice 'c' states the same thing as Choice 'b' in different words, and is incorrect. Choice 'a' is non-sensical and incorrect.

Where a historical shock factor does not exist for a security, for example because the security is new or was only thinly traded earlier, or because a particular emerging market was immature at the time of the historical scenario being considered, it is inappropriate to leave the position unshocked. By and large, the general rule to be followed when carrying out stress testing is to leave no position unshocked. Therefore Choice 'b' is the correct answer.

Choice 'd', Choice 'a' and Choice 'c' all represent valid approaches to estimating a shock factor in such cases.

Counterparty risk was difficult to gauge as it was impossible to know who the counterparty's counterparties were - this is true as the chain of financial transactions became excessively long with no central transparency of who owed who what. Bank A's credit depended upon the health of its counterparties, whose health in turn depended upon other counterparties. Thus Choice 'd' is a correct statement.

In an attempt to diversify, banks became more like each other - chasing yield, they piled into securitized products, and chasing diversification, they piled into different types of securitized products. The system as a whole became susceptible to small shocks in the assets underlying this vast edifice of structured products. Therefore Choice 'a' represents a correct statement.

Choice 'c' does not represent a correct statement. Central banks had little data on the interconnections between institutions. They were aware of the large volumes of OTC transactions, but had no data to figure out who was connected to who, and who had what kind of exposures.

Choice 'b' represents a correct statement. Most transactions, other than exchange cleared futures trades (which were a tiny fraction of all trades) were cleared on a bilateral basis. The existence of central counterparties (CCPs) could have limited the impact of the crisis significantly as market participants would not have lost trust in each other, and the 'collateral damage' that was witnessed from a fall in housing prices, and thereby mortgage assets, would have been more contained.