Pass the PRMIA PRM Certification 8008 Questions and answers with CertsForce

Under the contingent claims approach, credit risk is modeled as the value of a put option on the value of the firm's assets with a strike equal to the face value of the debt and maturity equal to the maturity of the obligation. The cost of credit risk is determined by the leverage ratio, the volatility of the firm's assets and the maturity of the debt. Cash flows are not a part of the equation. Therefore Choice 'a' is the correct answer.

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.

Simulations of liquidity needs can be of various types: historical simulations, where the current positions are subjected to the kind of liquidity shocks experienced in the past; static simulations, where a static view of current positions, counterparty credit position, and the business is considered; and dynamic simulations where all factors are dynamically changed including counterparty credit standing, changes to the current portfolio and behavioural aspects of the business. Choice 'b' is incorrect as dynamic simulations require no such assumptions.

Liquidity risk is often thought of in terms of market liquidity risk and funding liquidity risk. Market liquidity risk relates to the the liquidity for a particular type of asset drying up. For example, during the 2007-2009 crisis a large number of corporate bonds and structured products became extremely illiquid. Market liquidity risk manifests itself in the form of higher bid offer spreads, higher pricde impact, and a reduction in the normal market size (ie, the 'normal' size of a trade for which a dealer quote is valid for). Therefore Choice 'd' is correct. Similarly, Choice 'a' is incorrect as adverse price impact results from market liquidity risk and not funding liquidity risk.

Market liquidity risk applies to the entire market and all its participants. It is not idiosyncratic. Therefore Choice 'c' is incorrect too. Funding liquidity risk on the other hand applies to an individual institution that is under liquidity stress in the sense of not being able to meet its obligations such as margin or collateral calls because of a lack of liquid assets. Thus it is funding liquidity that is idiosyncratic. Market liquidity risk often leads to funding liquidity risks materializing as firms are unable to get to the funds they were relying upon due to assets becoming illiquid.

A standard model for representing asset returns in finance is the Geometric Brownian Motion process, and returns according to this model can be estimated by the expression given in Choice 'b'. Note that prices according to this model are log-normally distributed, and returns are normally distributed.

The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.

The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

The VaR in this case will be the top quintile of observations. In this case, since there are exactly 100 observations, this would mean the worst return would become the VaR. Therefore Choice 'b' is the correct answer. Choice 'a' and Choice 'c' make no sense. This highlights that at higher confidence levels, fewer and fewer observations impact the VaR if we are using historical simulation based VaR.

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 and n 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 three pillars are minimum capital requirements, supervisory review and market discipline. National regulation is not a pillar described under the accord. Choice 'c' is the correct answer.

The default correlation between two obligors goes up if the joint probability of default between them increases. This is intuitive. Also consider the formula for the default correlation between two obligors

Default correlation = [P(1,2) - P1 * P2] / √P1*(1-P1)*P2*(1-P2); where P(1,2) is the joint probability of default between the two and P1 and P2 are their individual probabilities of default. Obviously, an increase in P(1,2) will cause the default correlation to increase.

The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice 'a' is the correct answer.

Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.