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

When a default occurs, the proportion of the exposure represented by the recovery rate is recovered. For example, if the recovery rate is 40% for a loan, the actual loss in the event of a default would be $60 for a $100 loan. In other words, the loss given default = 1 - recovery rate. Hence Choice 'd' is the correct answer. All other choices are incorrect.

A default hazard rate is the rate of default in a continuous time setting. This question is asking for probability of survival at the end of 5 years. The formula to calculate the probability of survival at the end of t years where the default hazard rate is λ is e^(-λ *t) (or in Excel, =exp(-λ*t). Therefore the correct answer is Choice 'd'.

(It may be tempting to infer that if the probability of survival at the end of 1 year is 90% (1 - 10%), then the probability of survival in 5 years would be 90%^5. However this reasoning is not correct for the reason that the given rate is not the discrete rate of default, but the hazard rate which is nothing but the continuously compounded rate of default.)

If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of both of them defaulting together is affected by the default correlation between them. Marginal probability of default means the probability of default of each security on a standalone basis, ie, the probability of default of one security without considering the other security.

The relationship that expresses the probability of joint default of the two is given by the following expression:

It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p, ie the securities behave in an identical way, the expression resolves to just p, which is what we would expect.

From the above relationship, it is clear that the probability of joint default of A and B is the greatest when default correlation between the two is equal to 1, ie the securities behave in an identical way. Therefore Choice 'a' is the correct answer.