For a back office function processing 15,000 transactions a day with an error rate of 10 basis points, what is the annual expected loss frequency (assume 250 days in a year)
An error rate of 10 basis points means the number of errors expected in a day will be 15 (recall that 100 basis points = 1%). Therefore the total number of errors expected in a year will be 15 x 250 = 3750. Choice 'a' is the correct answer.
Credit exposure for derivatives is measured using
Current replacement values are a very poor measure of the credit exposure from a derivative contract, because the future value of these instruments is unpredictable, ie is stochastic, and the range of values it can take increases the further ahead in the future we look. Therefore it is common for credit exposures for derivatives to be measured using forward looking exposure profiles, which are distributions of the expected value of the derivative at the time horizon for which credit risk is being measured. To be conservative, a high enough quintile of this distribution is taken as the 'loan equivalent value' of the derivative as the exposure. Choice 'c' is the correct answer.
The notional value of derivative contracts generally tends to be quite high and unrelated to their economic value or the counterparty exposure. Therefore notional value is irrelevant.
What ensures that firms are not able to selectively default on some obligations without being considered in default on the others?
It is the cross-default clauses in debt agreements that generally provide that a default on one obligation is considered a credit event applying to all debts of the obligor, and therefore we are able to deal with credit risk at the borrower level, and not at the level of the individual security. It also helps avoid situations where borrowers can selectively default on some obligations while continuing to service others. Therefore Choice 'a' is the correct answer. The other choices are incorrect.
Which of the following statements are true:
1. A transition matrix is the probability of a security migrating from one rating class to another during its lifetime.
2. Marginal default probabilities refer to probabilities of default in a particular period, given survival at the beginning of that period.
3. Marginal default probabilities will always be greater than the corresponding cumulative default probability.
4. Loss given default is generally greater when recovery rates are low.
Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.
Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.
Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default - except in year 1 when they will be equal.
Statement IV is correct. LGD = 1 - Recovery Rate, therefore a low recovery rate implies higher LGD.
The probability of default of a security during the first year after issuance is 3%, that during the second and third years is 4%, and during the fourth year is 5%. What is the probability that it would not have defaulted at the end of four years from now?
The probability that the security would not default in the next 4 years is equal to the probability of survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%. Choice 'd' is the correct answer.
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