PRMIA 8010 - Operational Risk Manager (ORM) Exam

Let theprobability of default over a month be p. Therefore the probability of survival at the end of 12 months would be (1 - p)^12. Since the one year probability of default is 12%, we know that the probability of survival is 88%. Putting (1 - p)^12 = 88% and solving for p, we get p = 1.06%. Therefore Choice 'd' is the correct answer.

If capital calculations are done in a standard way regardless of risk (as reflected by credit ratings), then it creates a perverse incentive for the lenders' employees to lend to the riskiest borrowers that offer the highest expected returns as there is no incentive to 'save' on economic capital requirements that are equal for both safe and unsafe borrowers. Therefore statement I is correct.

Given that the portfolio of suchan institution is likely to then comprise poor quality borrowers, and economic capital would be based upon 'average' expected ratings, it is likely to carry lower economic capital given its exposures. Therefore any such economic risk capital model is likely to understate economic capital requirements. Therefore statement IV is correct.

Statements II and III are incorrect and Choice 'b' is the correct answer.

Unexpected loss for a credit portfolio refers to the excess of the VaR estimate over the average expected loss. Theterm 'unexpected loss' has this specific meaning in the context of credit risk, and not any other intuitive meaning. So if for a portfolio worth $100m expected losses are 4%, and the credit VaR at 99% is $12m, then unexpected losses at that VaR quintile are $8m. This is unrelated to actual realized losses versus expected losses.

Therefore Choice 'd' is the correct answer and the others are not.

Unexpected loss is used to determine the capital reserves to be maintained against a credit portfolio at a certain level of confidence.

One way to think about this question is this: we are provided with two pieces of information: if the portfolio is worth $100 to start with, it will be worth $95 at the end of year 1 and $85 at the end of year 2. What it isasking for is the probability of default in year 2, for the debts that have survived year 1. This probability is $10/$95 = 10.53%. Choice 'b' is the correct answer.

Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 2 as [1 - (1 - 5%)(1 - 10.53%)] = 15%.

The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.

Choice 'b' is the correct answer. All other answers areincorrect.

Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

Thedefault 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 persistence parameter, λ, is the coefficient of the prior day's variance in EWMA calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.

1 - λ is the coefficient of recent market returns. As λ is lowered, 1 - λ increases,giving a greater weight to recent market returns or shocks. Therefore, as λ is lowered, the model will react faster to market shocks and give higher weights to recent returns, and at the same time reduce the weight on prior variance which will tend to persist for a shorter period.

Operational risk capital estimated using the implied capital model is merely the capital that is not attributable to market or credit risk. Therefore Choice 'b' is the correct answer. All other responses are incorrect.

Choice'a' is the correct answer. Exposures such as those to a line of credit of which only a part (or none) may be drawn at the time of assessment present a difficulty when attempting to quantify credit risk. It is not correct to take the entire amount of the line as the exposure at default, and likewise the current exposure is likely to be too aggressively low a number to consider.

While the borrower has an information advantage in that he would be aware of the deterioration in credit standing before the bank and would probably draw cash prior to default, it is unlikely that the entire amount of the line of credit would be drawn in all cases. In some cases, none may be drawn. In other cases, the bank would become aware of the situation and curtail or cancel access to the credit line in a timely fashion.

Therefore a fixed proportion of existing credit lines is considered a reasonable approximation of the exposure at default against credit lines.