Which of the following are valid approaches to calculating potential future exposure (PFE) forcounterparty risk: I. Add a percentage of the notional to the mark-to-market value II. Monte Carlo simulation III. Maximum Likelihood Estimation IV. Parametric Estimation
Correct Answer: C
Explanation When a derivative position is entered into, its mark-to-market value is generally close to zero (though the notional may be high). With the passage of time, the derivative's value fluctuates in an unpredictable way, creating a counterparty exposure that may be difficult to estimate and risk manage. Counterparty risk in such cases is estimated based on Potential Future Exposure, which may be calculated using either: a) Take the mark-to-market at present, and add a certain percentage of the notional, or b) Perform a Monte Carlo simulation, capturing the stochastic nature of the PFE. Therefore I and II are valid choices. MLE and parametric estimation are not methods for calculating PFE.
Question 52
Which of the following steps are required for computing the total loss distribution for a bank for operational risk once individual UoM level loss distributions have been computed from the underlhying frequency and severity curves: I. Simulate number of losses based onthe frequency distribution II. Simulate the dollar value of the losses from the severity distribution III. Simulate random number from the copula used to model dependence between the UoMs IV. Compute dependent losses from aggregate distribution curves
Correct Answer: C
Explanation A recap would be in order here: calculating operational risk capital is a multi-step process. First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process: - Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution. - Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at onceand the joint probabilities of the different losses make the sum less than the sum of the parts. Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from theseverity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses and then identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM. Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', andcombined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.
Question 53
Changes in which of the following do not affect the expected default frequencies (EDF) under the KMV Moody's approach to credit risk?
Correct Answer: B
Explanation EDFs are derived from the distance to default. The distance to default isthe number of standard deviations that expected asset values are away from the default point, which itself is defined as short term debt plus half of the long term debt. Therefore debt levels affect the EDF. Similarly, asset values are estimated using equity prices. Therefore market capitalization affects EDF calculations. Asset volatilities are the standard deviation that form a place in the denominator in the distance to default calculations. Therefore asset volatility affects EDF too. The risk free rateis not directly factored in any of these calculations (except of course, one could argue that the level of interest rates may impact equity values or the discounted values of future cash flows, but that is a second order effect). Therefore Choice 'b' is the correct answer.
Question 54
A zero coupon corporate bond maturing in an year has a probability of default of 5% and yields 12%. The recovery rate is zero. What is the risk free rate?
Correct Answer: D
Explanation The probability of default would make the expected value of the future cash flows from both the corporate bond and the risk free bond identical. If p be the probability of default, the cash flows from the risky corporate bond would be = (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default)) => 5%*0 + (1 - 5%)*(1 + 12%) = (1 + Rf). therefore Rf = 6.4% (In reality investors would demand a 'credit risk premium' over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)
Question 55
If the odds of default are 1:5, what is the probability of default?
Correct Answer: A
Explanation Odds are the ratio between the probability of the occurence of an event to the probability that the event does not occur. If odds are H, then p = H/(1 + H) and H = p/(1-p). In this case the odds are 1:5, or 1/5, therefore the correct answer is Choice 'a', equal to (1/5)/(1 + 1/5) = 1/6 = 16.67%. All other choices are incorrect.
