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

All of the distributions referred to in the question can be used to model the loss severity distribution for op risk. Therefore Choice 'c' is the correct answer.

The total value of the portfolio is $370 (=$100 + $120 + $150). The modified duration of the portfolio is the weighted average of the MDs of the different bonds, ie =(5 * 100/370) + (10 * 120/370) + (12 * 150/370) = 9.46.

This means that for every 1% change in interest rates, the value of the portfolio changes by 9.46%. Since the daily volatility of interest rates is 2%, the 95% confidence level move will be 1.65 * 2% = 3.30%. Thus, the VaR of the portfolio at the 95% confidence level will be 3.3 * 9.46% * $370 = $115.51.

All other answers are incorrect.

The change in the price of a security that follows a Weiner process is determined by its standard deviation and expected return. To get the price itself, we need to add this change in price to the current price. Therefore the future price in a Weiner process is determined by all three of current price, expected return and standard deviation.

The probability that only one of the three bonds will default is equal to the sum of the probabilities of the three scenarios where one bond defaults and the other two survive. This probability is given by 1%*(1 - 2%)*(1 - 3%) + (1 - 1%)*2%*(1 - 3%) + (1 - 1%)*(1 - 2%)*3% = 5.7818%. Choice 'c' is the correct answer.

The peaks-over-threshold model is used when losses over a given threshold are recorded, as is often the case when using data based on external public sources where only large loss events tend to find a place. The generalized Pareto distribution is also used when attempting to model loss severity using EVT. Lognormal mixtures and generalized hyperbolic distributions are not used as extreme value distributions.

Choice 'd' is the correct answer.

The probability of default would make the future cash flows from both the bonds 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))

=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.

The cash flows from the treasury bond would be 1.04. These two should be equal, ie,

1.04 = (1- p)*1.085, implying p = 4.15%.

(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond 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.)

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 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%

Hazard rate x Loss given default = CDS quote. In other words, Hazard rate x (1 - recovery rate) = CDS quote. We can therefore calculate the hazard rate for this problem as 200 bps/(1 - 40%) = 3.33%.