PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 211:

  Changes in which of the following do not affect the expected default frequencies (EDF) under the KMV Moody's approach to credit risk?

  A. Changes in the debt level
  B. Changes in the risk free rate
  C. Changes in asset volatility
  D. Changes in the firm's market capitalization
  B. Changes in the risk free rate

  ---

  Explanation

  EDFs are derived from the distance to default. The distance to default is the 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 rate is 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 212:

  Random recovery rates in respect of credit risk can be modeled using:

  A. the beta distribution
  B. the omega distribution
  C. the normal distribution
  D. the binomial distribution
  A. the beta distribution

  ---

  Explanation

  The beta distribution is commonly used to model recovery rates. It is a distribution for variables whose values lie between 0 and 1, and the parameters of the distribution can be estimated using the mean and standard deviation of the data.

  Therefore Choice 'a' is correct and the others are wrong.

  Refer to the tutorial on distributions for an Excel model of the beta distribution.

• Question 213:

  The difference between true severity and the best approximation of the true severity is called:

  A. Approximation error
  B. Fitting error
  C. Total error
  D. Estimation error
  A. Approximation error

  ---

  Explanation

  This question relates to fitting a distribution to the true severity of the operational risk loss we are trying to model. The quality of the fit, or the precision of the fit, has two elements to the difference between the severity as represented by our model and the true severity. To understand this, consider the three data points below:

  a.

  The true severity,

  b.

  The best approximation of the true severity in the model space, and c. The fit based on the dataset.

  -True severity is what we are trying to model.

  -

  The model space refers to the collection of analytical distributions (log-normal, burr etc) that we are considering to arrive at the estimate of the severity.

  -

  The 'best approximation of the true severity in the model space' is reached by estimating the parameters of the distribution that optimizes the risk functional.

  -

  The 'fit' is the actual parameter estimates we settle for with the distribution we have determined best fits the true estimate of our severity. When estimating parameters, we have various methods available for estimation - the least squares

  method, the maximum likelihood method, for example, and we can get different estimates depending upon the method we choose to use.

  Our severity model will be different from the true severity, and the total difference can be split into two types of errors:

  1.Fitting error, represented by 'c - b' above: The difference between the fit based on the dataset and the best approximation of the true severity is called 'fitting error', ie, a measure of the extent to which we could have estimated the

  parameters better.

  2.Approximation error, represented by 'b - a' above: Approximation error is the difference between the true severity, and the best approximation of the true severity that can be achieved within the model space is called 'approximation error'.

  One can reduce the approximation error by expanding the model space by adding more distributions. This will reduce the approximation error, but generally has the effect of increasing the fitting error because the complexity of the model

  space increases, and there are more ways to fit to the true severity.

• Question 214:

  What ensures that firms are not able to selectively default on some obligations without being considered in default on the others?

  A. Cross-default clauses in debt covenants
  B. Chapter 11 regulations
  C. Exchange listing requirements
  D. The bankruptcy code
  A. Cross-default clauses in debt covenants

  ---

  Explanation

  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.

• Question 215:

  Which of the following statements are true:

  I - Common scenarios for stress tests include the 1997 Asian crisis, the Russian default in 1998 and other well known economic stress situations.

  II - Stress tests provide the assurance that an institution's worst case losses will be covered.

  III - Performing stress tests is highly recommended but is not mandated under Basel II.

  IV - Historical events can be modeled quite accurately as they have defined start and end dates.

  A. I, III and IV
  B. I only
  C. I and II
  D. All of the above
  B. I only

  ---

  Explanation

  Stress tests can cover known events, but since the future is unknown, and new events may be entirely different from what has happened in the past, they provide no assurance that an institution's worst case losses would be covered. Hence II is false. Stress testing is required to be performed as part of Basel II, and therefore III is false. Historical events do not have sharply defined start and end dates. Often, even after a crises ends, its after effects may continue to affect the markets for a long time. In such cases, it may be difficult to define the start and end of the crises. In many cases, the crises may persist for months or even years, making it difficult for the risk manager to identify a time period that covers the essence of the crises, and yet is focused enough to constitute a plausible scenario. Therefore IV is false too. Only I is true, and the correct answer is Choice 'b'.

• Question 216:

  Which of the following is true for the actuarial approach to credit risk modeling (CreditRisk+):

  A. Default correlations between obligors are accounted for using a multivariate normal model
  B. The number of defaults is modeled using a binomial distribution where the number of defaults are considered discrete events
  C. The approach considers only default risk, and ignores the risk to portfolio value from credit downgrades
  D. The approach is based upon historical rating transition matrices
  C. The approach considers only default risk, and ignores the risk to portfolio value from credit downgrades

  ---

  Explanation

  The actuarial model considers defaults to follow a Poisson distribution with a given mean per period, and these are binary in nature, ie a default happens or it does not happen. The model does not consider the loss of value from credit

  downgrades, and focuses only on defaults. The model also does not consider default correlations between obligors.

  Therefore Choice 'c' is the correct answer.

  The other choices are not true statements that would apply to the actuarial approach.

• Question 217:

  The returns for a stock have a monthly volatilty of 5%. Calculate the volatility of the stock over a two month period, assuming returns between months have an autocorrelation of 0.3. A. 8.062%

  B. 7.071%

  C. 5%

  D. 10%

  Correct Answer. A
  A

  ---

  Explanation

  The square root of time rule cannot be applied here because the returns across the periods are not independent. (Recall that the square root of time rule requires returns to be iid, independent and identically distributed.) Here there is a 'autocorrelation' in play, which means one period's returns affect the returns of the other period. This problem can be solved by combining the variance of the returns from the two consecutive periods in the same way as one would combine the variance of different assets that have a given correlation. In such cases we know that: Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B). The standard deviation can be calculated by taking the square root of the variance. Therefore the combined volatility over the two months will be equal to =SQRT((5%^2) + (5%^2) + 2*0.3*5%*5%) = 8.062%. All other answers are incorrect.

• Question 218:

  If the returns of an asset display a strong tendency for mean reversion, what is the relationship between annualized volatility calculated based on daily versus weekly volatilities (using the square root of time rule)?

  A. Either daily or weekly volatility will be greater, depending upon how the week went
  B. Daily and weekly volatilities will be the same
  C. Daily volatility will be greater than weekly volatility
  D. Weekly volatility will be greater than daily volatility
  C. Daily volatility will be greater than weekly volatility

  ---

  Explanation

  If returns display mean reversion, then clearly daily volatilities will be greater than weekly volatility, both annualized using the square root of time rule. Mean reversion would imply that the deviation from the mean will be lower over a longer time period than a shorter time period, and therefore annualized volatility based on daily volatility will be greater.

• Question 219:

  Which of the following is the most important problem to solve for fitting a severity distribution for operational risk capital:

  A. The risk functional's minimization should lead to a good estimate of the 0.999 quantile
  B. Determine plausible scenarios to fill the data gaps in the internal and external loss data
  C. Empirical loss data needs to be extended to the ranges below the reporting threshold and above large value losses
  D. The fit obtained should reduce the combination of the fitting and approximation errors to a minimum
  A. The risk functional's minimization should lead to a good estimate of the 0.999 quantile

  ---

  Explanation

  Ultimately, the objective of the operational risk severity estimation exercise is to calculate the 99.9th percentile loss over a one year horizon; and everything else we do with data, collecting loss information, modeling, curve fitting etc revolves around this objective. If we cannot estimate the 99.9th percentile loss accurately, then not much else matters. Therefore Choice 'a' is the correct answer. Minimizing the combination of fitting and approximation errors is one of the things we do with a view to better estimating the operational loss distribution. Likewise, empirical loss data generally is range bound because corporations do not require employees to log losses less than an threshold, and high value losses are generally rare. This problem is addressed by extrapolating both large and small losses, something that impacts the performance of our model. Likewise, one of the objectives of scenario analysis is to fill data gaps by generating plausible scenarios. Yet while all these are real issues to address, the primary problem we are trying to solve is estimating the 0.999th quantile.

• Question 220:

  The largest 10 losses over a 250 day observation period are as follows. Calculate the expected shortfall at a 98% confidence level:

  20m 19m 19m 17m 16m 13m 11m 10m 9m 9m

  A. 19.5
  B. 14.3
  C. 18.2
  D. 16
  C. 18.2

  ---

  Explanation

  For a dataset with 250 observations, the top 2% of the losses will be the top 5 observations. Expected shortfall is the average of the losses beyond the VaR threshold. Therefore the correct answer is (20 + 19 + 19 + 17 + 16)/5 = 18.2m . Note that Expected Shortfall is also called conditional VaR (cVaR), Expected Tail Loss and Tail average.