PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 101:

  For an option position with a delta of 0.3, calculate VaR if the VaR of the underlying is $100.

  A. 100
  B. 130
  C. 30
  D. 33.33
  C. 30

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  Explanation

  The first order approximation of the VaR of an option position is nothing but the VaR of the underlying multiplied by the option's delta. This is intuitive because the delta is the sensitivity of the option price to changes in the prices of the underlying, and in this case since the delta is 0.3 and the underlying's VaR is $100, the VaR of the options position is 0.3 x $100 = $30. Therefore Choice 'c' is the correct answer. (Note that the second order approximation of the VaR of an options position considers the option gamma too, and VaR reduces if gamma increases.)

• Question 102:

  If an institution has $1000 in assets, and $800 in liabilities, what is the economic capital required to avoid insolvency at a 99% level of confidence? The VaR in respect of the assets at 99% confidence over a one year period is $100.

  A. 200
  B. 1000
  C. 100
  D. 1100
  C. 100

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  Explanation

  The economic capital required to avoid insolvency is just the asset VaR, ie $100. This means that if the worst case losses are realized, the institution would need to have a buffer equivalent to those losses which in this case will be $100, and

  this buffer is the economic capital.

  The actual value of liabilities is not relevant as they are considered 'riskless' from the institution's point of view, ie they will be taken at full value. In this particular case, the institution has $200 in capital which is more than the economic capital

  required.

  Therefore Choice 'c' is the correct answer.

• Question 103:

  What would be the consequences of a model of economic risk capital calculation that weighs all loans equally regardless of the credit rating of the counterparty?

  A. Create an incentive to lend to the riskiest borrowers II. Create an incentive to lend to the safest borrowers III. Overstate economic capital requirements IV. Understate economic capital requirements
  B. III only
  C. I and IV
  D. II and III
  E. I only
  B. III only

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  Explanation

  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 such an 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.

• Question 104:

  Under the actuarial (or CreditRisk+) based modeling of defaults, what is the probability of 4 defaults in a retail portfolio where the number of expected defaults is 2?

  A. 4%
  B. 18%
  C. 9%
  D. 2%
  C. 9%

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  Explanation

  The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of and standard deviation equal to . The probability of n

  defaults is given by (^n e^-) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902. Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

• Question 105:

  A bank expects the error rate in transaction data entry for a particular business process to be 0.005%. What is the range of expected errors in a day within +/- 2 standard deviations if there are 2,000,000 such transactions each day?

  A. 80 to 120 errors in a day
  B. 60 to 80 errors in a day
  C. 0 to 200 errors in a day
  D. 90 to 110 errors in a day
  A. 80 to 120 errors in a day

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  Explanation

  Error rates are generally modeled using the Poisson distribution. Recall that the Poisson distribution has only one parameter - - which is its mean and also its variance. In the given case, the mean number of errors is 2,000,000 x 0.005% =

  100. Since this is the variance as well, the standard deviation is 100 = 10. Therefore the range of outcomes within 2 standard deviations of the mean is 100 +/- (2*10) = 80 to 120 errors in a day.

• Question 106:

  Which of the following statements is true:

  A. Both total expected losses and total unexpected losses are less than the sum of expected and unexpected losses on underlying exposures respectively
  B. Total expected losses are equal to the sum of individual underlying exposures while total unexpected losses are greater than the sum of unexpected losses on underlying exposures
  C. Total expected losses are equal to the sum of expected losses in the individual underlying exposures while total unexpected losses are less than the sum of unexpected losses on underlying exposures
  D. Total expected losses are greater than the sum of individual underlying exposures while total unexpected losses are less than the sum of unexpected losses on underlying exposures
  C. Total expected losses are equal to the sum of expected losses in the individual underlying exposures while total unexpected losses are less than the sum of unexpected losses on underlying exposures

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  Explanation

  Total expected losses which are average and anticipated are equal to the sum of expected losses in the underlying exposures. Total unexpected losses, which are the excess of worst case losses at a certain confidence level over the expected losses, benefit from the diversification effect and are lower than the sum of unexpected losses of the underlying exposures. Therefore Choice 'c' is the correct answer. The other choices are incorrect.

• Question 107:

  There are three bonds in a diversified bond portfolio, whose default probabilities are independent of each other and equal to 1%, 2% and 3% respectively over a 1 year time horizon. Calculate the probability that none of the three bonds will default.

  A. 94%
  B. 0.11%
  C. 0.0006%
  D. 2%
  A. 94%

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  Explanation

  The probability that only none of the three bonds will default is equal to the probability of all surviving. Since default correlation is zero, we can simply multiply the probabilities of survival. Therefore the correct answer is 94% = (1 - 1%) * (1 2%) * (1 - 3%)

• Question 108:

  Which of the following is not an event of default covered in the ISDA Master Agreement?

  I - failure to pay or deliver II - credit support default III - merger without assumption IV - Bankruptcy

  A. All are considered events of default
  B. II and III
  C. I
  D. IV
  C. I

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  Explanation

  Note that events of default under the ISDA MA are caused by one of the parties that is considered 'at fault'. In contrast, "termination events" are events for which no one is at fault, for example changes in legislation, illegality etc that still justify

  termination of the transactions under the contract.

  The ISDA MA describes the following 8 types of events of default:

  1.failure of pay or deliver

  2.breach of agreement

  credit support default

  4.misrepresentation

  5.default under specified transaction

  6.cross default

  7.bankruptcy

  8.merger without assumption

  All of the options presented in the question are events of default.

• Question 109:

  Which of the following is closest to the description of a 'risk functional'?

  A. A risk functional is the distribution that models the severity of a risk
  B. A risk functional is a model distribution that is an approximation of the true loss distribution of a risk
  C. Risk functional refers to the Kolmogorov-Smirnov distance
  D. A risk functional assigns a penalty value for the difference between a model distribution and a risk's severity distribution
  D. A risk functional assigns a penalty value for the difference between a model distribution and a risk's severity distribution

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  Explanation

  For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analytical distribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A 'risk functional' is a measure of the deviation of the model distribution from the risk's actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance). The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:

  

  Note that supx stands for 'supremum', which is a more technical way of saying 'maximum'. In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.) Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.

• Question 110:

  A risk analyst attempting to model the tail of a loss distribution using EVT divides the available dataset into blocks of data, and picks the maximum of each block as a data point to consider.

  Which approach is the risk analyst using?

  A. Block Maxima approach
  B. Peak-over-thresholds approach
  C. Expected loss approach
  D. Fourier transformation
  A. Block Maxima approach

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  Explanation

  The risk analyst is using the block maxima approach. The data points that result will then be used to fit a GEV distribution. Expected shortfall refers to the expected losses beyond a specified threshold. The peaks- over-threshold approach is an alternative approach to the block maxima approach, and involves considering exceedances above a threshold. Fourier transformation is not relevant in this context, and is a non-sensical option.