PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 361:

  Which of the following statements are true:

  I - Heavy tailed parametric distributions are a good choice for severity modeling in operational risk.

  II - Heavy tailed body-tail distributions are a good choice for severity modeling in operational risk.

  III - Log-likelihood is a means to estimate parameters for a distribution.

  IV - Body-tail distributions allow modeling small losses differently from large ones.

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

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  Explanation

  When modeling for operational risk, we are generally concerned with tail losses - this is because the horizon for operational risk is 1 year at the 99.9th percentile. Since the 99.9th percentile is in the tail region, we would like to ensure that the tails are modeled as accurately as possible. Operational risk distributions are modeled using heavy tailed distributions. Heavy tailed parametric distributions such as log-normal, pareto and others are therefore a good choice for modeling risk severity, therefore statement I is correct. Body-tail distributions are combinations of parametric distributions, with different types of distributions being used to model the body and the tail - this provides flexibility because small and medium losses upto a threshold can be modeled using one distribution, and losses beyond the threshold can be modeled using a different distribution that is a better estimate of the tail. Statement II is therefore correct. A log-likelihood function simplifies the optimization of a regular likelihood function. We generally maximize (or minimize the risk functional) a likelihood function with a view to estimating the parameters of the underlying distribution. If the likelihood function is complex, it may sometimes make it mathematically easier to optimize the log of the function - as that changes exponents and multiplications to additions, while behaving in the same way as the underlying function. Therefore statement III is correct, log-likelihood is a means to estimate parameters for a distribution. Statement IV is correct as body-tail distributions allow modeling different parts of the distribution differently from each other.

• Question 362:

  Which of the following statements is true:

  I - Recovery rate assumptions can be easily made fairly accurately given past data available from credit rating agencies.

  II - Recovery rate assumptions are difficult to make given the effect of the business cycle, nature of the industry and multiple other factors difficult to model.

  III - The standard deviation of observed recovery rates is generally very high, making any estimate likely to differ significantly from realized recovery rates.

  IV - Estimation errors for recovery rates are not a concern as they are not directionally biased and will cancel each other out over time.

  A. II and IV
  B. I, II and IV
  C. III and IV
  D. II and III
  D. II and III

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  Explanation

  Recovery rates vary a great deal from year to year, and are difficult to predict. Therefore statement III is true. Similarly, any attempt to predict these is hamstrung by a high standard error, which can be as high as the historical mean itself. The error does not cancel itself out due to the effect of the business cycle making the error directionally biased. Thus statement IV is false. Statement II is true as these are all factors that make forecasting recovery rates for any credit risk model rather difficult. Statement I is false because recovery rates are difficult to predict and assumptions are not easy to make.