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PRMIA 8007 Exam Syllabus Topics:

PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) arithmetic sequence, common difference 2
B) geometric sequence, common ratio 3
C) geometric sequence, common ratio 2
D) arithmetic sequence, common ratio 2

2. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

A) (i) only
B) (i) and (ii)
C) (i), (ii), and (iii)
D) (i) and (iii)

3. Find the roots, if they exist in the real numbers, of the quadratic equation

A) -4 and 2
B) 1 and 0
C) No real roots
D) 4 and -2

4. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

A) the CDF approaches 1 as its argument approaches infinity.
B) the definite integral of the CDF from minus infinity to plus infinity is undefined.
C) the definite integral of the PDF from minus infinity to plus infinity is zero.
D) the PDF is non-negative.

5. Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A) Changing all the correlations to be unity
B) Changing all the correlations to be zero
C) All of the above
D) Changing the volatilities to be greater than 100%

Solutions: