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

1. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 3
B) 0
C) 2
D) 1

2. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated variance has a t-distribution
B) The estimated mean divided by the estimated variance has a Chi2-distribution
C) The estimated mean divided by the estimated standard deviation has a t-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

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

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

4. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A) F(x)g(x) + f(x)G(x)
B) F(x)g(x) - F(x)g'(x)dx
C) f(x)G(x) - F(x)g'(x)dx
D) F(x)G(x)

5. A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

A) 10 basis point rise
B) 24 basis point rise
C) 24 basis fall
D) 30 basis points fall.

Solutions: