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PRMIA 8007 Exam Syllabus Topics:

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

Question 1

The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A. None of the above
B. 0
C. 0.5
D. 1

Question 2

Consider the following distribution data for a random variable X: What is the mean and variance of X?

A. 3.4 and 3.84
B. 3.5 and 3.45
C. None of these
D. 3.6 and 7.15

Question 3

The gradient of a smooth function is

A. a vector that shows the direction of fastest change of a function
B. matrix of second partial derivatives of a function
C. infinite at a maximum point
D. a matrix containing the function's second partial derivatives

Question 4

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A. a continuously-compounded rate of 4%
B. a quarterly-compounded rate of 4.1%
C. a lump-sum payment of $22 500 on maturity (in five years)
D. an annually compounded rate of 4.15%

Question 5

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A. -x/(x+y) - y/(x+y)
B. ln(x+y) x + ln(x+y) y
C. (x + y) / (x+y)
D. 1 / (x+y)

Solutions: