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PRMIA 8007 Exam Syllabus Topics:

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

Question 1

Every covariance matrix must be positive semi-definite. If it were not then:

A. The associated correlation matrix would not be positive semi-definite
B. It could not be used to simulate correlated asset paths
C. Some portfolios could have a negative variance
D. All the above statements are true

Question 2

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

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

Question 3

In statistical hypothesis tests, 'Type I error' refers to the situation in which...

A. The null hypothesis is rejected when in fact it should have been accepted
B. The null hypothesis is accepted when in fact it should have been rejected
C. Both null hypothesis and alternative hypothesis are accepted
D. Both null hypothesis and alternative hypothesis are rejected

Question 4

Which of the following statements is true?

A. Discrete and continuous compounding produce the same results if the discount rate is positive.
B. Continuous compounding is the better method because it results in higher present values compared to discrete compounding.
C. The constant plays an important role in the mathematical description of continuous compounding.
D. Continuous compounding can be thought as making the compounding period infinitesimally small.

Question 5

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

A. (0, 1, -1)
B. (1, 1, 1)
C. (0, 0, 0)
D. (0, 2, 1)

Solutions: