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

1. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

A) 8/11
B) None of these
C) 5/7
D) 6/11

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

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

3. The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?

A) None of the above
B) 0.5
C) 1
D) 1.5

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

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

5. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) a2
B) a
C) 42
D) 1

Solutions: