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

1. Two vectors are orthogonal when:

A) their components are linearly dependent
B) their determinant is zero
C) their scalar product (sum product) is zero
D) one is a scalar multiple of the other

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

A) Some portfolios could have a negative variance
B) One or more of its eigenvalues would be negative
C) All the above statements are true
D) There would be no Cholesky decomposition matrix

3. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

A) 0.125
B) 2.5
C) -1.25
D) -2.5

4. 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

5. Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

A) 2/5 and 3/5
B) 9/25 and 12/25
C) 1/3 and 8/17
D) 2/5 and 1/2

Solutions: