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

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

2. Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?

A) 2.75%
B) None of the above
C) 2.49%
D) 2.67%

3. For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)

A) convex, convex, concave
B) concave, convex, convex
C) convex, concave, concave
D) concave, concave, concave

4. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A) E(exp(X)) = 0.6065
B) E(exp(X)) = 1
C) E(exp(X)) = 2.7183
D) E(exp(X)) = 1.6487

5. Calculate the determinant of the following matrix:

A) -4.25
B) 4
C) 4.25
D) 2

Solutions: