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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) 42
B) 1
C) a2
D) a

2. The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A) x = 0, y = 20
B) None of the above
C) x = -1, y = 0
D) x = 5, y = 0

3. Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

A) x -1
B) x
C) ln(x)
D) -x

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

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

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

Solutions: