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

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

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

2. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A) 12.78
B) 12.49
C) 11.82
D) 12.33

3. The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:

A) 20
B) 12
C) 128
D) Infinity

4. Which of the provided answers solves this system of equations?
2y - 3x = 3y +x
y2 + x2 = 68

A) x = 1; y = square root of 67
B) x = 2; y = 8
C) x = -2; y = -8
D) x = 2; y = -8

5. Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

A) f'(g(x,y))
B) f(dg/dy)
C) f(g(x,y)) dg/dy
D) f'(g(x,y)) dg/dy

Solutions: