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

1. The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

A) 6%
B) 1.50%
C) None of the above
D) 6.14%

2. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A) -x/(x+y) - y/(x+y)
B) ln(x+y) x + ln(x+y) y
C) 1 / (x+y)
D) (x + y) / (x+y)

3. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A) 5
B) 10
C) 100
D) 25

4. Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%,
+3%, -3%, +9%, -9% .
What can you say about the annual geometric and arithmetic mean returns of this investment fund?

A) The arithmetic mean return is equal to the geometric mean return
B) The arithmetic mean return is negative and the geometric mean return is zero
C) None of the above
D) The arithmetic mean return is zero and the geometric mean return is negative

5. Let a, b and c be real numbers. Which of the following statements is true?

A) The distributivity of multiplication is defined by
B) The associativity of multiplication is defined by
C) The existence of negatives is defined by
D) The commutativity of multiplication is defined by

Solutions: