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

1. In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

A) 6.31
B) 5.66
C) 5.19
D) 4.18

2. The Newton-Raphson method

A) does provide an error bound along with every iteration
B) can be used for continuous but not differentiable functions
C) is based on finding a middle point between left and right end of the search interval
D) is based on Taylor series and uses the first derivative

3. Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter

A) (i), (ii), (iii), and (iv)
B) (i), (iii), and (iv)
C) (i) and (iv)
D) (i), (ii), and (iii)

4. The determinant of a matrix X is equal 2. Which of the following statements is true?

A) det(2X) =
B) det(2X) = 4 det(X)
C) det(2X) = 2 det(X)
D) det(2X) = det(X)2

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

Solutions: