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

1. Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

A) 2
B) 1
C) 0.5
D) 0

2. Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A) 2.362
B) 1.638
C) 0.377
D) 1.623

3. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) arithmetic sequence, common ratio 2
B) geometric sequence, common ratio 2
C) arithmetic sequence, common difference 2
D) geometric sequence, common ratio 3

4. Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

A) 75%
B) Cannot be determined without estimates of the volatilities of the individual returns
C) 64%
D) 98%

5. Find the first-order Taylor approximation p(x) for the function: at the point .

A) -x+1
B) x-1
C) -x
D) x+1

Solutions: