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

1. Variance reduction is:

A) A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
B) A method for reducing the number of simulations required in a Monte Carlo simulation
C) A technique that is applied in regression models to improve the accuracy of the coefficient estimates
D) A numerical method for finding the variance of the underlying that is implicit in a market price of an option

2. 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) 64%
B) 98%
C) 75%
D) Cannot be determined without estimates of the volatilities of the individual returns

3. The gradient of a smooth function is

A) a matrix containing the function's second partial derivatives
B) a vector that shows the direction of fastest change of a function
C) infinite at a maximum point
D) matrix of second partial derivatives of a function

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

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

5. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.2646
B) None of these
C) 0.7367
D) 0.3483

Solutions: