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

1. You are investigating the relationship between weather and stock market performance. To do this, you pick
100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of...

A) Multiple cross-section regression
B) Multiple time-series regression
C) Simple time-series regression
D) Simple cross-section regression

2. If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:

A) integrated of order 2
B) non-functional
C) non-linear
D) differential

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

4. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5292
B) 0.5288
C) 0.5290
D) 0.5286

5. Which of the following statements about variance and standard deviation are correct?
1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation
2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data
3. When considering independent variables, variance is additive, while standard deviation is not

A) Statements 2 and 3 are correct
B) All three statements are correct
C) Statements 1 and 2 are correct
D) Statements 1 and 3 are correct

Solutions: