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

1. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated standard deviation has a t-distribution
B) The estimated mean divided by the estimated variance has a t-distribution
C) The estimated mean divided by the estimated variance has a Chi2-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

2. 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), (ii), and (iii)
C) (i) and (iv)
D) (i), (iii), and (iv)

3. 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-linear
C) non-functional
D) differential

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

5. What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

A) 2 097 170
B) 1 048 574
C) 1 048 595
D) 2 097 172

Solutions: