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

1. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

A) 6/11
B) 8/11
C) None of these
D) 5/7

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. Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?

A) The normal distribution has lower kurtosis than the t distribution.
B) The normal distribution has higher kurtosis than the t distribution.
C) The distributions have the same kurtosis.
D) Which has the higher kurtosis depends on the degrees of freedom of the t distribution.

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. Which of the following statements is true?

A) Discrete and continuous compounding produce the same results if the discount rate is positive.
B) Continuous compounding is the better method because it results in higher present values compared to discrete compounding.
C) The constant plays an important role in the mathematical description of continuous compounding.
D) Continuous compounding can be thought as making the compounding period infinitesimally small.

Solutions: