PRMIA 8007 Exam : Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

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PRMIA 8007 Exam Syllabus Topics:

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

1. Consider the following distribution data for a random variable X: What is the mean and variance of X?

A) 3.5 and 3.45
B) 3.6 and 7.15
C) None of these
D) 3.4 and 3.84

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

3. You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A) None of the above
B) The commodity returns are stationary
C) The commodity prices are stationary
D) The commodity returns are integrated of order 1

4. In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

A) 4.18
B) 5.19
C) 6.31
D) 5.66

5. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

A) 90%
B) 66.60%
C) 95%
D) 99%

Solutions: