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

2. If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A) 37/45
B) None of these
C) 12/29
D) 3/4

3. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) a
B) a2
C) 42
D) 1

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

5. 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 cross-section regression
D) Simple time-series regression

Solutions: