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

1. Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

A) mean is 1/3, variance is 1/3
B) mean is 0, variance is 1/2
C) mean is 0, variance is 1/3
D) mean is 0, variance is 2/3

2. I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

A) 17.4%
B) 24.4%
C) 20%
D) 16%

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

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

5. A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?

A) 0.75
B) 0.375
C) 1.125
D) 0.3333

Solutions: