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

1. Which of the following is consistent with the definition of a Type I error?

A) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected
B) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected
C) The probability of a Type I error is 100% minus the significance level
D) A Type I occurs whenever data series are serially correlated

2. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

A) the definite integral of the CDF from minus infinity to plus infinity is undefined.
B) the PDF is non-negative.
C) the CDF approaches 1 as its argument approaches infinity.
D) the definite integral of the PDF from minus infinity to plus infinity is zero.

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

4. What is the probability of tossing a coin and getting exactly 2 heads out of 5 throws?

A) 8/15
B) 10/32
C) None of these
D) 9/23

5. Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A) Changing all the correlations to be unity
B) Changing the volatilities to be greater than 100%
C) Changing all the correlations to be zero
D) All of the above

Solutions: