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PRMIA 8007 Exam Syllabus Topics:

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

Question 1

I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

A. 30% and 40%
B. 5% and 35%
C. 10% and 70%
D. 10% and 40%

Question 2

Which statement regarding the matrix below is true?

A. It is positive definite
B. It is not positive definite
C. It is negative definite
D. It is positive semi-definite

Question 3

You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

A. test statistic = MEAN()/SD(), normal distribution
B. test statistic = MEAN()/SD(), t distribution
C. test statistic = SD()/MEAN(), t distribution
D. test statistic = SD()/MEAN(), normal distribution

Question 4

Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:

A. 0.00109
B. 0.40729
C. 0.00087
D. 0.32583

Question 5

You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

A. b=0.5, a=2.5
B. b=0.5, a=1.5
C. b=2, a=0
D. b=2, a=4

Solutions: