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

1. Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

A) -2.8
B) 1.3
C) None of the above
D) -1.2

2. A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay Duration of the bond?

A) 1.86
B) 2
C) 1.75
D) 1.95

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

4. I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

A) -2.50%
B) 5%
C) -5%
D) 2.50%

5. Let a, b and c be real numbers. Which of the following statements is true?

A) The commutativity of multiplication is defined by
B) The associativity of multiplication is defined by
C) The distributivity of multiplication is defined by
D) The existence of negatives is defined by

Solutions: