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

1. You invest $2m in a bank savings account with a constant interest rate of 5% p.a. What is the value of the investment in 2 years time if interest is compounded quarterly?

A) $2,208,972
B) None of them
C) $2,210,342
D) $2.205,000

2. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 1
B) 0
C) 0.5
D) None of the above

3. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.7367
B) 0.3483
C) None of these
D) 0.2646

4. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A) E(exp(X)) = 0.6065
B) E(exp(X)) = 1
C) E(exp(X)) = 1.6487
D) E(exp(X)) = 2.7183

5. 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

Solutions: