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

1. If the annual volatility of returns is 25% what is the variance of the quarterly returns?

A) 0.0625
B) 0.0156
C) None of the above
D) 0.1250

2. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A) 11.82
B) 12.78
C) 12.49
D) 12.33

3. 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)) = 2.7183
B) E(exp(X)) = 1.6487
C) E(exp(X)) = 0.6065
D) E(exp(X)) = 1

4. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 3
B) 2
C) 1
D) 0

5. Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

A) 20.78%
B) 36.33%
C) 36%
D) 26.33%

Solutions: