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PRMIA 8007 Exam Syllabus Topics:

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

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

2. I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

A) 17.4%
B) 20%
C) 24.4%
D) 16%

3. Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

A) The probability of an up move will not be constant
B) The lattice will not recombine
C) There will always be a downward drift in the lattice
D) None of the above

4. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5286
B) 0.5292
C) 0.5288
D) 0.5290

5. You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...

A) equal to -2
B) in the interval ]-,-2.5]
C) in the interval ]-2,+[
D) in the interval ]-2.5,-2[

Solutions: