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

1. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) a
B) a2
C) 1
D) 42

2. Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X 0 and Y 1.96 is approximately

A) 0.488%
B) 0.49%
C) 0.495%
D) 0.25%

3. For the function f(x) =3x-x3 which of the following is true?

A) x = 0 is a minimum
B) None of these
C) x = 2 is a maximum
D) x = -3 is a maximum

4. 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) $2.205,000
B) $2,210,342
C) None of them
D) $2,208,972

5. 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 100%. The volatility of my portfolio is

A) 14.4%
B) 20%
C) 4%
D) 24%

Solutions: