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

1. 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) 0.5288
B) 0.5290
C) 0.5286
D) 0.5292

2. 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) 5%
B) 2.50%
C) -5%
D) -2.50%

3. The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?

A) 0.5
B) 1.5
C) 1
D) None of the above

4. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A) 1 / (x+y)
B) ln(x+y) x + ln(x+y) y
C) -x/(x+y) - y/(x+y)
D) (x + y) / (x+y)

5. The fundamental theorem of analysis establishes a relation between

A) First and second derivative of a function
B) Integration and differentiation of functions
C) The derivative of a function and the derivative of its inverse function
D) The derivative of a function and the slope of its graph

Solutions: