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

1. Which of the following can induce a 'multicollinearity' problem in a regression model?

A) The omission of a relevant explanatory variable
B) A high positive correlation between the dependent variable and one of the explanatory variables
C) A high positive correlation between two explanatory variables
D) A large negative correlation between the dependent variable and one of the explanatory variables

2. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A) F(x)g(x) - F(x)g'(x)dx
B) f(x)G(x) - F(x)g'(x)dx
C) F(x)g(x) + f(x)G(x)
D) F(x)G(x)

3. An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

A) 4.59
B) 6.49
C) 4.54
D) 5.03

4. 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) -2.50%
B) -5%
C) 5%
D) 2.50%

5. A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay Duration of the bond?

A) 1.86
B) 1.75
C) 1.95
D) 2

Solutions: