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

1. Find the roots, if they exist in the real numbers, of the quadratic equation

A) 4 and -2
B) -4 and 2
C) 1 and 0
D) No real roots

2. Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A) Changing the volatilities to be greater than 100%
B) Changing all the correlations to be unity
C) Changing all the correlations to be zero
D) All of the above

3. Every covariance matrix must be positive semi-definite. If it were not then:

A) The associated correlation matrix would not be positive semi-definite
B) All the above statements are true
C) Some portfolios could have a negative variance
D) It could not be used to simulate correlated asset paths

4. 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) 26.33%
B) 36%
C) 36.33%
D) 20.78%

5. The bisection method can be used for solving f(x)=0 for a unique solution of x, when

A) The function f(x) is continuous and monotonic
B) The function f(x) is differentiable and we have an explicit expression for the derivative
C) The function f(x) is continuous
D) The function f(x) is differentiable

Solutions: