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

1. What is the simplest form of this expression: log2(165/2)

A) 32
B) log2 (5/2) + log2(16)
C) 5/2 + log2(16)
D) 10

2. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 0
B) 3
C) 1
D) 2

3. The gradient of a smooth function is

A) matrix of second partial derivatives of a function
B) a vector that shows the direction of fastest change of a function
C) infinite at a maximum point
D) a matrix containing the function's second partial derivatives

4. Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I would

A) trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.
B) trade the underlying in such a way as to make the portfolio delta and vega neutral.
C) trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.
D) trade the other option in such a way as to make the portfolio delta and vega neutral.

5. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated standard deviation has a t-distribution
B) The estimated mean divided by the estimated variance has a Chi2-distribution
C) The estimated mean divided by the estimated variance has a t-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

Solutions: