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

1. 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 variance 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 standard deviation has a t-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

2. At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A) 0
B) 2
C) 2.66667
D) -0.666666667

3. Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data

A) Statements 1 and 3 are correct
B) Statements 2 and 3 are correct
C) Statements 1 and 2 are correct
D) All three statements are correct

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

5. On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?

A) 0.905
B) 0.095
C) 0.100
D) 0.95

Solutions: