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

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

2. 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 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 neutral, and then trade the other option in such a way as to make the portfolio vega neutral.

3. You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A) The commodity prices are stationary
B) None of the above
C) The commodity returns are integrated of order 1
D) The commodity returns are stationary

4. The Newton-Raphson method

A) is based on finding a middle point between left and right end of the search interval
B) can be used for continuous but not differentiable functions
C) is based on Taylor series and uses the first derivative
D) does provide an error bound along with every iteration

5. What is a Hessian?

A) The point at which a minimum of a multidimensional function is achieved
B) Correlation matrix of market indices
C) A matrix of second derivatives of a function
D) The vector of partial derivatives of a contingent claim

Solutions: