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

2. A quadratic form is

A) an algebraic expression in two variables, x and y, involving , , and terms.
B) defined as a positive definite Hessian matrix.
C) a specific solution of the Black-Scholes pricing formula
D) an algebraic expression in two variables, x and y, involving , and terms.

3. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) 1
B) a
C) 42
D) a2

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

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

5. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

A) 95%
B) 66.60%
C) 90%
D) 99%

Solutions: