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

1. The determinant of a matrix X is equal 2. Which of the following statements is true?

A) det(2X) = 2 det(X)
B) det(2X) = det(X)2
C) det(2X) =
D) det(2X) = 4 det(X)

2. If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A) 3/4
B) None of these
C) 37/45
D) 12/29

3. The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

A) (1, 1, 1)
B) (0, 0, 0)
C) (0, 2, 1)
D) (0, 1, -1)

4. 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

5. I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

A) 30% and 40%
B) 5% and 35%
C) 10% and 70%
D) 10% and 40%

Solutions: