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

1. The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A) x = 5, y = 0
B) x = 0, y = 20
C) None of the above
D) x = -1, y = 0

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

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

4. 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)

5. In a quadratic Taylor approximation, a function is approximated by:

A) a constant
B) a parabola
C) a straight line
D) a cubic polynomial

Solutions: