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Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

Last Update May 3, 2024
Total Questions : 132

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Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Questions and Answers

Questions 1

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

Options:

A.

x = -1, y = 0

B.

x = 0, y = 20

C.

x = 5, y = 0

D.

None of the above

Questions 2

A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

Options:

A.

10 basis point rise

B.

24 basis fall

C.

24 basis point rise

D.

30 basis points fall.

Questions 3

Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

Options:

A.

mean is 0, variance is 2/3

B.

mean is 0, variance is 1/3

C.

mean is 0, variance is 1/2

D.

mean is 1/3, variance is 1/3

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