Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition (8007) Free Practice Test

Question 1

Every covariance matrix must be positive semi-definite. If it were not then:

A. All the above statements are true

B. Some portfolios could have a negative variance

C. It could not be used to simulate correlated asset paths

D. The associated correlation matrix would not be positive semi-definite

Correct Answer: A

Question 2

Maximum likelihood estimation is a method for:

A. Estimating the implied volatility of a simple European option

B. Finding parameter estimates of a given density function

C. Estimating the solution of a partial differential equation

D. Solving a portfolio optimization problem

Correct Answer: B

Question 3

Which of the following properties is exhibited by multiplication, but not by addition?

A. associativity

B. commutativity

C. distributivity

D. invertibility

Correct Answer: C

Question 4

Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

A. None of the above

B. x = 2, y = 0

C. x = -2, y = 2

D. x = 1, y = 0.5

Correct Answer: C

Question 5

There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds.
Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

A. None of these

B. 0.6

C. 0.3

D. 0.5

Correct Answer: B

Question 6

What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?

A. -25

B. 17

C. 1

D. 29

Correct Answer: D

Question 7

Find the roots, if they exist in the real numbers, of the quadratic equation

A. -4 and 2

B. No real roots

C. 1 and 0

D. 4 and -2

Correct Answer: B

Question 8

Evaluate the derivative of ln(1+ x2) at the point x = 1

A. 0

B. 1

C. 2

D. 0.5

Correct Answer: B

Question 9

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 other option in such a way as to make the portfolio delta and vega neutral.

C. 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.

D. trade the underlying in such a way as to make the portfolio delta and vega neutral.

Correct Answer: A

Question 10

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

A. 1.95

B. 1.75

C. 1.86

D. 2

Correct Answer: A

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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition (8007) Free Practice Test