PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition - 8007 FREE EXAM DUMPS QUESTIONS & ANSWERS]

Question 1

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. 29 B. 17 C. 1 D. -25

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Correct Answer: A Vote an answer

Question 2

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A. The commodity returns are stationary B. None of the above C. The commodity returns are integrated of order 1 D. The commodity prices are stationary

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Correct Answer: B Vote an answer

Question 3

Two vectors are orthogonal when:

A. their scalar product (sum product) is zero B. one is a scalar multiple of the other C. their components are linearly dependent D. their determinant is zero

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Correct Answer: A Vote an answer

Question 4

What can be said about observations of random variables that are i.i.d. a normally distributed?

A. The estimated mean divided by the estimated standard deviation has a Chi2-distribution B. The estimated mean divided by the estimated variance has a Chi2-distribution C. The estimated mean divided by the estimated variance has a t-distribution D. The estimated mean divided by the estimated standard deviation has a t-distribution

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Correct Answer: D Vote an answer

Question 5

Which of the following is not a sequence?

A. , , , , ... B. , , , , , , ... C. 30 D. , , , ... , , ...

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Correct Answer: C Vote an answer

Question 6

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A. (x + y) / (x+y) B. ln(x+y) x + ln(x+y) y C. -x/(x+y) - y/(x+y) D. 1 / (x+y)

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Correct Answer: A Vote an answer

Question 7

Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

A. 1/3 and 8/17 B. 2/5 and 1/2 C. 9/25 and 12/25 D. 2/5 and 3/5

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Correct Answer: C Vote an answer

Question 8

The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

A. 6.14% B. 1.50% C. None of the above D. 6%

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Correct Answer: A Vote an answer

Question 9

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

A. All the above statements are true B. There would be no Cholesky decomposition matrix C. Some portfolios could have a negative variance D. One or more of its eigenvalues would be negative

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Correct Answer: A Vote an answer