最新的PRMIA 8007免費考試真題

問題1

Find the first-order Taylor approximation p(x) for the function: at the point .

A. x-1

B. x+1

C. -x

D. -x+1

正確答案: D

問題2

What is a Hessian?

A. The point at which a minimum of a multidimensional function is achieved

B. The vector of partial derivatives of a contingent claim

C. Correlation matrix of market indices

D. A matrix of second derivatives of a function

正確答案: D

問題3

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

A. The function f(x) is differentiable and we have an explicit expression for the derivative

B. The function f(x) is continuous and monotonic

C. The function f(x) is differentiable

D. The function f(x) is continuous

正確答案: B

問題4

Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

A. 75%

B. 98%

C. 64%

D. Cannot be determined without estimates of the volatilities of the individual returns

正確答案: A

問題5

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

A. ln(x+y) x + ln(x+y) y

B. -x/(x+y) - y/(x+y)

C. (x + y) / (x+y)

D. 1 / (x+y)

正確答案: C

問題6

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

A. 6.14%

B. None of the above

C. 1.50%

D. 6%

正確答案: A

問題7

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

A. positive

B. not defined

C. zero

D. negative

正確答案: C

最新的PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition - 8007免費考試真題

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