8007 Exam Dumps - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

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Question # 9

When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

Take the square-root of 75 and raise it to the 5th power

Divide 75 by 2, then raise it to the 5th power

Multiply 75 by 2.5

Square 75, then take the fifth root of it

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Question # 10

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

10 basis point rise

24 basis fall

24 basis point rise

30 basis points fall.

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Question # 11

The gradient of a smooth function is

a vector that shows the direction of fastest change of a function

matrix of second partial derivatives of a function

infinite at a maximum point

a matrix containing the function's second partial derivatives

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Question # 12

Exploring a regression model for values of the independent variable that have not been observed is most accurately described asâ€¦

Estimation

Regression

Hypothesis testing

Prediction

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Question # 13

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

-x

-x+1

x-1

x+1

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Question # 14

Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

A structural break in the dependent variable

A high positive correlation between two explanatory variables

The omission of a relevant explanatory variable

Using an inappropriate functional form in the model

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Question # 15

Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

N(0) = 0.5

N'(0) â‰¥ 0

N(x) â†’ 0 as x â†’ âˆž

N'(x) â†’ 0 as x â†’ âˆž

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Question # 16

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

x = -1, y = 0

x = 0, y = 20

x = 5, y = 0

None of the above

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