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Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

Last Update 3 hours ago Total Questions : 132

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Question # 31

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.

0.3

B.

0.5

C.

0.6

D.

None of these

Question # 32

You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f ' (0) is …

A.

in the interval ]-2.5,-2[

B.

equal to -2

C.

in the interval ]-2,+∞[

D.

in the interval ]-∞,-2.5]

Question # 33

You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

A.

b=0.5, a=2.5

B.

b=0.5, a=1.5

C.

b=2, a=4

D.

b=2, a=0

Question # 34

Which of the provided answers solves this system of equations?

2y – 3x = 3y +x

y2 + x2 = 68

A.

x = 1; y = square root of 67

B.

x = 2; y = 8

C.

x = 2; y = -8

D.

x = -2; y = -8

Question # 35

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

A.

x = 1, y = 0.5

B.

x = -2, y = 2

C.

x = 2, y = 0

D.

None of the above

Question # 36

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

A.

16%

B.

17.4%

C.

20%

D.

24.4%

Question # 37

A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

A.

peaked and thin at the center and with heavy (fat) tails

B.

peaked and thin at the center and with thin tails

C.

flat and thick at the center and with heavy (fat) tails

D.

flat and thick at the center and with thin tails

Question # 38

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

A.

1.50%

B.

6%

C.

6.14%

D.

None of the above

Question # 39

What is a Hessian?

A.

Correlation matrix of market indices

B.

The vector of partial derivatives of a contingent claim

C.

A matrix of second derivatives of a function

D.

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

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