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87% Average Score

94% Same Questions
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Questions # 31:

A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

Options:

A.

0.7367

B.

0.3483

C.

0.2646

D.

None of these

Questions # 32:

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.)

Options:

A.

64%

B.

75%

C.

98%

D.

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

Questions # 33:

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

Options:

A.

Some portfolios could have a negative variance

B.

It could not be used to simulate correlated asset paths

C.

The associated correlation matrix would not be positive semi-definite

D.

All the above statements are true

Questions # 34:

The natural logarithm of x is:

Options:

A.

the inverse function of exp(x)

B.

log(e)

C.

always greater than x, for x>0

D.

46

Questions # 35:

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

Options:

A.

2.362

B.

1.623

C.

1.638

D.

0.377

Questions # 36:

Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

Options:

A.

the PDF is non-negative.

B.

the definite integral of the CDF from minus infinity to plus infinity is undefined.

C.

the CDF approaches 1 as its argument approaches infinity.

D.

the definite integral of the PDF from minus infinity to plus infinity is zero.

Questions # 37:

What is the simplest form of this expression: log2(165/2)

Options:

A.

10

B.

32

C.

5/2 + log2(16)

D.

log2 (5/2) + log2(16)

Questions # 38:

What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?

Options:

A.

90 degrees

B.

180 degrees

C.

57 degrees

D.

45 degrees

Questions # 39:

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

Options:

A.

1 / (x+y)

B.

(∆x + ∆y) / (x+y)

C.

-∆x/(x+y) - ∆y/(x+y)

D.

ln(x+y) ∆x + ln(x+y) ∆y

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