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

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Showing 1–3 of 10 questions

Question 1

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

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    -x

  • ○

    -x+1

  • ○

    x-1

  • ○

    x+1


Question 2

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.)

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  • ○

    64%

  • ○

    75%

  • ○

    98%

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


Question 3

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?

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  • ○

    0.7367

  • ○

    0.3483

  • ○

    0.2646

  • ○

    None of these