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

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PRMIA 8007 Exam Syllabus Topics:

PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5286
B) 0.5288
C) 0.5292
D) 0.5290

2. Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

A) -x
B) x
C) ln(x)
D) x -1

3. Which statement regarding the matrix below is true?

A) It is not positive definite
B) It is negative definite
C) It is positive definite
D) It is positive semi-definite

4. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

A) (i) only
B) (i), (ii), and (iii)
C) (i) and (iii)
D) (i) and (ii)

5. 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) Cannot be determined without estimates of the volatilities of the individual returns
B) 98%
C) 75%
D) 64%

Solutions: