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PRMIA 8007 Exam Syllabus Topics:

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

1. 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) 64%
B) 98%
C) Cannot be determined without estimates of the volatilities of the individual returns
D) 75%

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

A) x+1
B) -x
C) x-1
D) -x+1

3. Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

A) 2/5 and 3/5
B) 1/3 and 8/17
C) 2/5 and 1/2
D) 9/25 and 12/25

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

A) All the above statements are true
B) The associated correlation matrix would not be positive semi-definite
C) It could not be used to simulate correlated asset paths
D) Some portfolios could have a negative variance

5. What is the probability of tossing a coin and getting exactly 2 heads out of 5 throws?

A) 9/23
B) 10/32
C) 8/15
D) None of these

Solutions: