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PRMIA 8007 Exam Syllabus Topics:

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

1. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) a2
B) 42
C) a
D) 1

2. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A) 12.78
B) 11.82
C) 12.33
D) 12.49

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

A) There would be no Cholesky decomposition matrix
B) All the above statements are true
C) Some portfolios could have a negative variance
D) One or more of its eigenvalues would be negative

4. Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

A) zero
B) positive
C) negative
D) not defined

5. 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) Some portfolios could have a negative variance
D) It could not be used to simulate correlated asset paths

Solutions: