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

1. 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) 9/25 and 12/25
D) 2/5 and 1/2

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

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

3. Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A) Changing all the correlations to be zero
B) Changing all the correlations to be unity
C) Changing the volatilities to be greater than 100%
D) All of the above

4. Which of the following can induce a 'multicollinearity' problem in a regression model?

A) A large negative correlation between the dependent variable and one of the explanatory variables
B) A high positive correlation between the dependent variable and one of the explanatory variables
C) The omission of a relevant explanatory variable
D) A high positive correlation between two explanatory variables

5. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated variance has a Chi2-distribution
B) The estimated mean divided by the estimated standard deviation has a t-distribution
C) The estimated mean divided by the estimated variance has a t-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

Solutions: