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

1. 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

2. Variance reduction is:

A) A method for reducing the number of simulations required in a Monte Carlo simulation
B) A technique that is applied in regression models to improve the accuracy of the coefficient estimates
C) A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
D) A numerical method for finding the variance of the underlying that is implicit in a market price of an option

3. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 0
B) 0.5
C) None of the above
D) 1

4. Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter

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

5. Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

A) 26.33%
B) 20.78%
C) 36%
D) 36.33%

Solutions: