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

1. Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

A) Beta must be greater in absolute value than the correlation of the stocks ( )
B) Alpha must be positive ( )
C) The stocks must be positively correlated ( )
D) Beta must be positive ( )

2. Maximum likelihood estimation is a method for:

A) Finding parameter estimates of a given density function
B) Estimating the implied volatility of a simple European option
C) Estimating the solution of a partial differential equation
D) Solving a portfolio optimization problem

3. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

A) the definite integral of the CDF from minus infinity to plus infinity is undefined.
B) the CDF approaches 1 as its argument approaches infinity.
C) the definite integral of the PDF from minus infinity to plus infinity is zero.
D) the PDF is non-negative.

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

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

5. Evaluate the derivative of ln(1+ x2) at the point x = 1

A) 1
B) 2
C) 0
D) 0.5

Solutions: