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

1. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

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

2. Which of the following statements concerning class intervals used for grouping of data is correct?
When grouping data, attention must be paid to the following with regards to class intervals:
1. Class intervals should not overlap
2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup
3. The class intervals should be large enough so that they not obscure interesting variation within the group

A) Statements 1 and 3 are correct
B) Statements 1 and 2 are correct
C) All three statements are correct
D) Statements 2 and 3 are correct

3. 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) 36.33%
D) 36%

4. What is a Hessian?

A) A matrix of second derivatives of a function
B) Correlation matrix of market indices
C) The vector of partial derivatives of a contingent claim
D) The point at which a minimum of a multidimensional function is achieved

5. What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

A) 1 048 574
B) 2 097 172
C) 1 048 595
D) 2 097 170

Solutions: