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

1. An indefinite integral of a polynomial function is

A) none of the above
B) always positive
C) always less than the function itself
D) always increasing

2. Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data

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

3. Which of the following statements is true for symmetric positive definite matrices?

A) If a is its eigenvalue, then is also its eigenvalue
B) Its eigenvalues are all positive
C) One of its eigenvalues equals 0
D) If a is its eigenvalue, then -a is also its eigenvalue

4. 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) and (iii)
D) (i) only

5. Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

A) The probability of an up move will not be constant
B) None of the above
C) There will always be a downward drift in the lattice
D) The lattice will not recombine

Solutions: