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PRMIA 8007 Exam Syllabus Topics:

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

Question 1

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A. None of the above
B. The commodity prices are stationary
C. The commodity returns are stationary
D. The commodity returns are integrated of order 1

Question 2

What is a Hessian?

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

Question 3

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 1/2
B. 9/25 and 12/25
C. 2/5 and 3/5
D. 1/3 and 8/17

Question 4

You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...

A. equal to -2
B. in the interval ]-2,+[
C. in the interval ]-,-2.5]
D. in the interval ]-2.5,-2[

Question 5

An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

A. 0.14
B. 0.50
C. 0.25
D. 0.02

Solutions: