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

1. Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%,
+3%, -3%, +9%, -9% .
What can you say about the annual geometric and arithmetic mean returns of this investment fund?

A) The arithmetic mean return is zero and the geometric mean return is negative
B) The arithmetic mean return is equal to the geometric mean return
C) The arithmetic mean return is negative and the geometric mean return is zero
D) None of the above

2. Which of the following properties is exhibited by multiplication, but not by addition?

A) associativity
B) invertibility
C) distributivity
D) commutativity

3. For the function f(x) =3x-x3 which of the following is true?

A) None of these
B) x = 2 is a maximum
C) x = 0 is a minimum
D) x = -3 is a maximum

4. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A) E(exp(X)) = 0.6065
B) E(exp(X)) = 1.6487
C) E(exp(X)) = 1
D) E(exp(X)) = 2.7183

5. Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

A) A structural break in the dependent variable
B) A high positive correlation between two explanatory variables
C) Using an inappropriate functional form in the model
D) The omission of a relevant explanatory variable

Solutions: