PRMIA 8007 : Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

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PRMIA 8007 Exam Syllabus Topics:

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

1. Which of the following statements about variance and standard deviation are correct?
1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation
2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data
3. When considering independent variables, variance is additive, while standard deviation is not

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

2. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 1
B) 0.5
C) None of the above
D) 0

3. 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)) = 2.7183
B) E(exp(X)) = 0.6065
C) E(exp(X)) = 1
D) E(exp(X)) = 1.6487

4. Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses...

A) Many dependent variables, one independent variable, one error variable
B) Many dependent variables, many independent variables, many error variables
C) One dependent variable, one independent variable, many error variables
D) One dependent variable, many independent variables, one error variable

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

Solutions: