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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Numerical Methods & Financial Mathematics | 15% | - Time value of money - Root finding and approximation - Basics of risk modeling |
| Topic 2: Statistics and Regression Analysis | 20% | - Linear regression
|
| Topic 3: Calculus and Functions | 20% | - Single-variable calculus
|
| Topic 4: Probability Theory | 25% | - Random variables and distributions
|
| Topic 5: Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:
A) 0.00087
B) 0.00109
C) 0.40729
D) 0.32583
2. Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?
A) The normal distribution has lower kurtosis than the t distribution.
B) The normal distribution has higher kurtosis than the t distribution.
C) The distributions have the same kurtosis.
D) Which has the higher kurtosis depends on the degrees of freedom of the t distribution.
3. A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?
A) 1.95
B) 1.75
C) 1.86
D) 2
4. An asset price S is lognormally distributed if:
A) ln(dS/S) is normally distributed
B) 1/S is normally distributed
C) the change in price (dS) is normally distributed
D) ln(1+dS/S) is normally distributed
5. Every covariance matrix must be positive semi-definite. If it were not then:
A) One or more of its eigenvalues would be negative
B) There would be no Cholesky decomposition matrix
C) Some portfolios could have a negative variance
D) All the above statements are true
Solutions:
| Question # 1 Answer: B | Question # 2 Answer: A | Question # 3 Answer: C | Question # 4 Answer: D | Question # 5 Answer: D |

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