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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Topic 2: Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Topic 3: Numerical Methods & Financial Mathematics | 15% | - Time value of money - Basics of risk modeling - Root finding and approximation |
| Topic 4: Calculus and Functions | 20% | - Single-variable calculus
|
| Topic 5: Probability Theory | 25% | - Random variables and distributions
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by
- A. F(x)g(x) + f(x)G(x)
- B. F(x)g(x) - F(x)g'(x)dx
- C. F(x)G(x)
- D. f(x)G(x) - F(x)g'(x)dx
Correct Answer: B 🗳️
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. 0.00109
- B. 0.00087
- C. 0.32583
- D. 0.40729
Correct Answer: A 🗳️
If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?
- A. 90%
- B. 95%
- C. 66.60%
- D. 99%
Correct Answer: B 🗳️
In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:
- A. 0.5288
- B. 0.5292
- C. 0.5286
- D. 0.5290
Correct Answer: A 🗳️
Bond convexity is closely related to ...
- A. The integral of the bond's present value with respect to yield
- B. The second derivative of the bond's present value with respect to yield
- C. The sensitivity of the bond's present value with respect to yield
- D. The derivative of the bond's present value with respect to yield
Correct Answer: B 🗳️
