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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Probability Theory | 25% | - Basic probability concepts
|
| Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Time value of money - Basics of risk modeling |
| Calculus and Functions | 20% | - Multivariable calculus
|
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is
- A. 4%
- B. 20%
- C. 14.4%
- D. 24%
Correct Answer: B 🗳️
Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in
[0,4]?
- A. 1/7 and 1/9
- B. 1/4 and 1/7
- C. 1/4 and 1/6
- D. None of the above
Correct Answer: D 🗳️
In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.
- A. 5.19
- B. 6.31
- C. 4.18
- D. 5.66
Correct Answer: B 🗳️
The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?
- A. 6%
- B. None of the above
- C. 6.14%
- D. 1.50%
Correct Answer: C 🗳️
You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?
- A. b=2, a=4
- B. b=0.5, a=1.5
- C. b=0.5, a=2.5
- D. b=2, a=0
Correct Answer: D 🗳️
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