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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
| Topic 2: Calculus and Functions | 20% | - Single-variable calculus
|
| Topic 3: Probability Theory | 25% | - Basic probability concepts
|
| Topic 4: Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Basics of risk modeling - Time value of money |
| Topic 5: Statistics and Regression Analysis | 20% | - Descriptive statistics
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?
- A. 0
- B. 0.5
- C. 1
- D. None of the above
Correct Answer: A 🗳️
The bisection method can be used for solving f(x)=0 for a unique solution of x, when
- A. The function f(x) is differentiable
- B. The function f(x) is continuous
- C. The function f(x) is continuous and monotonic
- D. The function f(x) is differentiable and we have an explicit expression for the derivative
Correct Answer: C 🗳️
Let a, b and c be real numbers. Which of the following statements is true?
- A. The existence of negatives is defined by
- B. The associativity of multiplication is defined by
- C. The commutativity of multiplication is defined by
- D. The distributivity of multiplication is defined by
Correct Answer: D 🗳️
You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?
- A. 1
- B. a
- C. 42
- D. a2
Correct Answer: C 🗳️
When the errors in a linear regression show signs of positive autocorrelation, which of the statements below is true?
- A. The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated
- B. The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated
- C. The regression coefficient will be too low and the standard error of the regression coefficient will be overstated
- D. The regression coefficient will be too high and the standard error of the regression coefficient will be understated
Correct Answer: B 🗳️
