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PRMIA 8007 Exam Syllabus Topics:

Section	Weight	Objectives
Statistics and Regression Analysis	20%	- Linear regression 1. Hypothesis testing and confidence intervals 2. Simple and multiple regression - Descriptive statistics 1. Measures of location and dispersion 2. Correlation and covariance
Calculus and Functions	20%	- Multivariable calculus 1. Partial derivatives 2. Optimization - Single-variable calculus 1. Derivatives and applications 2. Limits and continuity 3. Integrals and applications
Probability Theory	25%	- Basic probability concepts 1. Axioms and rules 2. Conditional probability and independence - Random variables and distributions 1. Expected value, variance, covariance 2. Discrete and continuous distributions
Linear Algebra and Matrix Theory	20%	- Vectors and eigenvalues 1. Diagonalization 2. Eigenvalues and eigenvectors - Matrix operations 1. Determinants and trace 2. Addition, multiplication, inversion
Numerical Methods & Financial Mathematics	15%	- Basics of risk modeling - Time value of money - Root finding and approximation

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

1. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

A) [0, 3]
B) [1, 2]
C) [0, 1.5]
D) None of the above

2. 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) 95%
B) 66.60%
C) 90%
D) 99%

3. 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 50%. The volatility of my portfolio is

A) 17.4%
B) 16%
C) 20%
D) 24.4%

4. An asset price S is lognormally distributed if:

A) 1/S is normally distributed
B) the change in price (dS) is normally distributed
C) ln(dS/S) is normally distributed
D) ln(1+dS/S) is normally distributed

5. 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) 24%
B) 4%
C) 20%
D) 14.4%

Solutions:

Question # 1
Answer: A

Question # 2
Answer: A

Question # 3
Answer: A

Question # 4
Answer: D

Question # 5
Answer: C