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PRMIA 8007 Exam Syllabus Topics:

Section	Objectives
Topic 1: Probability and Statistics Foundations	- Random variables and probability distributions 1. Expectation, variance, and moments 2. Discrete and continuous distributions - Statistical inference 1. Estimation theory 2. Confidence intervals and hypothesis testing
Topic 2: Stochastic Processes and Time Series	- Time series analysis 1. AR, MA, and ARMA models 2. Autocorrelation and stationarity - Stochastic processes basics 1. Brownian motion (introductory level) 2. Markov processes
Topic 3: Simulation and Numerical Methods	- Monte Carlo simulation 1. Random number generation 2. Risk distribution simulation
Topic 4: Risk Measurement Techniques	- Value at Risk (VaR) 1. Historical simulation approach 2. Parametric and non-parametric VaR - Volatility and correlation 1. Variance-covariance methods 2. Correlation estimation techniques

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

1. An indefinite integral of a polynomial function is

A) always less than the function itself
B) always positive
C) none of the above
D) always increasing

2. 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

3. A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?

A) 0.3333
B) 0.75
C) 1.125
D) 0.375

4. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

A) -1.25
B) 0.125
C) 2.5
D) -2.5

5. The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?

A) None of the above
B) 1
C) 0.5
D) 1.5

Solutions:

Question # 1
Answer: C

Question # 2
Answer: A

Question # 3
Answer: D

Question # 4
Answer: D

Question # 5
Answer: D