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PRMIA 8007 Exam Syllabus Topics:

Section	Objectives
Topic 1: 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
Topic 2: Stochastic Processes and Time Series	- Time series analysis 1. AR, MA, and ARMA models 2. Autocorrelation and stationarity - Stochastic processes basics 1. Markov processes 2. Brownian motion (introductory level)
Topic 3: Probability and Statistics Foundations	- Statistical inference 1. Estimation theory 2. Confidence intervals and hypothesis testing - Random variables and probability distributions 1. Expectation, variance, and moments 2. Discrete and continuous distributions
Topic 4: Simulation and Numerical Methods	- Monte Carlo simulation 1. Random number generation 2. Risk distribution simulation

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

Question 1

The gradient of a smooth function is

A. a vector that shows the direction of fastest change of a function
B. a matrix containing the function's second partial derivatives
C. matrix of second partial derivatives of a function
D. infinite at a maximum point

Question 2

Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A. 3
B. 1
C. 2
D. 0

Question 3

What is the simplest form of this expression: log2(165/2)

A. 10
B. 5/2 + log2(16)
C. 32
D. log2 (5/2) + log2(16)

Question 4

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A. The commodity returns are integrated of order 1
B. The commodity prices are stationary
C. The commodity returns are stationary
D. None of the above

Question 5

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A. a quarterly-compounded rate of 4.1%
B. a lump-sum payment of $22 500 on maturity (in five years)
C. an annually compounded rate of 4.15%
D. a continuously-compounded rate of 4%

Solutions:

Question 1
Answer: A

Question 2
Answer: A

Question 3
Answer: A

Question 4
Answer: D

Question 5
Answer: A