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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Topic 1: Statistical Analysis- Descriptive and Inferential Statistics
  • 1. Maximum Likelihood Estimation
  • 2. Hypothesis Testing
  • 3. Confidence Intervals
  • 4. Moments and Distributions
Topic 2: Probability Theory- Fundamental Probability Concepts
  • 1. Probability Rules
  • 2. Random Variables
  • 3. Bayes' Theorem
  • 4. Conditional Probability
Topic 3: Linear Algebra- Matrix Methods
  • 1. Matrix Operations
  • 2. Eigenvalues and Eigenvectors
  • 3. Covariance Matrices
  • 4. Positive Definiteness
Topic 4: Numerical Methods- Quantitative Techniques
  • 1. Monte Carlo Methods
  • 2. Optimization Methods
  • 3. Numerical Approximation
  • 4. Simulation Techniques
Topic 5: Calculus- Differential and Integral Calculus
  • 1. Differentiation
  • 2. Integration
  • 3. Functions and Limits
  • 4. Multivariable Calculus
Topic 6: Regression and Time Series Analysis- Modeling Techniques
  • 1. Time Series Forecasting
  • 2. Multivariate Regression
  • 3. Linear Regression
  • 4. Model Diagnostics
Topic 7: Risk Measurement Applications- Quantitative Risk Analysis
  • 1. Sensitivity Analysis
  • 2. Portfolio Risk Measurement
  • 3. Volatility Modeling
  • 4. Value at Risk Methodologies

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

1. You are investigating the relationship between weather and stock market performance. To do this, you pick
100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of...

A) Simple time-series regression
B) Multiple cross-section regression
C) Multiple time-series regression
D) Simple cross-section regression


2. The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

A) None of the above
B) 1.50%
C) 6.14%
D) 6%


3. Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%,
+3%, -3%, +9%, -9% .
What can you say about the annual geometric and arithmetic mean returns of this investment fund?

A) None of the above
B) The arithmetic mean return is zero and the geometric mean return is negative
C) The arithmetic mean return is equal to the geometric mean return
D) The arithmetic mean return is negative and the geometric mean return is zero


4. In statistical hypothesis tests, 'Type I error' refers to the situation in which...

A) The null hypothesis is rejected when in fact it should have been accepted
B) The null hypothesis is accepted when in fact it should have been rejected
C) Both null hypothesis and alternative hypothesis are accepted
D) Both null hypothesis and alternative hypothesis are rejected


5. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A) E(exp(X)) = 2.7183
B) E(exp(X)) = 1.6487
C) E(exp(X)) = 0.6065
D) E(exp(X)) = 1


Solutions:

Question # 1
Answer: B
Question # 2
Answer: C
Question # 3
Answer: B
Question # 4
Answer: A
Question # 5
Answer: B

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