PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition - 8007

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  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Sep 08, 2026
  • Q & A: 133 Questions and Answers
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PRMIA 8007 Exam Syllabus Topics:
SectionWeightObjectives
Topic 1: Numerical Methods & Financial Mathematics15%- Root finding and approximation
- Basics of risk modeling
- Time value of money
Topic 2: Probability Theory25%- Basic probability concepts
  • 1. Axioms and rules
    • 2. Conditional probability and independence
      - Random variables and distributions
      • 1. Discrete and continuous distributions
        • 2. Expected value, variance, covariance
          Topic 3: Statistics and Regression Analysis20%- 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
                  Topic 4: Calculus and Functions20%- Single-variable calculus
                  • 1. Limits and continuity
                    • 2. Derivatives and applications
                      • 3. Integrals and applications
                        - Multivariable calculus
                        • 1. Partial derivatives
                          • 2. Optimization
                            Topic 5: Linear Algebra and Matrix Theory20%- Vectors and eigenvalues
                            • 1. Diagonalization
                              • 2. Eigenvalues and eigenvectors
                                - Matrix operations
                                • 1. Determinants and trace
                                  • 2. Addition, multiplication, inversion
                                    PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
                                    Question #1

                                    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 prices are stationary
                                    • B. The commodity returns are integrated of order 1
                                    • C. None of the above
                                    • D. The commodity returns are stationary
                                    Answer: C
                                    Question #2

                                    What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?

                                    • A. 45 degrees
                                    • B. 57 degrees
                                    • C. 90 degrees
                                    • D. 180 degrees
                                    Answer: C
                                    Question #3

                                    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. 99%
                                    • B. 95%
                                    • C. 90%
                                    • D. 66.60%
                                    Answer: B
                                    Question #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. 0.125
                                    • B. -2.5
                                    • C. 2.5
                                    • D. -1.25
                                    Answer: B
                                    Question #5

                                    Which of the following statements about skewness of an empirical probability distribution are correct?
                                    1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
                                    2. When the mean is significantly less than the median, this is an indication of negative skewness
                                    3. Skewness is a sign of asymmetry in the dispersion of the data

                                    • A. All three statements are correct
                                    • B. Statements 2 and 3 are correct
                                    • C. Statements 1 and 2 are correct
                                    • D. Statements 1 and 3 are correct
                                    Answer: A

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