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

  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Sep 12, 2026
  • Q & A: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

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

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

                              Question #1

                              A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

                              • A. flat and thick at the center and with heavy (fat) tails
                              • B. peaked and thin at the center and with thin tails
                              • C. peaked and thin at the center and with heavy (fat) tails
                              • D. flat and thick at the center and with thin tails
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Question #2

                              The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

                              • A. (0, 2, 1)
                              • B. (0, 1, -1)
                              • C. (1, 1, 1)
                              • D. (0, 0, 0)
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

                              Question #3

                              When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

                              • A. Take the square-root of 75 and raise it to the 5th power
                              • B. Multiply 75 by 2.5
                              • C. Divide 75 by 2, then raise it to the 5th power
                              • D. Square 75, then take the fifth root of it
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

                              Question #4

                              Which of the following statements about variance and standard deviation are correct?
                              1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation
                              2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data
                              3. When considering independent variables, variance is additive, while standard deviation is not

                              • A. Statements 2 and 3 are correct
                              • B. All three statements are correct
                              • C. Statements 1 and 2 are correct
                              • D. Statements 1 and 3 are correct
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

                              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. Statements 2 and 3 are correct
                              • B. All three statements are correct
                              • C. Statements 1 and 2 are correct
                              • D. Statements 1 and 3 are correct
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

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