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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Topic 1: Probability and Statistics Foundations- Statistical inference
  • 1. Estimation theory
    • 2. Confidence intervals and hypothesis testing
      - Random variables and probability distributions
      • 1. Discrete and continuous distributions
        • 2. Expectation, variance, and moments
          Topic 2: 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 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. Parametric and non-parametric VaR
                        • 2. Historical simulation approach
                          - Volatility and correlation
                          • 1. Variance-covariance methods
                            • 2. Correlation estimation techniques

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

                              If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

                              • A. None of these
                              • B. 3/4
                              • C. 37/45
                              • D. 12/29
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?

                              • A. The normal distribution has lower kurtosis than the t distribution.
                              • B. The distributions have the same kurtosis.
                              • C. The normal distribution has higher kurtosis than the t distribution.
                              • D. Which has the higher kurtosis depends on the degrees of freedom of the t distribution.
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

                              Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

                              • A. 36.33%
                              • B. 26.33%
                              • C. 20.78%
                              • D. 36%
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              The Newton-Raphson method

                              • A. is based on finding a middle point between left and right end of the search interval
                              • B. does provide an error bound along with every iteration
                              • C. is based on Taylor series and uses the first derivative
                              • D. can be used for continuous but not differentiable functions
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

                              • A. None of these
                              • B. 11/16
                              • C. 7/8
                              • D. 9/16
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

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