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: Jul 30, 2026     Q & A: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

SectionWeightObjectives
Probability Theory25%- Basic probability concepts
  • 1. Axioms and rules
    • 2. Conditional probability and independence
      - Random variables and distributions
      • 1. Expected value, variance, covariance
        • 2. Discrete and continuous distributions
          Statistics and Regression Analysis20%- Descriptive statistics
          • 1. Measures of location and dispersion
            • 2. Correlation and covariance
              - Linear regression
              • 1. Simple and multiple regression
                • 2. Hypothesis testing and confidence intervals
                  Calculus and Functions20%- Multivariable calculus
                  • 1. Optimization
                    • 2. Partial derivatives
                      - Single-variable calculus
                      • 1. Limits and continuity
                        • 2. Derivatives and applications
                          • 3. Integrals and applications
                            Linear Algebra and Matrix Theory20%- Vectors and eigenvalues
                            • 1. Eigenvalues and eigenvectors
                              • 2. Diagonalization
                                - Matrix operations
                                • 1. Determinants and trace
                                  • 2. Addition, multiplication, inversion
                                    Numerical Methods & Financial Mathematics15%- Time value of money
                                    - Basics of risk modeling
                                    - Root finding and approximation

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

                                    1. Consider two securities X and Y with the following 5 annual returns:
                                    X: +10%, +3%, -2%, +3%, +5%
                                    Y: +7%, -2%, +3%, -5%, +10%
                                    In this case the sample covariance between the two time series can be calculated as:

                                    A) 0.40729
                                    B) 0.00087
                                    C) 0.00109
                                    D) 0.32583


                                    2. 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 less than 1?

                                    A) 0.32
                                    B) 1.92
                                    C) 0.96
                                    D) 0.64


                                    3. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

                                    A) f might have either a minimum or a maximum or neither of them at this point
                                    B) f has necessarily neither a minimum nor a maximum at this point
                                    C) f has necessarily a maximum at this point
                                    D) f has necessarily a minimum at this point


                                    4. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

                                    A) 0.5292
                                    B) 0.5288
                                    C) 0.5290
                                    D) 0.5286


                                    5. 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) 9/16
                                    B) 7/8
                                    C) None of these
                                    D) 11/16


                                    Solutions:

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

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