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PRMIA 8007 Exam Syllabus Topics:

SectionWeightObjectives
Topic 1: Numerical Methods & Financial Mathematics15%- Time value of money
- Root finding and approximation
- Basics of risk modeling
Topic 2: 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 3: Calculus and Functions20%- Single-variable calculus
          • 1. Derivatives and applications
            • 2. Integrals and applications
              • 3. Limits and continuity
                - Multivariable calculus
                • 1. Partial derivatives
                  • 2. Optimization
                    Topic 4: Probability Theory25%- Random variables and distributions
                    • 1. Expected value, variance, covariance
                      • 2. Discrete and continuous distributions
                        - Basic probability concepts
                        • 1. Axioms and rules
                          • 2. Conditional probability and independence
                            Topic 5: Linear Algebra and Matrix Theory20%- Matrix operations
                            • 1. Determinants and trace
                              • 2. Addition, multiplication, inversion
                                - Vectors and eigenvalues
                                • 1. Eigenvalues and eigenvectors
                                  • 2. Diagonalization

                                    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) 0.00087
                                    B) 0.00109
                                    C) 0.40729
                                    D) 0.32583


                                    2. 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 normal distribution has higher kurtosis than the t distribution.
                                    C) The distributions have the same kurtosis.
                                    D) Which has the higher kurtosis depends on the degrees of freedom of the t distribution.


                                    3. A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?

                                    A) 1.95
                                    B) 1.75
                                    C) 1.86
                                    D) 2


                                    4. An asset price S is lognormally distributed if:

                                    A) ln(dS/S) is normally distributed
                                    B) 1/S is normally distributed
                                    C) the change in price (dS) is normally distributed
                                    D) ln(1+dS/S) is normally distributed


                                    5. Every covariance matrix must be positive semi-definite. If it were not then:

                                    A) One or more of its eigenvalues would be negative
                                    B) There would be no Cholesky decomposition matrix
                                    C) Some portfolios could have a negative variance
                                    D) All the above statements are true


                                    Solutions:

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

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