PRM Exam II

The following syllabus and objective statements are as per the latest PRM Guide.

Note: If an LOS is a link, that means the material for that LOS is available. The dates mentioned against each LOS is the date when the study material for that LOS is scheduled to arrive.

  • Foundations

    • Describe Rules of algebraic operations
    • List the Order of algebraic operations
    • Characterize Sequences
    • Characterize Series
    • Characterize Exponents
    • Characterize Logarithms
    • Characterize Exponential function and Natural Logarithms
    • Solve Linear equalities and inequalities in one unknown
    • Demonstrate the Elimination method
    • Demonstrate the Substitution method
    • Solve Quadratic equations in one unknown
    • Characterize Functions and Graphs
    • Demonstrate continuous compounding
    • Differentiate between discrete compounding and continuous compounding
  • Descriptive Statistics

    • Describe various forms of Data
    • Discuss Graphical representation of data
    • Explain the concept of The Moments of a Distribution
    • Define, Discuss and Calculate the Measures of Location or Central Tendency
    • Define, Discuss and Calculate the Measures of Dispersion
    • Calculate Historical Volatility from Returns Data
    • Define, Discuss and Calculate Negative Semi-variance and Negative Semi-deviation
    • Define, Discuss and Calculate Skewness
    • Define, Discuss and Calculate Kurtosis
    • Describe Bivariate Data
    • Discuss Covariance and Covariance Matrix
    • Discuss Correlation Coefficient and Correlation Matrix
    • Calculate the volatility of a portfolio
  • Calculus

    • Explain the concept of differentiation
    • Demonstrate the application of the rules of differentiation to polynomial, exponential and logarithmic functions
    • Calculate the modified duration of a bond
    • Discuss Taylor Approximations
    • Demonstrate the concept of convexity
    • Demonstrate the concept of delta, gamma and vega
    • Demonstrate Partial Differentiation
    • Demonstrate Total Differentiation
    • Discuss the Fundamental Theorem of Analysis
    • List the Indefinite Integral(s) of function(s)
    • Apply the Rules of Integration
    • Discuss Optimisation of Univariate and Multivariate functions
    • Demonstrate Constrained Optimisation using Lagrange Multipliers
  • Linear Mathematics and Matrix Algebra

    • Demonstrate basic operations of Matrix Algebra
    • Solve two Linear Simultaneous Equations using Matrix Algebra
    • Demonstrate Portfolio Construction
    • Demonstrate Hedging of a Vanilla Option Position
    • Describe Quadratic Forms
    • Discuss the Variance of Portfolio Returns as a Quadratic Form
    • Define Positive Definiteness
    • Demonstrate Cholesky Decomposition
    • Demonstrate Eigenvalues and Eigenvectors
    • Describe Principal Components
  • Probability Theory

    • Explain the concept of probability
    • Describe the different approaches to defining and measuring probability
    • Demonstrate the rules of probability
    • Define the discrete and continuous random variable
    • Describe the probability distributions of a random variable
    • Describe Probability density functions and histograms
    • Describe the Algebra of Random variables
    • Define the Expected Value and Variance of a discrete random variable
    • Describe the Algebra of Continuous Random Variables
    • Demonstrate Joint Probability Distributions
    • Discuss covariance and correlation
    • Discuss linear combinations of random variables
    • Discuss the Binomial Distribution
    • Demonstrate the Poisson Distribution
    • Describe the Uniform Continuous Distribution
    • Discuss the Normal Distribution
    • Discuss the Lognormal Probability Distribution and its use in derivative pricing
    • Discuss the Student’s t Distribution
    • Discuss the Bivariate Normal Joint Distribution
  • Regression Analysis

    • Define Regression Analysis and the different types of regression
    • Demonstrate Simple Linear Regression
    • Demonstrate Multiple Linear Regression
    • Discuss the evaluation of the Regression Model
    • Describe Confidence Intervals
    • Describe Hypothesis Testing
    • Demonstrate Significance Tests for the Regression Parameters
    • Demonstrate Significance Test for R2
    • Describe Type I and Type II Errors
    • Demonstrate the concept of Prediction
    • Describe the OLS Assumptions and main breakdowns of them
    • Describe Random Walks and Mean Reversion
    • Describe Maximum Likelihood Estimation
  • Numerical Methods

    • Demonstrate the Bisection method for solving Non-differential Equations
    • Demonstrate the Newton-Raphson method for solving Non-differential Equations
    • Describe the application of Goal Seek equation solver in Excel
    • Demonstrate Unconstrained Numerical Optimisation
    • Demonstrate Constrained Numerical Optimisation
    • Demonstrate Binomial Lattices for valuing options
    • Demonstrate Finite Difference Methods for valuing options
    • Demonstrate Simulation using Excel
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