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# 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