Module Two
Risk and Return
This unit deals with the classical portfolio theory of Markowitz, the Capital Asset Pricing Model, more recent developments of these theories, also option types and strategies.
Further Mathematical Methods
(Optional Lecture)
• Further first order differential equations
• Error Function, Gamma and Beta Functions
• Further Complex Numbers
• Generalized Functions
• Double Integration: Introduction and examples
• Transform Methods: Definition and standard results; Application to the heat equation
• Numerical Methods: Integration, interpolation, numerical linear algebra, root finding, heat equation
Portfolio Management
• Measuring risk and return
• Benefits of diversification
• Modern Portfolio Theory and the Capital Asset Pricing Model
• The efficient frontier
• Optimising your portfolio
• How to analyse portfolio performance
• Alphas and Betas
Martingale Theory – Fundamentals
• Advanced stochastic calculus
• Martingale theory and definitions
• Elementary measure theory
• Change of measure and the Radon Nicodym derivative
Fundamentals of Optimization and Application to Portfolio Selection
• Fundamentals of portfolio optimization
• Formulation of optimization problems
• Solving unconstrained problems using calculus
• Kuhn-Tucker conditions
• Derivation of CAPM
Products and Strategies
• The time value of money
• Equities, commodities, currencies and indices
• Fixed and floating interest rates
• Futures and forwards
• No-arbitrage
• The definitions of basic derivative instruments
• Option jargon
• No arbitrage again and put-call parity
• How to draw payoff diagrams
• Simple option strategies
Value at Risk and Volatility
• The meaning of Value at Risk (VaR)
• How VaR is calculated in practice
• Simulations and bootstrapping
• Simple volatility estimates
• The exponentially weighted moving average
Binomial Model
• A simple model for an asset price random walk
• Delta hedging
• No arbitrage
• The basics of the binomial method for valuing options
• Risk neutrality