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.

• Simulations: The lognormal random walk, probability density functions.
• Risk and reward: Measuring return, expectation and standard deviation.
• Modern Portfolio Theory (Markowitz): Expected returns, variances and covariances, benefits of diversification, the opportunity set and the efficient frontier, the Sharpe ratio, and utility functions.
• Capital Asset Pricing Model: Single-index model, beta, diversification, optimal portfolios, the multiindexmodel.
• Value at risk: Profit and loss for simple portfolios, tails of distributions, Monte Carlo simulations and historical simulations, stress testing and worst-case scenarios. Portfolios of derivatives.
• Introducing futures, forwards and options: Simple contingent claims, definitions and uses.
• Review of option strategies: Building up special payoff structures using vanilla calls and puts,
  horizontal, vertical and diagonal spreads.
• Review of options as speculative investments: Taking a view, gearing, strategies that benefit from
  moves in the asset or in volatility.
• The binomial model: Up and down moves, delta hedging and self-financing replication, no
  arbitrage, a pricing model, risk-neutral probabilities.
• Martingale theory: Fundamental definitions, concepts, results and tools.

Lecture 2.1

• Measuring risk and return
• Benefits of diversification
• Modern Portfolio Theory and the Capital Asset Pricing Model
• The efficient frontier
• Optimizing your portfolio
• How to analyze portfolio performance
• Alphas and betas

Lecture 2.2

• 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

Lecture 2.3

• The meaning of Value at Risk (VaR)
• How VaR is calculated in practice
• Simulations and bootstrapping
• Simple volatility estimates
• The exponentially weighted moving average

Lecture 2.4

• A simple model for an asset price random walk
• Delta hedging
• No arbitrage
• The basics of the binomial method for valuing options
• Risk neutrality

Lecture 2.5

• Martingale definitions and concepts
• Important results and tools

Lecture 2.6: Methods for Quantitative Finance: II

• Numerical Methods
• Stochastic Calculus

Preparatory reading:

• P. Wilmott, Paul Wilmott Introduces Quantitative Finance, second edition, 2007, John Wiley.
  Chapters 1, 2, 3, 20-22
• M. Jackson and M. Staunton, Advanced Modelling in Finance Using Excel and VBA, 2001, John Wiley.
  Chapters 6—8, 10
• E.G. Haug, The Complete Guide to Option Pricing Formulas, second edition, 2007, McGraw-Hill Professional.
  Chapter 7

Further reading:

• S.N. Neftci, An Introduction to the Mathematics of Financial Derivatives, 1996, Academic Press
• E.J. Elton & M.J. Gruber, Modern Portfolio Theory and Investment Analysis, 1995, John Wiley
• R.C. Merton, Continuous Time Finance, 1992, Blackwell
• N. Taleb, Dynamic Hedging, 1996, John Wiley

Follow-up recording(s), extra lecture(s):

• Investment Lessons from Blackjack and Gambling
• Lagrange Optimization
• Quants Toolbox
• Symmetric Downside Sharpe Ratio
• Beyond Black-Litterman: Views on Generic Markets