STA4028Z - Portfolio Theory

Course Outline:

The course introduces the historical development of idea’s from Economics, gambling and Finance with a South African perspective for portfolio control. Data-wrangling, portfolio optimization, sequential historic back-testing and simulation, and their attribution are developed in R. The static mean-variance theoretical foundations of portfolio choice, asset pricing and notions of market equilibrium are developed from first principles. Following an operations research approach tactical and strategic portfolios are formulated to admit short-term departures from long-term equilibrium for asset allocation. The theory is used to demonstrate the Generalised Fundamental Law of Asset Management, the Roll Critique and a Bayesian Black-Litterman portfolio choice framework. Active management and its complexities due to estimation and intrinsic uncertainties are demonstrated via case-studies. Various performance measures are derived from theoretical considerations. Performance attribution is used to measure the impact of information, return, risk and performance within a sequence of single-period portfolio control decisions. There is an emphasis on understanding the implications of back-test over-fitting. The course introduces indexation methods and the integration of the developed tools within a standard portfolio management workflow. Advanced topics such as cluster-based portfolio choice, risk-parity models and machine-learning extensions may be included.