Syllabus
Course Description:
The course will develop a general quantitative approach to modern portfolio theory, optimization, and trading. We begin by discussing utility functions, and the theory of rational decision making under uncertainty. Expected utility maximization is shown to give rise to mean-variance optimization for elliptical distributions. We go on to give a mathematical background in optimization including Lagrange multipliers, the dual problem, and Karush-Kuhn-Tucker conditions. We then cover the Capital Asset Pricing Model (CAPM) and Ross’ Arbitrage Pricing Theory (APT) in some detail, with some practical examples. We use APT-style factor models to develop the general approach tomodelingportfoliorisk that is in use at most large banks and hedge funds. This approach includes discussions of VaR, expected shortfall, variance decompositions, contributions to risk, dynamic volatilities and correlations, etc. We shall also discuss portfolio optimization in the context of factor models and Black-Litterman optimization. We then cover trading costs, slippage modeling and market impact, and how to incorporate trading costs into portfolio optimization including multi-period optimization. We then discuss valuation including fundamental analysis and dividend discount models; forecasting; event studies and cross-sectional studies; the information ratio and information horizons; Fundamental Law of Active Management, Information Coefficient, Transfer Coefficient and related issues. In each case, the focus will be on using advanced statistics to achieve a deeper understanding of the model and the data. Where appropriate, we will apply the relevant statistical models to real financial data.
Main Text:
The instructor’s notes, distributed in class and online, will be the main reference material for the course. Certain parts of the course may follow particular sections from the recommended texts below, and this will be indicated where appropriate.
Recommended Texts:
Grinold, Richard, and Ronald N. Kahn. Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Selecting Superior Money Managers. Irwin/McGraw-Hill, 1999. Gregory Connor, Lisa R. Goldberg, and Robert A. Korajczyk. Portfolio Risk Analysis. Princeton University Press, 2010. Alexander J. McNeil, Rüdiger Frey, and Paul Embrechts. Quantitative RiskManagement: Concepts, Techniques, and Tools. Princeton Series in Finance. Princeton University Press, 2005. Hyun Song Shin. Risk and liquidity. Clarendon Lectures in Finance. Oxford University Press, Oxford, 2010. Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press (avail- able online)
Homework:
All homework assignments are due in one week unless otherwise announced. Late homework will not be accepted. The homework will typically be a mix of theory and application, with some coding required in either R or Java.
Final grade:
Homework assignments, 50%; Midterm Exam, 15% (in class); Final Exam, 35%.
Prerequisites:
Linear algebra and multivariable calculus. Statistics at the level of a standard undergraduate sequence including multivariate statistics. Familiarity with financial markets and trading. Some coding experience in either R, Java, or C++.