Course objective:

At the end of the module, the student should feel comfortable with the terminology and some of the different methodologies used in portfolio selection. Moreover, the student should be able to construct and test the performance of optimal efficient portfolios.

Learning outcomes:

After completing the course, students should be able to:

• understand the concept of portfolio diversification and its benefits for risk-averse investors,

• compute optimal mean-variance portfolios,

• compute optimal portfolios that take into account alternative risk measures,

• construct optimal bond portfolios,

• factor investing theory,

• construct empirical test to evaluate the performance of optimal portfolios,

• understand the limitations of the mean-variance theory.

Assessment:

The student should write a report related to an investment strategy. This investment strategy will be assigned to the student and will be based on the theory of factor investing, which is one of the topics covered during the lectures. The student should adopt the role of a professional asset manager that is in charge of developing a new strategy for the firm. The final report will provide details of the empirical performance of this strategy and also a deep explanation of all relevant concepts that would help the CEO of the company to decide whether it is a good investment plan or not. The report must be clearly written in a professional way. In addition, the student must be able to relate the results from the project with the concepts covered in the stream. However, the student is not limited to the topics covered in the class. Interpretation of results is a relevant element of the report and the student should always provide an answer to questions such as “How did we obtain this?” and “Why did we obtain this?”.

Lecture Outline:

Part #1: Introduction to the Markowitz Paradigm

This section covers the foundations of quantitative portfolio selection. In particular, it introduces the concept of portfolio diversification, which is the cornerstone of modern portfolio theory.

• statistical review: expectation, variance, and covariance

• diversification

• mean-variance analysis: the efficient frontier

Reading:

• Markowitz, H.M. (1952). "Portfolio Selection". The Journal of Finance, pp. 77–91.

• Brandt, Michael W. (2010). “Portfolio choice problems”. Handbook of Financial Econometrics, Volume 1: Tools and Techniques, pp. 269-336.

Part #2: Alternative investment methods

In the classical mean-variance analysis, variance is considered the portfolio risk measure, however it is well accepted that this is not a representative proxy for risk. This section introduces more appropriate risk measures. In addition to this, this section considers the problem of constructing bond portfolios. A simple model to obtain optimal bond portfolios is included in this section.

• statistical review: quantiles

• Value-at-Risk

• optimal bond portfolios

Reading:

• Korn, Olaf and Koziol, Christian (2006). “Bond Portfolio Optimization: A Risk-Return Approach”, The Journal of Fixed Income, pp. 48-60.

• Dowd, Kevin (1999). “A Value at Risk Approach to Risk-Return Analysis”, The Journal of Portfolio Management, pp 60-67.

Part #3: Factor investing

Quantitative investment firms do not pick stocks. The quantitative investment industries make use of factor investing or, similarly, smart beta investing. This investment technique uses firm attributes in order to identify mispriced firms or sources for risk premia. In this section, we will learn how we can use factor investing techniques to construct portfolios.

Reading:

• Smart beta guide, by Andre Ang (2015). BlackRock smart beta book.

Part #4: Practical problems with optimal portfolios

This last section covers the practical matters of portfolio selection. In particular, this section focuses on two main practical problems: parameter uncertainty and trading costs. Moreover, this section sheds light on the practical implementation of portfolio problems in Excel.

- Are optimal portfolios really optimal? – Parameter uncertainty

- Rebalancing: When should we revise our portfolio?

- Excel implementation

Reading

• DeMiguel, V.; Garlappi, L.; and Uppal, R. (2009) . “Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?”. The Review of Financial Studies, pp. 1915—195.

• Guofu Zhou (2008) “On the Fundamental Law of Active Portfolio Management: What Happens If Our Estimates Are Wrong?” The Journal of Portfolio Management, pp. 26-33

• Ledoit, O. and Wolf, M. (2004). “Honey, I shrunk the sample covariance matrix”. Journal of Portfolio Management 30, Volume 4, 110-119.

Some other interesting reading material (however unnecessary for the course) are listed below:

• Somerset, Merryn (2014). “Messy portfolios and the ‘be busy’ syndrome”, Financial Times.

• Temperton, Paul (2012). “Building castles and portfolios on the beach” , Financial Times.

• Temperton, Paul (2007). “Trading with the help of 'guerrillas' and 'snipers”, Financial Times.

• Temperton, Paul (2007). “A straightforward approach to asset allocation”, Financial Time.

• Book: “The Quants How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It”, by Scott Patterson, Random House Business Books 2010.

• Book: “Flashboys: Cracking the Money Code”, by Michael Lewis, Allen Lane 2014.

• Book: “The Big Short: Insider the Doomsday Machine”, by Michael Lewis, W. W. Norton & Company, 2010.

• Ang, Andrew, Factor Investing (June 10, 2013). Columbia Business School Research Paper No. 13-42. Available at SSRN