B2210 - PORTFOLIO THEORY

Learning outcomes

The course aims to give an in-depth overview of modern portfolio theory. At the end of the course, students are expected to know how to examine risk-return trade-off, portfolio optimization, index models and the implications of modern portfolio theory for the equilibrium structure of expected rates of return on risky assets; the capital asset pricing model, multifactor descriptions of risk, the arbitrage pricing theory, the efficient market hypothesis, and principles of behavioural finance.

Course contents

1. Expected utility, Risk aversion measures. The Canonical portfolio model and related theorems. Risk measures and Stochastic Dominance (First and Second Order).

2.The Mean Variance Model and the Capital Asset Pricing Model (CAPM). 

3.The mathematics of portfolio theory. Separation theorem. The case with and without risk free asset. The non-unicity of market portfolio. A four-moments CAPM. Extensions.

4. Factor Models and Arbitrage Pricing Theory (APT).

5. The Bayesian approach to Portfolio Theory: Priors, Posteriors. Flat, conjugates priors. Shrinkage estimator. The Jorion's portfolio model. The role of views: Theil's model. The Black and Littermann model and its variants. 

6. Pitfalls of the CAPM: the role of estimation bias in portfolio theory. Accurate portfolio allocation emerging as combination of complex portfolio rules. On the equivalence between Ambiguity and Bayesian approach in portfolio theory. 

7. Measuring performance of investments: the structure of an investment fund (costs, fees, Net Asset Value definition). The role of index as benchmarks. Performance attribution measures: Sharpe, Sortino, Modigliani and Modigliani, Treynor-Mazuy, Henriksson-Merton, Treynor. Pain indexes. 

8.Intertemporal portfolio theory. The recursive investment problem. The pricing kernel. Three puzzles: equity premium puzzle, volatility puzzle, risk-free puzzle. Solutions to Equity premium: Epstein-Zin utility function, Habit Formation model.

9. Heteroskedastic disturbances and equity premium. The model of Bansal and Yaron (2004). Investment in the long run: intertemporal vs. myopic portfolio theory. 

10. The Term Structure of Interest rates and fixed income pricing. The link between financial and real variables. The role of macroeconomic shocks in financial markets. 

10. (Tentative) A continuous time approach to portfolio theory. The Hamilton-Jacobi-Bellmann equation. Cox-Ingersoll-Ross model. 

The prerequisites are represented by basic knowledge of algebra and probability theory, multivariate calculus and linear algebra. All necessary analytical tools will be provided in lectures.

Readings/Bibliography

Danthine, J.P., and J. Donaldson, Intermediate financial theory, third edition, Elsevier, N.Y., 2014.

Campbell, J., Financial Decisions and Markets, Princeton University Press, 2018.

M.Marzo, Asset Management, Il Mulino, 2022 (in italian). 

Additional material (slides, problem sets, past exam) will be provided during lectures and it will be published on Virtuale

Teaching methods

In presence lectures 

Assessment methods

In class written exam. An optional oral exam is possible, after the written exam. It is possible to access oral exam only after passing the written exam. The oral exam can improve the grade of the written exam by no more than 4 points. In case of a bad oral exam the final grade can go further down the grade obtained in the written exam. 
The evaluation grid goes as follows: 

<18: failed. 

18-23: sufficient.

24-27: good.

28-30: very good.

30 with laude: excellent. 

The in class written exam will be two-hour long. 

Teaching tools

Slides. Papers from the literature. There will be an extensive use of specific software, like Matlab. Other software, like R and Python are possible. However, Matlab is more efficient and reliable. 

Office hours

See the website of Massimiliano Marzo