Course Syllabus
MAFS5310 – Portfolio Optimization with R
MSc in Financial Mathematics
Fall 2025-26, HKUST
Description
Modern portfolio theory started with Harry Markowitz’s 1952 seminal paper “Portfolio Selection,” for which he would later receive the Nobel prize in 1990. He put forth the idea that risk-adverse investors should optimize their portfolio based on a combination of two objectives: expected return and risk. Until today, that idea has remained central in portfolio optimization. However, the vanilla Markowitz portfolio formulation does not seem to behave as expected in practice and most practitioners tend to avoid it.
During the past half century, researchers and practitioners have reconsidered the Markowitz portfolio formulation and have proposed countless of improvements and variations, namely, robust optimization methods, alternative measures of risk (e.g., CVaR or ES), regularization via sparsity, improved estimators of the covariance matrix via random matrix theory, robust estimators for heavy tails, factor models, mean models, volatility clustering models, risk-parity formulations, etc.
This course will explore the Markowitz portfolio optimization in its many variations and extensions, with special emphasis on R programming. Each week will be devoted to a specific topic, during which the theory will be first presented, followed by an exposition of a practical implementation based on R programming.
Textbooks
- Daniel P. Palomar (2025). Portfolio Optimization: Theory and Application. Cambridge University Press. portfoliooptimizationbook.com
- Yiyong Feng and Daniel P. Palomar, A Signal Processing Perspective on Financial Engineering. Foundations and Trends® in Signal Processing, Now Publishers, 2016. [pdf]
- Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [pdf]
- G. Cornuejols and R. Tutuncu, Optimization Methods in Finance. Cambridge Univ. Press, 2007.
- F. J. Fabozzi, P. N. Kolm, D. A. Pachamanova, and S. M. Focardi, Robust Portfolio Optimization and Management. Wiley, 2007.
Prerequisites
Good knowledge of linear algebra and some programming knowledge in R (or similar). Willingness to spend countless of hours programming in R.
Grading
| Homework: | 25% | |
| Class participation: | 10% | (class participation) |
| Weekly portfolio game (in R): | 40% | |
| Final lightening presentation: | 25% |
Course Schedule
| Date | Week | Lect | Topic |
|---|---|---|---|
| 2-Sep | 1 | 1 | Theory: Introduction to convex optimization |
| 2 | Practice: R for finance primer | ||
| 9-Sep | 2 | 3 | Theory: Convex optimization problems |
| 4 | Practice: Solvers in R | ||
| 16-Sep | 3 | 5 | Portfolio optimization |
| 6 | (cont’d) | ||
| 23-Sep | 4 | 7 | Backtesting portfolios |
| 8 | Data cleaning | ||
| 30-Sep | 5 | 9 | Financial data - iid modeling (robust estimators, shrinkage, factor models, Black-Litterman) |
| 10 | (cont’d) | ||
| 14-Oct | 6 | 11 | High-order portfolios |
| 12 | Graph-based portfolios | ||
| 21-Oct | 7 | 13 | Portfolio optimization with alternative risk measures |
| 14 | (cont’d) | ||
| 28-Oct | 8 | 15 | Risk parity portfolios |
| 16 | (cont’d) | ||
| 4-Nov | 9 | 17 | Index tracking of financial markets |
| 18 | (cont’d) | ||
| 11-Nov | 10 | 19 | Robust portfolio optimization |
| 20 | (cont’d) | ||
| 18-Nov | 11 | 21 | Pairs trading |
| 22 | (cont’d) | ||
| 25-Nov | 12 | Project presentations by students |
Lecture Information
Lecture Time: Tue 7:30pm – 10:20pm
Lecture Venue: G010, CYT Bldg
Teaching Team
Instructor: Prof. Daniel P. PALOMAR (https://www.danielppalomar.com)
Email: palomar@ust.hk
Office: 2398 (Lifts 17/18)
Office hours: By email appointment
TAs: Xiwen WANG (xwangew@connect.ust.hk) and Rui ZHOU (rzhouae@connect.ust.hk)
Course Summary:
| Date | Details | Due |
|---|---|---|