Course Syllabus
MAFS5310 - Portfolio Optimization with R
MSc in Financial Mathematics
Fall 2022-23, 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
- 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 Links to an external site.]
- 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 attendance or Zoom video on) |
Weekly portfolio game (in R): | 40% | |
Final lightening presentation: | 25% |
Course Schedule
Date | Week | Lect | Topic |
---|---|---|---|
6-Sep | 1 | 1 | Theory: Introduction to convex optimization |
2 | Practice: R for finance primer | ||
13-Sep | 2 | 3 | Theory: Convex optimization problems |
4 | Practice: Solvers in R | ||
20-Sep | 3 | 5 | Portfolio optimization |
6 | (cont’d) | ||
27-Sep | 4 | 7 | Backtesting portfolios |
8 | Data cleaning | ||
7-Oct (Fri) Venue: LTE | 5 | 9 | High-order portfolios |
10 | Shrinkage estimators | ||
18-Oct | 6 | 11 | Robust estimators under heavy tails and outliers |
12 | (cont’d) | ||
25-Oct | 7 | 13 | Robust portfolio optimization |
14 | (cont’d) | ||
1-Nov | 8 | 15 | Portfolio optimization with alternative risk measures |
16 | (cont’d) | ||
8-Nov | 9 | 17 | Risk parity portfolio |
18 | (cont’d) | ||
15-Nov | 10 | 19 | Index tracking of financial markets |
20 | (cont’d) | ||
22-Nov | 11 | 21 | Time series modeling of financial data |
22 | (cont’d) | ||
29-Nov | 12 | 23 | Pairs trading |
24 | (cont’d) | ||
6-Dec | 13 | Project presentations by students |
Lecture Information
Lecture Time: Tue 19:30 – 22:20
Lecture Venue: LTG
Teaching Team
Instructor: Prof. Daniel P. PALOMAR (https://www.danielppalomar.com Links to an external site.)
Email: palomar@ust.hk
Office: 2398 (Lifts 17/18)
Office hours: By email appointment
TAs: Vinicius Cardoso (jvdmc@connect.ust.hk) and Rui ZHOU (rzhouae@connect.ust.hk)
Course Summary:
Date | Details | Due |
---|---|---|
Tue Sep 13, 2022 | Assignment Homework #0 | due by 6pm |
Sun Sep 25, 2022 | Assignment Portfolio Game Round #1 | due by 1pm |
Sun Oct 2, 2022 | Assignment Portfolio Game Round #2 | due by 1pm |
Tue Oct 4, 2022 | Assignment Homework #1 | due by 6pm |
Sun Oct 16, 2022 | Assignment Portfolio Game Round #3 | due by 1pm |
Sun Oct 23, 2022 | Assignment Portfolio Game Round #4 | due by 1pm |
Sun Oct 30, 2022 | Assignment Portfolio Game Round #5 | due by 1pm |
Sun Nov 6, 2022 | Assignment Portfolio Game Round #6 | due by 1pm |
Thu Nov 10, 2022 | Assignment Homework #2 | due by 6pm |
Sun Nov 13, 2022 | Assignment Portfolio Game Round #7 | due by 1pm |
Mon Dec 5, 2022 | Assignment Lightning Final Project Presentations | due by 11:59pm |