37008 Quantitative Portfolio Analysis
Warning: The information on this page is indicative. The subject outline for a
particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2025 is available in the Archives.
Credit points: 8 cp
Subject level:
Postgraduate
Result type: Grade and marksRequisite(s): 24 credit points of completed study in spk(s): STM91543 Core Subjects (Mathematics)
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 25876 Quantitative Portfolio Analysis
Description
This subject equips students with a rigorous understanding of portfolio analysis through quantitative tools. It covers a comprehensive mathematical treatment of the Markowitz framework for portfolio optimisation, the index-tracking problem, Arbitrage Pricing Theory (APT) and factor models for asset pricing, portfolio performance measurement, portfolio risk measures, and capital allocation. The subject also tackles a continuous-time portfolio optimisation problem (the Merton problem) via a stochastic optimal control approach. The theoretical discussion of concepts is complemented by practical problems involving statistical estimation and computational implementation.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Apply the Markowitz portfolio optimization framework and the Capital Asset Pricing Model (CAPM) to analyze portfolio risk-return profiles |
|---|---|
| 2. | Explain the Arbitrage Pricing Theory and its implications on the construction of equity portfolios |
| 3. | Estimate and apply factor models to construct equity portfolios |
| 4. | Critically compare equity portfolios in terms of quantitative portfolio performance and risk measures |
| 5. | Formulate and resolve Merton’s optimal portfolio problem using continuous-time stochastic models |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Appraise advanced knowledge and critically evaluate the information's source and relevance, with a focus on applications of mathematical methodologies to quantitative finance problem solving. (1.1)
- Practice professionally adhering to confidentiality requirements, ethical conduct, data management, and organisation and collaborative skills in the context of applying mathematical and statistical modelling to quantitative finance problems. (3.1)
- Develop and present complex ideas and justifications using appropriate communication approaches from a variety of methods (oral, written, visual) to communicate with mathematicians, data analysts, scientists, industry, and the general public. (5.1)
Contribution to the development of graduate attributes
This subject provides students a solid foundation in modern portfolio theory and its extensions. As such, it provides a detailed exposition of the classical Markowitz portfolio optimization framework, the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory, factor models, and empirical methods for portfolio construction, performance measurement, and risk management. The disciplinary knowledge acquired in this subject contributes to the students’ toolkit as a quantitative finance practitioner. Furthermore, students are provided opportunities to apply and implement portfolio construction and optimization techniques using financial data and communicate their findings and insights through written and/or oral reports.
This subject contributes to the development of the following graduate attributes:
GA 1. Disciplinary Knowledge – acquire detailed and specialized quantitative finance knowledge and professional competency required to work as a quantitative finance professional in the modern finance industry.
GA3. Professional, Ethical, and Social Responsibility – develop an enhanced capacity to work ethically and professionally using collaborative skills in the workplace.
GA5. Communication – develop professional communication skills for a range of technical and non-technical audiences.
Teaching and learning strategies
The subject is presented in a seminar format, complemented by online subject materials. The theoretical concepts are presented in lectures and are supplemented by on-campus seminar sessions in which the students’ conceptual understanding is reinforced by hands-on exercises. During the seminars, students can work collaboratively and receive feedback on their solutions. The teaching and learning strategies in this subject enable students to experience a seamless integration of online and face-to-face learning.
Relevant and challenging problem sets will also be provided for each topic and students are required to solve these during the on campus seminars. The problems sets will prepare students for the successful completion of the subject assessment tasks and will encourage critical thinking and innovation.
Students will receive verbal feedback on their work during the seminars. Students will receive summative feedback through marked assessment activities.
Content (topics)
The subject tackles and investigates quantitative methods in modern portfolio theory, continuous-time portfolio optimization, portfolio risk measurement, and capital allocation. Emphasis will be placed on the mathematical foundations of these portfolio analysis frameworks and on the implementation of basic quantitative portfolio analyses using software.
- Markowitz’s mean-variance portfolio optimization framework
- Non-mean-variance portfolio analysis
- Index tracking
- Arbitrage Pricing Theory and factor models
- Performance and diversification indicators
- Portfolio risk measures and capital allocation
- Continuous-time portfolio optimization (the Merton Problem)
Assessment
Assessment task 1: In-Class Test
| Intent: | This assessment task contributes to the development of the following graduate attributes: |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 10% |
| Criteria: | Disciplinary knowledge is demonstrated by the accuracy of the solutions to the applied problems and the mastery of the mathematical and quantitative methods used to address the applied problems. |
Assessment task 2: Project
| Intent: | This assessment task contributes to the development of the following graduate attributes: |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 3.1 and 5.1 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 45% |
| Criteria: | Disciplinary knowledge is demonstrated by the accuracy of the solutions to the applied problems and the mastery of the mathematical and quantitative methods used to address the applied problems. |
Assessment task 3: Final Examination
| Intent: | This assessment task contributes to the development of the following graduate attributes: |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 3.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 45% |
| Criteria: | Disciplinary knowledge is demonstrated by the accuracy of the solutions to the applied problems and the mastery of the mathematical and quantitative methods used to address the applied problems. |
Minimum requirements
Students must achieve at least 50% of the subject’s total marks to pass the subject.
Required texts
There are no required texts for this subject. Lecture notes and other materials shall be made available on the subject Canvas site.
Recommended texts
Rogers, L. C. G. (2013). Optimal Investment. Springer.
Brugiere, P. (2020). Quantitative Portfolio Management: With Applications in Python. Springer.