FE630 Portfolio Theory and Applications
Course Catalog Description
Yangyang Yu - Teaching Assistant
This course will be taught in a hybrid manner including lectures and Socratic method discussions. Each week, there will be assigned readings. Students must do the read- ings before class. I will call on on-campus students frequently to explain concepts from the readings. Students’ answers will count toward their grade. Web-campus students who cannot attend classes in real-time will be given small written assign- ments in lieu of in-class answers. There will be also a number of quizzes that may be taken in class during lecture or remotely.
After successful completion of this course, students will be able to
- Compute Absolute Risk Aversion (ARA), Certainty Equivalent of Risky (CER) of risky gamble and Risk-premiums;
- Solve Optimal Decision Problems arising in Modern Portfolio Theory and im- plement the solution using a high level language such as R, Matlab or Python;
- Design Markowitz efficient portfolios and use the One-fund Theorem and the Two-fund theorem to build efficient Portfolios with Target Return or Target Risk;
- Use CAPM, APT and Factor Model to compute security Expected Returns and Risk and Covariance;
- Apply Markowitz Allocation to design, implement and backtest Optimal Port- folios using historical price time series, analyze the sensitivity to various inputs, and manage Fixed Income portfolios.
The following books are recommended, but not required:
- Francis and Kim, Modern Portfolio Theory, Wiley, 2013. ISBN: 111837052X.
- Grinold and Kahn, Active Portfolio Management, 2e, McGraw Hill, 1999. ISBN:0070248826.
- Hubert, Essential mathematics for Market Risk Management, 2e, Wiley, 2012. ISBN 9781119979524
- Prigent, Portfolio Optimization and Performance Analysis, Chapman & Hall/CRC Financial Mathematics Series, , ISBN 1-58488-578-5
- Other Readings: Journal Papers or any material of interest, as needed.
Grades will be based on a combination of quizzes, exams, homework, a project, attendance, and participation.
- Quizzes:There will be between four to five short multiple choice quizzes (10 to 15 minutes) to test the depth of understanding of the concepts and the reading assignments.
- Exams: There will be a mid-term individual project and final project (indi- vidual or group project).
- Homework: There will be four to six homework assignments in which stu- dents will do theoretical analysis and write programs for portfolio management in both Matlab, R or Python. Homework will be submitted via Canvas and will consist in a PDF file and computer code. There will be written homework assignments in which students will be tested on both the theory and the ap- plication and will have to write programs for portfolio management in both Matlab, R or Python.
- Project: There will be 2 projects. An individual midterm project and a group final project. The final project has extensive requirements in coding, portfolio reporting and writing of the final report. A special introduction to the detailed requirements and grading of the final project will be held in class (project components, e.g. project plan, drafts, group work, individual contribution, final presentation).
- Attendance and Participation: Attendance is mandatory. The class will be interactive. Students are required to participate and answer questions on the reading assignments.
Weights: The final weighting will be approximately:
Final Exam or Project (35%)
Attendance and Participation (5%)
|Weeks 1 & 2
Orientation & One period Utility
|Course Introduction, Course Overview. Student Intro- duction and Initial Assessment. First Motivating Exam- ples. One-Period Utility Analysis. Absolute and Rela- tive Risk Aversion, Certainty Equivalent and Risk Pre- mium.|
| Weeks 3 & 4
Computational Tools, Algebra & Optimization Review
|Portfolio expected return and risk. Portfolio weights. Attainable regions of risk-return space. Risk reduction and diversification. Review of algebra for Portfolio and matrix calculus. Basics of nonlinear optimization and Convex Constrained Optimization. Equality and In- equality Constraints. KKT conditions and closed-form solution to Markowitz Allocation.|
| Weeks 5, 6 & 7
Mean-Variance Efficient Frontier CAPM, APT and Factor Models
|Mean-variance Frontier Portfolios. The Markowitz Effi- cient Frontiers with and without Risk-free security. One and two-fund theorems. Market Price of Risk and Secu- rity Market Line, CAPM, APT, Single index and Multi- Index models. Pricing and Arbitrage opportunities.|
|Week 8||Mid-semester Review and Midterm Project.|
| Week 9
Sensitivity to Inputs & Robust Allocation
|Models of uncertainties of Expected Returns and Risk Matrices. Worst Case Optimization. Matrix Calibra- tion. Black-Litterman Allocation..|
| Weeks 10 & 11
Portfolio Characteristics Active and Bond Portfolios
|Portfolio Characteristics, Active Portfolios, Perfor- mance attribution. Asset Versus Risk Allocation. Ac- tive and Passive Bond portfolio management. Portfolio construction to mitigate interest rate risk sensitivity.|
| Week 12
Overture to Dynamic Allocation
|Dynamic Portfolio Allocation & Risk Sensitive Asset Al- location|
| Week 13 & 14
|Final review, Course evaluation and presentation of Fi- nal Projects|