Introduction

This course introduces the modern portfolio theory and optimal portfolio selection using optimization techniques such as linear programming. Topics include contingent investment decisions, deferral options, combination options and mergers and acquisitions. The course then focuses on financial risk management with emphasis on Value-at-Risk (VAR) methods using general and parametric distributions and VAR as a risk measure. Real world scenarios are studied.

Pre-requisite:

Background in Algebra, Optimization, Stochastic Calculus. Most of what we will need in Algebra and Optimization will be covered. It is assumed that you are comfortable with the material presented in FE 543 or FE610 (Stochastic Calculus for Financial Engineering) and FE620 (Pricing and Hedging).

Students must have some familiarity with Matlab and R, (and / or Python). These languages will be used extensively and interchangeably in the course.

Course Description

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.

Course Outcomes

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.

Textbook

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.

Grading Policies

Grades will be based on a combination of quizzes, exams, homework, a project, attendance, and participation.

1. 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.
2. Exams: There will be a mid-term individual project and final project (indi- vidual or group project).
3. 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.
4. 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).
5. 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:

Quizzes (5%)

Homeworks (20%)

Midterm (25%)

Final Exam or Project (35%)

Attendance and Participation (5%)