FE630 Portfolio Theory and Applications
Course Catalog Description
Introduction
Prerequisite:
Campus  Fall  Spring  Summer 

On Campus  X  X  
Web Campus  X  X  X 
Instructors
Professor  Office  

Papa Ndiaye

Papa.Ndiaye@stevens.edu  
Yangyang Yu  Teaching Assistant

yyu8@stevens.edu 
More Information
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 oncampus students frequently to explain concepts from the readings. Studentsâ€™ answers will count toward their grade. Webcampus students who cannot attend classes in realtime will be given small written assign ments in lieu of inclass 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 Riskpremiums;
 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 Onefund Theorem and the Twofund 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.
Course Resources
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 1584885785
 Other Readings: Journal Papers or any material of interest, as needed.
Grading
Grading Policies
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 midterm 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:
Quizzes (5%)
Homeworks (20%)
Midterm (25%)
Final Exam or Project (35%)
FAttendance and Participation (5%)
Lecture Outline
Topic  Reading  

Weeks 1 & 2 Orientation & One period Utility 
Course Introduction, Course Overview. Student Intro duction and Initial Assessment. First Motivating Exam ples. OnePeriod 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 riskreturn 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 closedform solution to Markowitz Allocation.  
Weeks 5, 6 & 7 MeanVariance Efficient Frontier CAPM, APT and Factor Models 
Meanvariance Frontier Portfolios. The Markowitz Effi cient Frontiers with and without Riskfree security. One and twofund theorems. Market Price of Risk and Secu rity Market Line, CAPM, APT, Single index and Multi Index models. Pricing and Arbitrage opportunities.  
Week 8  Midsemester 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. BlackLitterman 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 Finals 
Final review, Course evaluation and presentation of Fi nal Projects 