AMS 512 -- Capital Markets & Portfolio Theory

Spring 2023 (COVID-19 On-Line Revision)


Prof. Robert J. Frey




Course Lecture:

     Monday, 02:40 PM - 05:20P PM

     via Zoom    


Office Hours:

    Please email for appointment.



Jason Bohne, Teaching Assistant


Office Hours:

    Wednesday, 09:00 AM - 11:00 AM
    Online via Zoom




  • Be sure to check the Announcements and Updates section on my home page for information about schedule changes, class cancellations, up coming seminars and events, and other important news.


On-Line Revision for COVID-19 Social Distancing 


This is the course page which represents the transition to on-line instruction in order to maintain the social distancing required to combat the spread of the COVID-19 coronavirus. Class lectures will be deliver theed via Zoom. Students are asked to familiarize themselves with this system, If you login into Stony Brook's Blackboard site you will be greeted with a prominent banner that will take you to instructions that will help you transition to on line delivery. You can also access https://it.stonybrook.edu directly for the same information.

Beginning with the Fall 2023 Semester, Brightspace has replaced Blackboard. Note that Brightspace and Zoom are separate systems with separate security features.
It is important that we must all give ourselves time to adjust to the new situation that we find ourselves in. If you are having any difficulties of any sort, please contact me. Now is the time for compassion, and my intent is to give students the flexibility needed to resolve any and all problems. However, I cannot help you or make allowances unless you communicate me. Email me, but if time is of the essence, text me with a callback number or directly call me. My personal mobile number is on my home page
One innovation is that class lectures will videoed by Zoom and will be made available to students for later review. We are all learning and as things develop I will keep you informed via email from Blackboard and by updating this page.

On This Page



Course Overview


Development of capital markets and portfolio theory in both discrete and continuous time and both single and multi-period settings. Techniques for the optimal trade-off of risk and reward under various metrics and assumptions. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment, Mathematica, will also be assigned. Prerequisite: AMS 511. 3 credits.


Texts and Software (required):

  • Class lectures will be covered by a set of modules covering the main topics of the course. The modules can be downloaded below and will be implemented as Mathematica notebooks. They will contain links to additional reading material.


  • Mathematica, Version 13 is used extensively for class notes and all assignments. A working knowledge of Mathematica is assumed from AMS 511, the immediate prerequisite for this course. A free student version of Mathematica can be downloaded by registered Stony Brook students via SoftWeb: http://it.stonybrook.edu/services/catalog/category/software. Mathematica is also available on machines in the Math/Physics SINC Site. Mathematica tutorials and similar resources can be found on Wolfram Research's web site here.


  • Students will need access to the Internet to be able to download exercises and data and submit certain assignments via email.


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Course Objectives


Effective portfolio management requires the analyst to understand the financial markets whose constituent instruments form the building blocks of investment portfolios. The portfolio analyst must be able first to formulate the problem in a form that can be subject to economic and mathematical analysis, second to develop an approach that solves the resulting problem through such techniques as nonlinear programming or Monte Carlo simulation, and third to estimate the parameters required based on both theoretical reasoning and empirical data analysis.


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General Teaching Approach and Course Policies


The schedule class lectures will develop the mathematical foundations required for successful completion of the course. Additional readings, available online, will also be assigned. Solutions to selected assignments will also be covered.


Homework Assignments and Class Project


Homework assignments and the class project will be used to further develop the material covered during class, including many important practical applications, and so will introduce important new content. Homework assignments are due the first class of the week after assignment. In addition to the weekly assignments, students will be assigned a class project that they will have two to four weeks to complete.

All assignments must be submitted by email. Homework assignments are submitted to the course grader, Zeyu Cao. Workshops are submitted to the course instructor, Robert J. Frey. The subject line of the email must begin with AMS-512 and your student ID number followed by a brief description of the submission, e.g.,


AMS-512 123456789 Homework 3


Please note that all emails to Prof. Frey must include "AMS-512" in the subject line. Prof. Frey receives a large number of emails daily, and failure to follow this protocol may cause your email to be deleted as spam or simply be missed among hundreds of others. Many problems will be avoided if all students follow this simple rule. Also, while the TA may make other arrangements, material submitted to Prof. Frey must be submitted via email and not via Blackboard, unless specific instructions to the contrary are given.


Also, on any files you attach to your email please ensure that the filename includes your student ID and for any Mathematica notebooks that your student ID also appears at the top of the file. This will ensure that each file clearly identifies which student's work it is and will avoid many problems as files are collected for review and grading.




There will be  a final examination. There will also be open book quizes taken on line. Right this will probably be done via Respondus, but the precise delivery method may change as we get more experience with the facilities available to us.



Quizes and homework assignments will be graded on a "Pass/Fail" basis and the project and examination will be graded on an "A-to-F" basis. I do not follow a strict grade distribution. If you are diligent and complete all homework and workshop assignments to receive full credit, then this will go a long way towards increasing your final grade.


The contribution of each to the final grade is as follows:


  • Quizes and Homework Assignments -- 20%


  • Class Project -- 40%


  • Final Examination -- 40%


Positive trends in a student's performance will, however, receive due consideration.


Effects of Other  Classes' Workloads


Students must expect that  and must manage their time to take this fact of life into account. It is simply not practical for the scheduled dates for assignments, projects or examinations in one class to be adjusted because they occur at times similar to those of another class.


Other Issues


Throughout our time together the sooner you inform me of any problem, personal or academic, which may affect your attendance or performance, the better the chance we have of solving it together. It is important that we work together to make each student as successful as possible in completing the class.

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University Policies and Procedures


Student Accessibility Support Center


If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748 or at sacs@stonybrook.edu.They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.


Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center.


Office of Diversity, Inclusion, Intercultural Initiatives


Stony Brook University is committed to a learning and working environment in which all members of our community can thrive. Maintaining an environment that is free from discrimination and sexual violence is a major part of that commitment.

To that end, the University is providing education and awareness training for all members of our community to help continue to foster the positive environment that is key to your success here at Stony Brook. More information about your rights and responsibilities can found at the Office of Diversity, Inclusion,and Intercultural Initiatives.


Emergency Management


Information on class closings due to weather and other emergency alerts can be found on the University's Emergency Management page which also contains a link so you can sign up for alerts.


Critical Incident Management


Stony Brook University expects students to respect the rights, privileges, and property of others. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Further information about most academic matters can be found in the Undergraduate and Graduate Bulletins, the Class Schedules, and the Faculty-Employee Handbook.


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Class Schedule & Assignments


The schedule planned for this semester is listed below; however, this schedule will be adjusted as needed throughout the semester if certain topics take up more or less time than planned. Students must read the chapters indicated under Coverage for each week before coming to class.

Lectures below correspond roughly to class meetings, although more than one lesson may be covered in a class or a lesson may span more than one class.



  • Notes - These are Mathematica notebooks covering the notes for that lecture. Every attempt will be made to link the class notes in advance of the class. The Notes cover the assigned readings but also include material and examples intended to amplify or extend the content presented in the textbook. They are not a substitute for studying the text or attending class.


  • Assignment - These are Mathematica notebooks containing assigned problems in addition to those assigned from the text under Coverage. Every attempt will be made to link the assignments in advance of the class. Assignments are due the next class.


  • Solution - The solutions of each class's assigments will be linked after the respective due date. These solutions are usually Mathematica notebooks.


  • Project - The project will be specified in a Mathematica notebook.


  • Project Solution - A sample solution of the project will be provided as a Mathematica notebooks.


  • Additional documents required such as tutorials, data needed for assignments, additional software and so forth will also be included as needed.


The supplementary materials and exercises below are intended to amplify or extend the content presented in the main text and classroom lectures. They are not a substitute for studying the notes or attending class. Many lectures will be completed in a single class meeting; however, some will take additional class meetings to complete.


Mathematica Styesheet Required


To properly use the notebooks below you will need to download a copy of my StonyBrook.nb stylesheet and install it on your system. Type in "install stylesheet" in the search box of Mathematica's Documentation Center (accessed under Help on the main menu) for detailed instructions on how to install a stylesheet on your system. Please see me if you have any problems, and I will help you with the installation.


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Notebooks & Files

Content & Comments





Assignment 01

Review of basic mean-variance optimization and optimization software
Review of univariate and multivariate distributions
Techniques for modeling dependency structures




Organizing Files
Thoughts on constructing and using models effectively
Ex Post (In Sample) vs. Ex Ante (Out of Sample)

Modeling Extreme Events

Power Law Models

Value-at-Risk (VaR) and Expected Shortfall (CVaR)

3 GeneratingRandomPortfolios.nb
Generating Random Portfolios
Alternative Portfolio Distributions
Portfolio Selection (Using VaR and CVaR)
Modeling Market Draw Downs
4 EstimatingFiniteNormalMixtures.nb

The EM Algorithm and Finite Mixtures
Factors Models: Structure and Estimation

Estimation of Parameters

Structuring Optimizations
Effects of Factor Heteroskedasticity

Missing Value Imputation
Correlation Denoising
6 PortfoliosOnMixtures.nb
Optimization with Mixture Portfolios
Factor Models with Neural Networks
7 PortfoliosOnMixtures.nb

Portfolios on Mixtures
Cross Validation
Non-Linear Factor Model
LOESS - local linear and quadratic fits


 Data Analysis Example: COVID
 Natural Language Processing: Sentiment Analysis
Extended Optimization
 More Extended Optimization
 Variance Stabilization


  Wednesday, May 17, 2023 from 11:15 AM to 01:45 PM.


Notebooks & Files

Content & Comments

Stony Brook