AMS 512 -- Capital Markets & Portfolio Theory

Spring 2017


Prof. Robert J. Frey


Course Lecture:

     Monday, 04:00PM - 05:40P PM,

     Frey Hall 301


Office Hours:

    Please email for appointment.



Teaching Assistant



Office Hours:




  • 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 This Page



Course Overview


Development of capital markets and portfolio theory in both continuous time and multi-period settings. Utility theory and its application to the determination of optimal consumption and investment policies. Asymptotic growth under conditions of uncertainty. Applications to problems in strategic asset allocation over finite horizons and to problems in public finance. 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):

  • Meucci, Attilio, Risk and Asset Allocation, 3rd Edition, Springer, 2007. This text will form the foundation for the overall organization and material covered in the course; however, this coverage will be amplified by additional material as noted below. It can purchased on most book websites and is also available as an e-book from Amazon (Kindle) or Apple (iBooks).



  • The readings in Risk and Asset Allocation will be amplified by readings in other free publicly available sources such as Wikipedia. The class notes made available for download in the syllabus below also contain a great deal of material which illustrate important examples and programming techniques, introduce additional models and economic theories, and cover many mathematical and statistical topics at a more advanced level.


  • Mathematica, Version 11 is used extensively for most class notes and 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: 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 homework and workshop assignments via email.


Top of Page

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 then be able:


  • First, to clearly understand the investor's needs so that risk and reward can be measured and balanced in an appropriate manner.


  • Second, to formulate the problem in a form that can be subject to economic and mathematical analysis.


  • Third, to estimate the parameters required based on both theoretical reasoning and empirical data analysis.


  • Fourth, to develop an approach that solves the resulting problem through the combination of nonlinear programming, Monte Carlo simulation, and allied techniques.


Top of Page

General Teaching Approach and Course Policies


The schedule class lectures will develop the foundations required for successful completion of the course. We will introduce many additional economic concepts and practical applications not covered in the textbook through examples worked out during class lectures, in assignments, or in additional assigned reading.


Additonal Lectures


Guest lectures may conduct certain classes to cover areas that deal with active research problems.


Homework Assignments and Workshops


Homework assignments and workshops will be used to 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 two workshop assignments 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, [TBD]. Workshops are submitted to the course instructor, Prof. Robert J. Frey, at 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 ensure that all email submissions include "AMS-512" in the subject line and are only submitted to the address. 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 email submissions please ensure that your student ID is included in the email's subject line and that any attached files contain your student ID in both the filename and at the top of the first page of the file itself. This will prevent any confusion as to which student has submitted a given file. Failure to follow these instructions may cause you not to receive credit for work submitted.




There will be two examinations, a mid-term and a final. For in-class examinations students will be able to bring in an 8.5" x 11" sheet of paper with whatever content her or she desires for use during the test; however, this sheet must be generated by the student him- or herself. Students may use calculators, but not laptops or other computers, during the examinations.




Homework assignments will be graded on a "Pass/Fail" basis (i.e., full or zero credit). Homework is part of the learning experience and we consider it unfair to penalize students at that stage. If you show reasonable effort in attempting to solve the problems and submit the homework on time, then you will receive full credit. The workshops and examinations 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, then this will go a long way towards increasing your final grade.


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


  • Homework assignments -- 10%


  • Mid-Term Workshop -- 10%


  • Final Workshop -- 30%


  • Mid-Term Examination -- 20%


  • Final Examination -- 30%


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


Effects of Other Classes' Workloads


It is natural that the mid-terms etc. of classes tend to occur at approximately the same time. Students must expect this and must manage their time to take this fact of life into account. It is simply not practical for the scheduled dates for assignments, workshops or examinations in one class to be adjusted because they occur at times similar to those of another class. You are responsible for managing your workload and planning accordingly.


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.


Americans with Disabilities Act (ADA) Notification


If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services. 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, Disability Support Services, and Environmental Health and Safety.


Office of Diversity and Affirmative Action


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 responsibilites can found at the Office of Diversity and Affirmative Action website.


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.


Top of Page

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 are encouraged to read the chapters indicated under Coverage for each week before coming to class. The Coverage column also contains the textbook question assigned each lecture. Additional questions will be assigned, however, as noted below.



  • Notes - These are Mathematica notebooks covering the notes for that class's 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.


  • Workshop - Each of the two workshops will be specified in a Mathematica notebook. Both workshops will require that you download actual financial data from the Internet. The due date for each workshop will be noted in the Content & Comments column and will be two to four weeks after assignment.


  • Workshop Solution - After each workshop due date has passed, a sample solution of the workshop will be linked. These solutions are usually 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 text or attending class. Neither is simply reading the text a substitute for class attendance: There will be material covered in the text that will not be covered in the lectures and visa versa. On occasion, the entire text of the lectures will not be covered in class, and students are expected to read this material on their own.


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.


Top of Page


Lectures often span

multiple classes



Content & Comments






Chap. 1 & 2

  • Overview of Course
  • Univariate Distributions and Statistics
  • Multivariate Distributions and Statistics
  • Security Invariants
  • Downloading Financial Data with Mathematica







Chap. 3
  • Geometry of Covariance
  • Factor Models
  • Robustness
  • Jackknife, Shrinkage, and Bootstrapping
  • Cross Validation






  • Mean-Variance Optimization
  • Quadratic Programming
  • Power Law Models
  • Value-at-Risk and Expected Shortfall



Notes (PDF)  
  • Combining Analytical Appraoches
    • Covariance-like Risk
    • Tail Modeling
  • Modeling Maximum Draw Downs (S&P Case Study)


Notes Chap. 4
  • More on VaR and CVaR Estimation
  • Mid-Term Examination Review


Notes & Workshop 1




Finite Mixture Tutorial

Missing Data Tutorial

  • Estimation of Mean and Covariance with Missing Data
  • Fitting Factor Models
  • Portfolio Optimization
  • Tutorials using the EM Algorithm
  • Workshop 1


  • Ex Post and Ex Ante Performance
  • Simulation Studies




  • Additional Results on Ex Ante Performance
  • Comprehensive Simulation Study.




Solution (02)

  • Shrinkage Estimators
  • Specialized QP Forms
  • Simulation Tests




Final Workshop


Hints and Sugestions    



Content & Comments