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Notes:
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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.
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):
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.
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 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.
Examinations
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:
Positive trends in a student's performance will, however, receive due consideration.
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. 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. 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.
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.
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.
Documents
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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Lectures |
Notebooks & Files |
Content |
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1
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QuadraticProgramming.m |
Review of basic mean-variance
optimization and optimization software Review of univariate and multivariate distributions Techniques for modeling dependency structures |
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2
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ExPostVsExAnte.nb ExtremeEvents.nb UsingModels.nb OrganizingFiles.nb Assignment02.nb Solution02.nb mxSP500Index.m distSP500ST.m QuadraticProgramming.m |
Organizing
Files Modeling Extreme Events Power Law Models Value-at-Risk (VaR) and Expected Shortfall (CVaR) |
| 3 | GeneratingRandomPortfolios.nb RWRI_DD_Frey_202103.pdf HMMUG_20091222_05.nb PortfolioSelection.nb Assignment03.nb Solution03.nb mnLogRet.m QuadraticProgramming.m |
Generating Random Portfolios Alternative Portfolio Distributions Portfolio Selection (Using VaR and CVaR) Modeling Market Draw Downs |
| 4 | EstimatingFiniteNormalMixtures.nb FactorModels.nb EmMixtureFactorModels.pdf FactorFitMLE.m vsTickers.m vsNames.m buffer.m vmnDJIReturns.m |
The EM
Algorithm and Finite Mixtures Estimation of Parameters Structuring
Optimizations |
| 5 |
MeanCovarianceWithMissingData.nb MissingValuesAndDenoising.nb MeanCovMissingMLE.m dbReturns.m Solution05.nb |
Missing Value Imputation Correlation Denoising |
| 6 | PortfoliosOnMixtures.nb NeuralNetworks.nb SimpleAutoencoderSim.nb FactorFitMLE.m MeanCovMissingMLE.m QuadraticProgramming.m |
Optimization with Mixture
Portfolios Factor Models with Neural Networks |
| 7 | PortfoliosOnMixtures.nb CrossValidation.nb NonLinearFactor.nb Loess.wl mnTrain.m mnTest.m mnIBMReturn.m mnSP500Return.m Assignment07.nb Solution07.nb |
Portfolios on
Mixtures |
8 |
Regularization.nb COVID.nb NLP_SentimentAnalysis.nb ridgeDataIn.wl ridgeDataOut.wl ridgeDataTest.wl dsCovidWithAdminDivs.m dsCovidWoutAdminDivs.m |
Regularization Data Analysis Example: COVID Natural Language Processing: Sentiment Analysis |
| Workshop |
Workshop.nb MeanCoMissingMLE.m QuadraticProgramming.m WorkshopSuggestionsAndHints.nb WorkshopSolutions.nb WorkshopSolutionsExtended.nb |
Workshop |
| 9 |
ExtendedPortfolioOptimization.nb dbWorkshopReturns.wl |
Extended Optimization |
| 10 |
ExponentialSmoothing.nb Solution09Exten.nb dbWorkingReturns.wl Solution10.nb |
More Extended Optimization Variance Stabilization |
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| Final |
SampleFinalQuestionsSpring2023.nb AMS512_Final_Spring2023.nb |
Wednesday, May 17, 2023 from 11:15
AM to 01:45 PM.
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Lectures
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Notebooks & Files |
Content |
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