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AMS 511 - Foundations of Quantitative Finance

Fall 2010


   

Prof. Robert J. Frey (Instructor)

frey@ams.sunysb.edu

http://www.ams.sunysb.edu/~frey

   

Lecture:

    Monday, 5:30 PM - 8:30 PM

    Physics P-118

   


   

Ms. Xiaochu Zhang (Teaching Assistant)

xczhang@ams.sunysb.edu

   

Recitation:

    Contact directly for information

   

   


Notes:

  

  

  • 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.

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Course Overview

 

Introduction to capital markets and modern portfolio theory, including the organization and operation of securities markets, the Efficient Market Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing Theory and more general factor models. Common stocks and their valuation, statistical analysis, and portfolio selection in a single-period, mean-variance context will be explored along with its solution as a quadratic program. Fixed income securities and their valuation, statistical analysis, and portfolio selection. Discussion of the development and use of financial derivatives. Whenever practical examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned.Ę Prerequisites: AMSĘ505 or AMSĘ510, and AMSĘ507. 3 credits.

    

Required texts and software (required):
  

  • Luenberger, David G., Investment Science, Academic Press, 1997.

    

  • Access to Mathematica, Version 7 . Low cost versions of Mathematica are available for $5 at the Seawolves Marketplace in the SAC. Mathematica is also available on machines in the Math/Physics SINC Site. A Mathematica tutorial can be found here.

    

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

The following texts provides useful background. They are not required texts:
   

  • Sharpe, William F., Gordon Alexander & Jeffrey Baily, Investments (6th Edition), Prentice-Hall, 1998.

   

  • Don, Eugene, Schaum's Outline of Theory and Problems of  Mathematica, McGraw-Hill, 2001.

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Course Objectives

 

Financial resources must be managed in the face of uncertain investmemt performance and future consumption. The risk and reward of available investments must be modeled and estimated. These insights must then be translated into a set of specific investment decisions. All of this must be done in the context of the objectives and constraints imposed by both the organization and the larger legal and economic environment it finds itself in.

    

We will cover almost all of Luenberger's text. This will cover the basics of financial instruments and markets and address the issues involved in allocating financial resources in the face of an uncertain future. To introduce the student to Mathematica we will also cover selected material in Don's text.

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General Teaching Approach and Course Policies

   

The lectures will develop the mathematical foundations required for successful completion of the course. We will also introduce many economic concepts and practical applications through examples worked out during class. Homework assignments and workshops, however, play a key role.

 

Homework Assignments and Workshops

    

Homework assignments and workshops 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 two workshop assignments that they will have two to three weeks to complete.

All assignments must be submitted by email. Homework assignments are submitted to the course grader, Xiaochu Zhang, at xczhang@ams.sunysb.edu. Workshops are submitted to the course instructor, Robert J. Frey, at frey@ams.sunysb.edu. The subject line of the email must begin with AMS-511 and your student ID number followed by a brief description of the submission, e.g.,

   

AMS-511 123456789 Homework 03

    

Examinations

    

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 he or she desires for use during the test; however, this sheet must be generated by the student him- or herself. Students may use calculators during the examinations.

   

Grading

    

Homework assignments will be graded Pass-Fail and the workshops and examinations will be graded A-B-C-F. The contribution of each to the final grade is as follows:

   

  • Homework Assignments -- 10%

   

  • Midterm Workshop -- 10%

   

  • Final Workshop -- 30%

   

  • Midterm Examination -- 20%

   

  • Final Examination -- 30%

   

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

   

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.

 

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.

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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. The letter "I" is used to indicate Investment Science, and students must read the chapters indicated for each week before coming to class. The letter "S" refers to Schaum's Outline, and these readings are suggested.

    

Under the "Documents" heading links for any "Notes" and "Exercises" will be updated before each class. Links for "Solutions" of assignments and examinations will be updated after their respective due dates.

    

The "Notes" below are supplementary material and exercises 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.

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Week - Class
Documents
Coverage
Assignments & Comments
Content

01

30 Aug 2010

Notes

Solutions

I: 1 - 3

S: 1, 2

I: 2 (1, 3, 8)

I: 3 (3, 10, 15)

Theory of Interest and Fixed Income Securities; Mathematica.

02

06 Sep 2010

      Labor Day - No Classes

03

13 Sep 2010

Notes

Solutions

I: 4-5

S: 3-7, 12

I: 4 (2, 6, 14)

I: 5 (2, 4, 12)

Term Structure of Interest; Interest Rate Analysis; Mathematica

04

20 Sep 2010

Notes

Solutions

I: 6, 7

S: 8-10

I : 6 (2, 4, 8)

I: 7 (2, 6)

Portfolio Theory; Capital Asset Pricing Model; Mathematica

05

27 Sep 2010

     

Class Canceled

06

04 Oct 2010

Notes

Solutions

I: 8 I: 8 (2, 6, 8)

Mean-Variance Portfolios

Factor Models - Theory & Estimation

07

11 Oct 2010

Notes

Workshop 1

 

Midterm Review Session

Workshop 1 Assigned

Chapters 1 to 8 + Basic Mathematica forms

08

18 Oct 2010

   

Midterm

Chapters 1 to 8 + Basic Mathematica forms

09

25 Oct 2010

I: 9

I: 9 (2, 6, 10, 14)

Utility Theory & Applications

10

01 Nov 2010

  I: 10

I: 10 (6, 8, 10)

Workshop 1 Due

Forwards, Futures & Swaps

11

08 Nov 2010

  I: 11 I: 11 (4, 6, 10) Asset Dynamics

12

15 Nov 2010

  I: 12

I: 12 (4, 10)

Workshop 2 Assigned

Options Theory

13

22 Nov 2010

  I: 13

I: 13 (4. 6)

Black-Scholes

14

29 Nov 2010

I: 13

 

Option "Greeks" & Implied Volatility

15

06 Dec 2010

I: 15

I: 15 (2, 6)

Workshop 2 Due

Optimal Portfolio Growth

Final

Dec 2010

    Final

TBA