Lagrangian Multipliers

There is a section in the assigned “Optimization” reading due Thursday, January 21 on pp. 74-76 entitled “Lagrangian Multipliers” which (as noted in footnote 9 of that reading) may be skipped without loss of continuity. The primary purpose of this chapter is to re-acquaint students with basic calculus and how to use calculus to solve so-called optimization problems. Since the course only requires solving unconstrained optimization problems, there’s no need for Lagrangian multipliers.

Besides reading the articles entitled “Optimization” and “How long does it take to double (triple/quadruple/n-tuple) your money?” in preparation for this coming Thursday’s meeting of Finance 4335, make sure you have completed the student information survey, subscribed to the Wall Street Journal, and subscribed to the course blog (if you haven’t already done so).

On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)

Besides going over the course syllabus during the first day of class on Tuesday, January 19, we will also discuss a particularly important “real world” example of financial risk. Specifically, we will look at the relationship between stock market returns (as indicated by daily percentage changes in the SP500 stock market index) and stock market volatility (as indicated by daily percentage changes in the CBOE Volatility Index (VIX)):

As indicated by this graph from page 22 of the lecture note for the first day of class, daily percentage changes on closing prices for VIX (which is the x-axis variable) and the SP500 (which is the y-axis variable) are strongly negatively correlated. The blue points represent 7,712 daily observations on these two variables, spanning the time period from January 3, 1990, through August 10, 2020. When we fit a regression line through this scatter diagram, we obtain the following equation:

{R_{SP500}} = 0.0621 - 0.1156{R_{VIX}},

where {R_{SP500}} corresponds to the daily return on the SP500 index and {R_{VIX}} corresponds to the daily return on the VIX index. The slope of this line (-0.1156) indicates that on average, daily VIX returns during this time period were inversely related to the contemporaneous daily return on the SP500; i.e., when volatility, as measured by VIX, went down (up), then the stock market return as indicated by SP500 typically went up (down). Nearly half of the variation in the stock market return during this time period (specifically, 48.75%) can be statistically “explained” by changes in volatility, and the correlation between {R_{SP500}} and {R_{VIX}} comes out to -0.698. While a correlation of -0.698 does not imply that {R_{SP500}} and {R_{VIX}} always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily returns on {R_{SP500}} and {R_{VIX}} during this period moved inversely 78.62% of the time.

You can see how the relationship between the SP500 and VIX evolves prospectively by entering http://finance.yahoo.com/quotes/^GSPC,^VIX into your web browser’s address field.

Welcome to the Spring 2021 edition of Finance 4335!

Happy new year! My name is Dr. James R. Garven, and I am your professor for the Spring 2021 edition of the Risk Management course at Baylor University. Here are a few things to keep in mind as we head into the beginning of the Spring 2021 semester:

1. Finance 4335 will meet on Tuesdays and Thursdays from 2-3:15 p.m. via Zoom (beginning on January 19).

2. The home page for the Finance 4335 course website is at http://fin4335.garven.com, and the course syllabus is available at http://fin4335.garven.com/syllabus.pdf. Course-related documents (e.g., assigned readings, problem sets, sample exams, lecture notes, etc.) are distributed from the course website. (Important Note: the password for gaining access to password-protected page links is listed in item 3 on the Spring 2021 Finance 4335 Canvas home page).

3. The course blog is at http://risk.garven.com and linked from the “Course Blog” button on the home page of the course website. I use the course blog to post important announcements and provide insights linking course topics with the “real” world. I require that all students enrolled in Finance 4335 subscribe to the course blog via email; instructions for doing so are provided here.  Students may also follow the course blog on Facebook or Twitter but are not required to do so.

4. I use Canvas for scheduling class meetings, administering quizzes and exams, collecting problem sets, and posting grades.

5. The Baylor Bookstore lists the required textbook for Finance 4335 (Integrated Risk Management, by Neil A. Doherty) as out-of-stock. However, the book is available from Amazon (https://www.amazon.com/gp/product/0071358617), and assigned book chapters (in PDF format) are available from the course website (see http://fin4335.garven.com/textbook), so this is a manageable “problem”.

6. Please complete the Finance 4335 Student Information Survey (at https://bit.ly/FIN4335survey) prior to the first day of class on January 19 so I can read up on all of your names, academic backgrounds, interests, and aspirations (similar information about me is available at http://garven.com). I count the Finance 4335 Student Information Survey as a problem set which receives a grade of 100 (if successfully completed any time between now and the second day of class on January 21), and 0 otherwise.

In closing, I hope you have had a wonderful Christmas break and that you are looking forward to a happy and productive Spring 2021 semester at Baylor University (particularly in Finance 4335)!

Sincerely,

Dr. Garven

Calculus and Probability & Statistics recommendations…

Since many of the topics covered in Finance 4335 require a basic knowledge and comfort level with algebra, differential calculus, and probability & statistics, the second class meeting during the Spring 2021 semester will include a mathematics tutorial, and the third and fourth class meetings will cover probability & statistics. I know of no better online resource for brushing up on (or learning for the first time) these topics than the Khan Academy.

So here are my suggestions for Khan Academy videos that cover these topics (unless otherwise noted, all sections included in the links which follow are recommended):

Finally, if your algebra skills are generally a bit on the rusty side, I would also recommend checking out the Khan Academy’s review of algebra.

Course Requirement: Email subscription to the Risk Management Course Blog (instructions given here)

A course blog has been established for Finance 4335 at the address http://risk.garven.com; it is also linked from the “Course Blog” button located on the course website. This resource provides a convenient means for Dr. Garven to distribute important announcements outside of class. Topics covered on the course blog typically include things like changes in the course schedule, clarifications, and hints concerning problem sets, information about upcoming exams, announcements concerning extra credit opportunities, and short blurbs showing how current events relate to many of the topics covered in Finance 4335.

All students enrolled in Finance 4335 are required to subscribe to the course blog via email. Students may also follow the course blog on Facebook or Twitter but are not required to do so.

Email Subscription Instructions:

In order to subscribe to the course blog via email, go to http://risk.garven.com and enter your email address in the form provided on the right-hand side of that webpage:

After clicking “Subscribe”, the following information will appear on the screen:

Next, check for an email from “Risk Management Blog <donotreply@wordpress.com> ”:

Screen Shot 2016-06-16 at 7.15.43 PM
Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:

Screen Shot 2016-06-16 at 7.21.17 PM

From that point forward, whenever I post to the course blog, you will immediately receive a nicely formatted version of the blog posting via email.

How to obtain a Wall Street Journal subscription

A subscription to the Wall Street Journal is required for Finance 4335. For online access only, sign up for a “Student Digital Pack” at https://education.wsj.com/search-students. A Student & Digital Pack option (which provides daily home delivery in addition to online access) is available at https://r.wsj.com/PROFxypa.

Throughout the semester, I will often reference specific WSJ articles on the course blog and in class. Finance 4335 topics (as well as topics in many of your other business school courses) come to life in the world outside the Baylor bubble when you read make a habit of reading the WSJ on a regular basis. Furthermore, if you expect to interview for jobs or internships anytime soon, reading the WSJ will give you a leg up on the competition, since you will be better informed and have more compelling ideas and insights to share with recruiters.

In closing, the following (2 minute) video provides a helpful introduction to the WSJ, providing time-saving tips to help you get the most from WSJ and succeed not only in Finance 4335 but also your other courses and careers:

Important notice concerning Section III.C.16 of Baylor’s Honor Code Policy and Procedures document

According to Section III.C.16 of Baylor’s Honor Code Policy and Procedures, using, uploading, downloading, or purchasing any online resource that has been derived from material pertaining to a Baylor course without the written permission of the professor constitutes dishonorable conduct; i.e., an act of academic dishonesty.  Section IV.A. of the same document obligates faculty members who suspect that a student has engaged in dishonorable conduct of this sort to either handle the matter directly with the student or refer it to the Honor Council.

While you may use course-related documents that I distribute in class and on the course website for strictly personal academic purposes, anything other than your personal use of these documents is in violation of Section III.C.16 of Baylor’s Honor Code Policy and Procedures and therefore, expressly forbidden.  Examples include sharing course-related documents with students who are not enrolled in Finance 4335 and uploading such documents to so-called course-sharing websites such as Quizlet, Coursehero, and Chegg, etc.  Furthermore, the use of course-related documents (e.g., old problem sets and exams) from any other source other than me also represents an honor code violation.

I close by citing the “Academic Honesty and Integrity” section of the Finance 4335 course syllabus:

Plagiarism, or any form of cheating, involves a breach of student-teacher trust. This means that work on quizzes, problem sets, and exams submitted under your name is expected to be your own, neither composed by anyone else as a whole or in part, nor handed over to another person for complete or partial revision. Instances of plagiarism, or any other act of academic dishonesty, will be reported to the Honor Council and may result in failure of the course or expulsion from the University.

Baylor’s honor code and the Finance 4335 honor code are important resources for understanding various types of academic dishonesty, and I expect my students to be intimately familiar with both of these documents. The standards set forth in both of these honor codes will be applied to all of your work in Finance 4335.

Finance 4335 Honor Code – Based on Section III.C.16 of Baylor’s Honor Code Policy and Procedures

It has come to my attention that past problem set and exam solutions for Finance 4335 are available from one or more so-called “course sharing” websites.  These documents were uploaded to these sites without my knowledge or permission and as such, constitute copyright infringement and theft of intellectual property.

According to Section III.C.16 of Baylor’s Honor Code Policy and Procedures, “… using, uploading, downloading, or purchasing any online resource that has been derived from material pertaining to a Baylor course without the written permission of the professor” constitutes dishonorable conduct; i.e., an act of academic dishonesty.  Section IV.A. of this very same document obligates faculty members who suspect that a student has engaged in dishonorable conduct to either handle the matter directly with the student or refer it to the Honor Council.

While students are encouraged to use course-related documents that I distribute in class and on the course website for personal academic purposes, anything other than your personal use of these documents, (including sharing such documents with others who are not enrolled in Finance 4335 or uploading such documents to course-sharing websites) is in violation of Section III.C.16 of Baylor’s Honor Code Policy and Procedures and therefore, expressly forbidden. This policy also applies to the use of course-related documents from any source other than me.