### Rules for calculating (math) derivatives

Here’s a particularly useful list of rules for calculating (math) derivatives:

### Assignments for Thursday, January 19 in Finance 4366

As indicated on the http://fin4366.garven.com/readings page of the course website, the readings assigned for the second day of class (Thursday, January 19) include

1. Calculating (Math) Derivatives, by James R. Garven
2. Optimization (chapter 2 from Managerial Economics, by W. Bruce Allen, Neil Doherty, Keith Weigelt, and Edwin Mansfield, 6th edition (2005))
3. How long does it take to double (triple/quadruple/n-tuple) your money?, by James R. Garven

Pages 74-76 of the “Optimization” reading  (entitled “Lagrangian Multipliers”)  may be skipped without loss of continuity. The primary purpose of this reading is to re-acquaint students with basic calculus and how to use calculus to solve (unconstrained) optimization (i.e., maximization and minimization) problems. Since none of our work in Finance 4366 requires solving constrained optimization problems, there’s no need (in this course, anyway) for Lagrangian multipliers.

Besides reading these three articles in preparation for the second day of class, Finance 4366 students are also required to complete Quiz 1 on Canvas,  fill in the Student information survey, and sign up for a free WSJ student membership at https://wsj.com/ActivateBaylor.

### 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 17, we will also discuss a particularly important “real world” example of financial risk. Specifically, we will study the relationship between realized daily stock market returns (as measured by daily percentage changes in the SP500 stock market index) and changes in forward-looking investor expectations of stock market volatility (as indicated by daily percentage changes in the CBOE Volatility Index (VIX)):
As indicated by this graph (which also appears in the lecture note for the first day of class), daily percentage changes on closing prices for the SP500 (the y-axis variable) and for the VIX (the x-axis variable) are strongly negatively correlated with each other. The blue dots are based on 8,315 contemporaneous observations of daily returns for both variables, spanning the 33-year period of time starting on January 2, 1990 and ending on December 30, 2022. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = .00062 - .1147{R_{VIX}}$,

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 (-0.1147) indicates that on average, daily closing SP500 returns are inversely related to daily closing VIX returns.  Furthermore, nearly half of the variation in the stock market return during this time period (specifically, 48.87%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ came out to -0.70. While a correlation of -0.70 does not imply that daily closing values for ${R_{SP500}}$ and ${R_{VIX}}$ always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily values recorded for ${R_{SP500}}$ and ${R_{VIX}}$ during this period moved inversely 78.59% of the time.

### Calculus and Probability & Statistics recommendations…

Since many of the topics covered in Finance 4366 require a basic knowledge and comfort level with algebra, differential calculus, and probability & statistics, the second class meeting during the Spring 2023 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.

### Required Text Materials in Finance 4366

The required textbook for the Options, Futures, and Other Derivatives (Finance 4366) course at Baylor University (coincidentally) shares the same title as the course. Authored by University of Toronto finance professor John Hull, the “Options, Futures and Other Derivatives” textbook is quite expensive; indeed, the campus bookstore currently offers used copies for \$286.25, and new copies for \$381.50.

Although I list the 10th (US) edition as “required” for Finance 4366 in the course syllabus, earlier editions of this book; e.g., the 8th and 9th (US and international) editions will also suffice, since the chapters we cover in Finance 4366 are virtually identical across the 8th through 10th editions. Just make sure that the book author (John C. Hull) and title (Options, Futures, and Other Derivatives) are the same, that the edition of the book is no earlier than the 8th edition, and that you are buying the textbook and not the solutions manual or instructor’s manual.

Finally, don’t worry about whether the book you buy or rent includes the “Derivagem” software. Derivagem is an Excel spreadsheet template that you can download from the course website.

### 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 4366 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 4366 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 4366 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 4366.

### Course Requirement: Email subscription to the Options, Futures and Other Derivatives Course Blog (instructions given here)

A course blog has been established for Finance 4366 at the address http://derivatives.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 4366.

All students enrolled in Finance 4366 are required to subscribe to the course blog via email.

Email Subscription Instructions:

In order to subscribe to the course blog via email, go to derivatives.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 your screen:

Next, check for an email from “Options, Futures, and Other Derivatives <donotreply@wordpress.com>”:

Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:

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.