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 4335 requires solving constrained optimization problems, there’s no need (in this course, anyway) for Lagrangian multipliers.
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:
where corresponds to the daily return on the SP500 index and 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 and came out to -0.70. While a correlation of -0.70 does not imply that daily closing values for and always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily values recorded for and during this period moved inversely 78.59% of the time.
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 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):
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.
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 entering your email address and clicking on the Subscribe button, go to your email inbox where you will see an email asking you to confirm your subscription:
Click on the Confirm now button, and then you will receive a confirmation email, and you’ll be good to go:
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.
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.