Barron’s in Education 30-minute live event: How Student Loan Policy May Change Under A Biden Administration

This Wednesday, 1/27/21, at 11 AM CT: How Student Loan Policy May Change Under A Biden Administration. Join MarketWatch reporter Jillian Berman and Seth Frotman, Founder and Executive Director of the Student Borrower Protection Center for a discussion on the student loan market, the challenges borrowers are facing, and the policy changes we could see under the Biden administration. 

Click here to register for Barron’s Live.

Bullish Stock Bets Explode as Major Indexes Repeatedly Set Records

This is a fascinating WSJ  article about recent (historically unprecedented) trading volumes in options markets. The article features a 21-year-old student at Syracuse University named Ben Austin, who apparently “… primarily trades calls to position for big events that have the potential to lift stocks”, and attributes the following quote to Mr. Austin: “There’s way more potential for higher gains in a shorter amount of time.” While this is technically correct (after all, as we shall soon learn in Finance 4366, call options represent leveraged bets on stocks), there’s also way more potential for larger losses in a shorter amount of time, particularly since Mr. Austin is probably not hedging his options positions with positions in the stocks against which the call options are written.
wsj.com
“Options activity in January is building on 2020’s record volumes in the latest sign of optimism.”

On the ancient origin of the word “algorithm”

The January 26th assigned reading entitled “The New Religion of Risk Management” (by Peter Bernstein, March-April 1996 issue of Harvard Business Review) provides a succinct synopsis of the same author’s 1996 book entitled “Against the Gods: The Remarkable Story of Risk“. Here’s a fascinating quote from page 33 which explains the ancient origin of the word “algorithm”:

“The earliest known work in Arabic arithmetic was written by al­Khowarizmi, a mathematician who lived around 825, some four hun­dred years before Fibonacci. Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “al­Khowarizmi” fast. That’s where we get the word “algo­rithm,” which means rules for computing.”

Note: The book cover shown above is a copy of a 1633 oil-on-canvas painting by the Dutch Golden Age painter Rembrandt van Rijn.

Origin of the “Product Rule”, and Visualizing Taylor polynomial approximations

This blog entry provides a helpful follow-up for a couple of calculus-related topics that we covered during today’s Mathematics Tutorial.

  1. See page 12 of the above-referenced lecture note.  There, the equation for a parabola (y = {x^2}) appears, and the claim that \frac{{dy}}{{dx}} = 2x is corroborated by solving the following expression:
    In the 11-minute Khan Academy video at https://youtu.be/HEH_oKNLgUU, Sal Kahn takes on the solution of this problem in a very succinct and easy-to-comprehend fashion.
  2. In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn replicates the tail end of today’s Finance 4366 class meeting in which we approximated y = ex with a Taylor polynomial centered at x=0 (as also shown in pp. 18-23 of the Mathematics Tutorial lecture note).  Sal approximates y = ex with a Taylor polynomial centered at x=3 instead of x=0, but the same insight obtains in both cases, which is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.

How to know whether you are on track with Finance 4366 assignments

At any point in time this semester, you can make sure that you are on track with Finance 4366 assignments by monitoring due dates on Canvas and on the course website.  Links for future class meetings, quizzes, problem sets, and exams appear on the Canvas “To Do” list.  Links for readings (along with their due dates) appear on http://fin4366.garven.com/readings/, and links for problem sets (along with their due dates) appear on http://fin4366.garven.com/problem-sets/.  In the case of assigned readings, students are required to complete a short (10-minute) readings quiz prior to the start of class for each reading assignment due date; the window for completing this task begins at 10:30 a.m. CT the day before the reading assignment is due.

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 4366, 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}} = 0.0594 - 0.1126{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 4366!

Happy new year! My name is Dr. James R. Garven, and I am your professor for the Spring 2021 edition of the Finance 4366 (Options, Futures, and Other Derivatives) course. Here are a few things to keep in mind as we head into the beginning of the Spring 2021 semester:

1. Finance 4366 will meet on Tuesday and Thursday from 11 a.m. – 12:15 p.m. via Zoom (beginning on January 19).

2. The home page for the Finance 4366 course website is at http://fin4366.garven.com, and the course syllabus is available at http://fin4366.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 4366 Canvas home page).

3. The course blog is at http://derivatives.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 4366 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. Be sure to read “Required Text Materials in Finance 4366” at https://wp.me/paORhh-2c4 prior to making a textbook purchase, as the information provided there may save you some money!

6. Please complete the Finance 4366 Student Information Survey (at https://bit.ly/FIN4366survey) 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 4366)!

Sincerely,

Dr. Garven

How to obtain a Wall Street Journal subscription

A subscription to the Wall Street Journal is required for Finance 4366. 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 in class and on the course blog. Finance 4366 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 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 4366 but also in your other courses and careers: