Rules for calculating (math) derivatives

Here’s a particularly useful list of rules for calculating (math) derivatives (taken from the “Optimization” reading assignment):

Computers and productivity: Evidence from laptop use in the college classroom

In the April 2017 issue of Economics of Education Review, an article entitled “Computers and productivity: Evidence from laptop use in the college classroom” provides convincing empirical evidence against allowing laptop use in the classroom (which is why laptops are generally not allowed in Finance 4335 – see the first bullet point under section 8.2 of the course syllabus). Anyway, here are the highlights from this article:

• Computer use in college classrooms is commonplace.
• We use a quasi-experimental design to identify the effects of laptop use in college classrooms.
• We find that computer use has a significant negative effect on student grades.
• The negative effects of computer use are concentrated among males and low performing students.

The 17 equations that changed the course of history (spoiler alert: we use 3 of these equations in Finance 4335!)

Equations (2), (3), and (7) play particularly important roles in Finance 4335!

From Ian Stewart’s book, these 17 math equations changed the course of human history.

How to know whether you are on track with Finance 4335 assignments

At any given point in time during the upcoming semester, you can ensure that you are on track with Finance 4335 assignments by monitoring due dates which are published on the course website. See http://fin4335.garven.com/readings/ for due dates pertaining to reading assignments, and http://fin4335.garven.com/problem-sets/ for due dates pertaining to problem sets. Also keep in mind that short quizzes will be administered in class on each of the dates indicated for required readings. As a case in point, since the required readings entitled “Optimization” and ” How long does it take to double (triple/quadruple/n-tuple) your money?” are listed for Thursday, August 23, this means that a quiz based upon these readings will be given in class on that day.

Important assignments due on the second class meeting of Finance 4335 (scheduled for Thursday, August 23) include: 1) filling out and emailing the student information form as a file attachment to risk@garven.com, 2) subscribing to the Wall Street Journal, and 3) subscribing to the course blog. A completed student information form is graded as a problem set and receives 100 points; if you fail to turn in a student information form, then you will receive a 0 for this “problem set”. Furthermore, tasks 2 and 3 listed above count toward your class participation grade in Finance 4335.

Regarding the student information form, I prefer that you complete this form (by either typing or writing) and email it to risk@garven.com prior to the beginning of class on Thursday.  However, if you prefer, you may turn in a hard copy instead at the beginning of class on Thursday.

Risk and Uncertainty – on the role of Ambiguity

This March 2017 WSJ article addresses how to measure uncertainty and also explains the subtle, yet important differences between risk and uncertainty. Risk reflects the “known unknowns,” or the uncertainties about which one can make probabilistic inferences. Ambiguity (AKA “Knightian” uncertainty; see https://en.wikipedia.org/wiki/Frank_Knight) reflects the “unknown unknowns,” where the probabilities themselves are a mystery.

A researcher whose work foreshadowed the VIX now has his eye on an entirely different barometer of market uncertainty—ambiguity.

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

Besides going over the course syllabus tomorrow, we will also discuss a “real world” example of financial risk. Specifically, we will look at the relationship between short-term stock market volatility (as indicated by the CBOE Volatility Index (VIX)) and returns (as indicated by the SP500 stock market index).

As indicated by this graph from page 25 of the lecture note for the first day of class, daily percentage changes on closing prices for VIX and the SP500 are strongly negatively correlated. In the graph above, the y-axis variable is the daily return on the SP500, whereas the x-axis variable is the daily return on the VIX. The blue points represent 7,215 daily observations on these two variables, spanning the time period from January 2, 1990 through August 17, 2018. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = 0.0587 - 0.1139{R_{VIX}}$,

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 (-0.1139) indicates that on average, daily VIX returns during this time period were inversely related to the 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, 48.4%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ comes out to -0.696. While a correlation of -0.696 does not imply that ${R_{SP500}}$ and ${R_{VIX}}$ will always move in opposite directions, it does indicate 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 78.3% 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.

The Finance Industry’s Incredible Ability to Keep the Money Rolling In

Quoting from this article (which appeared in last Saturday’s Wall Street Journal),

“From the era of railroads and the telegraph to that the internet and smartphones, the price charged by the finance industry to turn a dollar of savings into a dollar of investment has mostly remained between 1.5 cents and 2 cents for every dollar that passes through the finance industry.”

Instructions for subscribing to the Risk Management Course Blog

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. I recommend that you follow the risk management course blog regularly via email, RSS, Facebook, and/or Twitter.

The risk management course blog provides me with a convenient means for distributing important announcements to the 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 which we cover in Finance 4335.

If you already are familiar with RSS, this is a great way to subscribe to the options, futures, and other derivatives course blog. By going to the http://risk.garven.com/feed webpage, you can subscribe by using Firefox’s Live Bookmarks feature, Internet Explorer’s RSS feed subscription feature, or an RSS reader. If you are either a Facebook or Twitter user, everything that is posted on the options, futures, and other derivatives course blog is automatically posted to Facebook and “tweeted”, so you can also subscribe by “liking” the Finance 4335 Facebook page or by “following” @fin4335 on Twitter. Finally, you can also subscribe via email. The remainder of this blog entry explains how to subscribe to the risk management course blog via email.

Email Subscription Instructions:

Email Subscription Instructions: If you would like to receive the risk management course blog via email, you can do this by going to http://risk.garven.com and entering your email address in the form provided on the left 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> ”:

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. Also, you can opt to change your delivery preferences, or even cancel your subscription.

Calculus and Probability & Statistics recommendations…

Since many of the topics covered in Finance 4335 require a basic knowledge and comfort level with differential calculus and probability & statistics, the second class meeting (August 23) will include a mathematics tutorial, and the third and fourth class meetings (August 28-30) 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 which cover these topics (unless otherwise noted, all sections included in the links which follow are recommended):

Finally, if your algebra is a bit rusty, I would also recommend checking out the Khan Academy’s review of algebra.

How to obtain a Fall 2018 Wall Street Journal subscription

A subscription to the Wall Street Journal is required for Finance 4335. In order to subscribe to the Wall Street Journal (WSJ) for the Fall 2018 semester, go to http://r.wsj.net/j73NM. Your WSJ subscription includes access to print, online, tablet and mobile editions, and only costs \$1 for a 15 week subscription. At your option, you may choose to receive both the digital and paper versions of WSJ or only the WSJ digital version.

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: