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

Besides going over the syllabus during the first day of class on Tuesday, January 9, 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 next Tuesday’s lecture note, 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 7,056 daily observations on these two variables, spanning the time period from January 2, 1990 through December 29, 2017. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = 0.00058 - 0.1187{R_{VIX}}$,

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 (-0.1187) 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, 49.2%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ comes out to -0.7014. While a correlation of -0.7014 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% of the time.

# 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 options, futures, and other derivatives 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.

# How to obtain a Spring 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 Spring 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 in class and on the course blog. 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:

# 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 (January 11) will include a mathematics tutorial, and the third and fourth class meetings (January 16-18) 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.