# 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, August 22, 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 24 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 6,959 daily observations on these two variables, spanning the time period from January 2, 1990 through August 11, 2017. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = 0.0005 - 0.1198{R_{VIX}}$,

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 (-0.1318) 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, 49.5%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ comes out to -0.703. While a correlation of -0.703 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.

# Lessons of the Möbius Bagel

Quoting from this WSJ article, “Almost everything in our modern world depends on calculus in some way, from electricity and automation to the weather forecast and the construction of roads and bridges”. To this quote, I would also add, “and to modeling the evolution of asset prices and valuation of financial derivatives”…

Speculative math isn’t useless. Real-world applications often follow, though it may take some time.

# The 17 equations that changed the course of history (spoiler alert: we use 4 of these equations in Finance 4366!)

I especially like the fact that Ian Stewart includes the famous Black-Scholes equation (equation #17) on his list of the 17 equations that changed the course of history; Equations (2), (3), (7), and (17) play particularly important roles in Finance 4366!

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

# 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 4366 – 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 Stupidest Thing You Can Do With Your Money

I highly recommend this Freakonomics podcast (and transcript) about passive versus actively managed investment strategies. It provides historical context for the development of some of the most important ideas in finance (e.g., the efficient market hypothesis) and the implications of these ideas for investing in the long run. Along the way, you get to “virtually” meet with many of the best, brightest and most influential academic and professional finance thinkers who played important roles in shaping this history.

Prior to listening to this podcast, I was not aware of how a quip in a 1974 Journal of Portfolio Management article authored by the MIT economist Paul Samuelson inspired Vanguard founder Jack Bogle to launch the world’s first index fund in late 1975. Samuelson suggested that, “at the least, some large foundation should set up an in-house portfolio that tracks the S&P 500 Index — if only for the purpose of setting up a naive model against which their in-house gunslingers can measure their prowess.” (source: “Challenge to Judgment”, available from http://www.iijournals.com/doi/abs/10.3905/jpm.1974.408496).

It’s hard enough to save for a house, tuition, or retirement. So why are we willing to pay big fees for subpar investment returns? Enter the low-cost index fund.

# Talk Is Cheap: Automation Takes Aim at Financial Advisers—and Their Fees

From page 1 of today’s Wall Street Journal – how automation is increasingly (and in many cases, adversely) affecting the livelihoods of financial advisors.

Services that use algorithms to generate investment advice, deliver it online and charge low fees are pressuring the traditional advisory business. The shift has big implications for financial firms that count on advice as a source of stable profits, as well as for rivals trying to build new businesses at lower prices. It also could mean millions in annual savings for consumers and could expand the overall market for advice.

# Derek Zoolander, spherical cows, the Guardian, and econophysics

Wonderful explanation of the logical fallacy associated with dismissing theories based upon modeling assumptions that are not literally true… HT to Scott Cunningham.

In Zoolander, the titular character is presented with a model of a building.  He inspects the model and responds with anger and indignation:

Derek Zoolander: What is this? [smashes the model for the reading center] A center for ants?

Mugatu: What?

Derek Zoolander: How can we be expected to teach children to learn how to read… if they can’t even fit inside the building?

# Markets’ Steady Climb in 2017 Defies Historic Odds

This WSJ article provides helpful historical context concerning stock market volatility and performance.  The lowest daily VIX closing price ever recorded in its 27-1/2 year history was 9.31 on December 22, 1993 (followed by 9.48 the following day – December 23, 1993).   The closing price for VIX of 9.51 on July 14 is the third lowest close on record. The long-run average for VIX comes in at around 20, and the highest close ever recorded was 80.86 on November 20, 2008 (during the throes of the global financial crisis of 2008).

Three major stock-market benchmarks in the U.S., Europe and Asia have avoided pullbacks this year, commonly defined as 5% declines from recent highs.

# Small Companies Are Gone, but Should They be Forgotten?

Quoting from this article, “The number of stocks has halved over the past two decades, to less than 3,600 from nearly 7,400, with most of the declines coming among the smallest companies.” According to a March 2017 Journal of Financial Economics paper by Doidge, Karolyi and Stulz, the U.S. has “abnormally few listed firms” compared with other countries; this “U.S. listing gap” is apparently due to a decrease in new listings coupled with an increase in delistings over this period.

How much should you care about the decline in the number of publicly traded companies?