Category Archives: Finance

Fewer Listed Companies: Is That Good or Bad for Stock Markets?

 Today’s WSJ provides an interesting historical perspective of the cumulative effects of the dot-com bust, implementation of Sarbanes-Oxley, M&A activity, share buybacks, and growth of private equity on the number of listed shares in US stock markets during the course of the past couple of decades. Also see http://derivatives.garven.com/?p=6639 for an academic perspective of the so-called “U.S. listing gap”, which is apparently due to a decrease in new listings coupled with an increase in delistings over this period.
As the Dow Jones Industrial Average broke through 25000 and other stock market indexes continue rising to new highs, the number of publicly traded U.S. companies keeps shrinking.

Khan Academy “Finance and capital markets” videos

Not only are the Khan Academy Calculus and Statistics videos that I referenced in a previous posting quite useful; I am also a big fan of the Khan Academy “Finance and capital markets” videos which are located at https://www.khanacademy.org/economics-finance-domain/core-finance; these videos do a great job of effectively presenting many of the most important concepts which are typically covered in undergraduate and MBA level finance curricula (indeed, the content provided by the “Options, swaps, futures, MBSs, CDOs, and other derivatives” subsection of the “Finance and capital markets” page effectively subsumes most of the Finance 4366 course content!

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 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 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.

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.