by Salil Mehta, Statistical Ideas
This treemap graphs the volatility, per year. We normally think of market volatility in single linear dimensions, such as standard deviations. But here we map it into 2-dimensional boxes, with all the boxes then chronologically assembled to fit into a larger 100% view. Given our triumphs in TARP and central bank easing it is no surprise that volatility has tamped down. As we'd see with any probability and statistics inquiry, descriptive visuals offer another way to discern how low volatility has been this year, and how it's become equally so in the past 3 years.
For example, in the yellow rectangle below we see that roughly 10% of all volatility in the past 7 years, was just in the past 1 year (an equal spread of 1/7 would equal 14%). In fact, nearly 29% of all the volatility in the past 7 years has happened somewhat uniformly in the past 3 years.
If we now focus on just the high volatility periods (top quartile over the past 7 years is >24.7%), then we notice that nearly 1/2 of these occurrences occurred in the year through June 2009 (so more than 6 years ago). It's also noteworthy that -despite any "volatility" fears that come from the news at times- only a de minimis number of these occurrences happened in the past 3 years.
On the contrary, if we now focus on just the low volatility periods (bottom quartile is <14.7%), then we notice that a gargantuan ~3/4 of these occurrences happened in just the past 2 years. It's also noteworthy now that only a de minimis number of these occurrences happened in all of the 4 years through June 2012 (3 years ago).
Removing the top and bottom quartiles leaves us with the center 50% (or the interquartile range or IQR), embodying volatility of 14.7%-24.7%. If we explore the volatility distribution, then we notice that things get more stable only in the recent 3 years (though only taking 32% of the volatility when 3/7 is still 43%). The past year in yellow is also the same size as it is in the top-most chart above, showing how low volatility is recently.
Incidentally, the IQR frequency distribution is quite similar to the severity distribution shown immediately above. And as we can deduce from the graphic illustrations above, the past 3 years has a low 36% of the IQRs (again with the balance being low volatility periods). For reference, see these distribution tables below.
| 6/22/2009 | 6/22/2010 | 6/22/2011 | 6/22/2012 | 6/22/2013 | 6/22/2014 | 6/22/2015 | |
| Total severity | 26% | 16% | 13% | 16% | 10% | 9% | 10% |
| Top Q. frequency | 47% | 23% | 7% | 23% | 0% | 0% | 0% |
| Bottom Q. frequency | 0% | 0% | 0% | 0% | 25% | 40% | 35% |
| IQR severity | 6% | 19% | 26% | 18% | 14% | 7% | 10% |
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