by Salil Mehta, Statistical Ideas
This treemap graphs the volatility, per year. Ā We normally think of market volatility in single linear dimensions, such as standard deviations. Ā But here we map it into 2-dimensional boxes, with all the boxes then chronologically assembled to fit into a larger 100% view. Ā Given our triumphs in TARP and central bank easing it is no surprise that volatility has tamped down. Ā 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 becomeĀ 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%). Ā 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 1/2Ā of these occurrences occurred in the year through June 2009 (so more than 6 years ago). Ā 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 ~3/4Ā of these occurrences happened in just the past 2 years. Ā 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%. Ā 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%). Ā The past year inĀ yellowĀ is also the same size as it is in the top-most chart above, showing howĀ low volatility is recently.
Incidentally, the IQR frequency distribution is quite similar to the severity distribution shown immediately above. Ā 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). Ā 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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