A lot has been made of the "idiosyncratic" behavior of U.S. markets recently. Some have bewailed that markets are quiet and volatility remains unnaturally constrained, and that markets are operating within too narrow a range. These same people have erroneously suggested that either Greece, or poor Q2 earnings, or a poor Automatic Data Processing (ADP) report, or China would create serious market fracas. But when we look at recent volatility changes, through pertinent prisms of marginal distributions and nonparametric measures of changes, we confirm that volatility is -in fact- on the lower side of things. What is also unmasked is that we have had near-term experiences where volatility can rapidly rise, at a speed on the higher side of what we would expect from history.
One popular way to think about changes in volatility is simply to discover how the recent change (X-axis, in percent) relates to the upcoming change (Y-axis, in %). See the chart below, where we cover the entire history of the VIX since early 1990 (~6,500 trading days).
As an example, we end the first half of this month on August 14, at a volatility level of 12.8, which is a -5% drop from the August 13 level of 13.5. Similarly, volatility on August 13 was a -1% drop from the August 12 level of 13.6. So we plot this data on the chart above, at -1% on the horizontal axis followed by 5% on the vertical axis. It already happens to be colored blue, a subset only of the past one month's worth of data (mid-July through mid-August) from the entire >25 year history. Incidentally, the blue numbers on the data marker reflect the number of days ago that data represents. We can note (and shown on the histogram below the plot) that the central 90% of the entire historical distribution is between -9%, and 10%. But for the past one month meanwhile, the range does eclipse both the high and low ends of that, or between -15%, and 13%.
We can now explore some new compelling perspectives, such as the absolute difference in the volatility level, instead of the percent change. The general pattern might look the same. Here we instead focus on the data associated with the bottom decile (in purple) and top decile (in red). See our associated deciles data in the Volatility in motion article (a Top 10 article on this blog).
So for example, on August 14, the volatility level changed -0.7 (12.8-13.5), while on August 13 it changed -0.1 (13.5-13.6). And a volatility of 13.5 we noted, on the above mentioned article, is 3rd decile (so the data remains grey color). We plot this data on the chart above, at 0.1 on the horizontal axis followed by -0.7 on the vertical axis. Notice the bottom decile changes are clustered tightly near the upper-left of the central of the diagram, while the top decile changes are distributed throughout. Additionally, we have drawn a blue box around the range of changes (along the horizontal axis) that represents the past one month's worth of data (again, from mid-July through mid-August). We note that the central 90% of the entire historical distribution is between -2.0, and 2.2. So for the past one month meanwhile, the range does eclipse just the lower end of that, or between -2.2, and 1.5. We also appreciate that the recent volatility values that have not been completely "outside of historical range".
Now to get a flavor of marginal distributions, we will acutely look at the difference in the volatility deciles. This is based off of the associated joint marginal copulas on the overall deciles noted in the article cited above. The general pattern of course changes with the unit of measure being discretely ordinal. Here we instead "jitter" the visual data slightly so one can see the amount of data over any joint value, and we truncate the minimal data beyond 3 on any side. We again use the same decile-coloring schema above: the bottom decile (in purple) and top decile (in red).
Last, we show a non-parametric series, where we examine the directional change only. A rise in volatility is 1 (right side), and a drop in volatility is -1 (left side).
As should be clear by the above examples, volatility fell on August 13, so this is among the ~50% of data on the left side under "-1". Additionally, volatility fell again on August 14, so this would be seen in the white color box labeled "Momentum on -1" (representing ~50% of the left side outcomes). The four partitioned segments above are nearly identical in size, which is not an unknown concept to our blog followers (here, here). To see more recent experience, and any break-down in the auto-correlation equilibrium, we redo this illustration below for only the past one month.
And here, straight away, we observe that volatility drops (left side is enlarged to >60%) more often than typical. And of course those drops (left side) are also sequentially followed by volatility drops (>60% again as shown in white and labeled as "-1"). Given the nature of nonparametric analysis, there is little to observe in terms of outliers though. Additionally, much of this past month (mid-July through mid-August) has been spent vibrating between deciles 2 and 3. And as a result we do notice that volatility is certainly low, but also haven't seen the nature of oscillations in the highest decile either, in order to more fully cast final judgment on the nature of what some note to be market quiet. Put differently, it could simply be too soon to tell, even if one bewails the annoyance of same.
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