Streaks in curbed market volatility

So much for a terrifying "President Trump stock market".  Instead, October 11 was the last day we saw a drop of greater than 1% in the markets (88 days ago).  On the other hand, since then we’ve had three days where we saw a market rise of greater than 1% (the last one being 48 days ago).  Both of these streaks individually are among the top couple percent in the history of the S&P 500 (past 67 years).  Add them together though, 88+48=136, and we get a “combination streak” that is among the top decile.  Of course we could look only at the joint minimum or maximum streak as well, though for this probability exercise we’ll look at the more earnest combination of both (and it has the statistical advantage of consuming all trading days and not cherry-picking some).  What we learn, similar to our deep dive on solely a drop of 1% or more, is that the combination streak continues to have forthcoming stock market changes that are inhibited in both average change as well as volatility.  We correctly divined then that despite the decade length streak of no 1% drop days that it would still not happen anytime soon.  And this overall research carries across here in that generally purchasing large hedges or some volatility ETNs -despite the record low price- is unfeasible since there is likely to be an extreme change in the markets, though still not abruptly.  Though writing insurance options for very short-term expected duration might be viable.  It should be highlighted that in the past year, we've also gone quiet in the broad bond market.  

Now one can see in the chart below that a combination streak of 136 is a level we have not seen since 1995.  And of the course the market rose significantly more after that period, which incorrectly threatened years in advance, of “irrational exuberance”.

Another way to visualize this combination streak is to see it detached between the streak without a -1% change (88 days on horizontal axis), and the streak without a 1% change (48 days on vertical axis).  Stimulatingly, even though the market largely rises over time, the recognized negative skew implies that we can get a far bigger streak of lack of >1% days (see vertical axis top 400 days while the horizontal axis is less than ½ of this).

On the chart below we quantile map the distribution of curbed volatility streaks in both directions.  Each of these ventile partitions represents 5% of the combination streaks.  And we see that there tends to be potential co-movement of the no >1% streak and the no <-1% streak when looking at them in combination, through the medium blue colored cloud in the lower right of the map below.  And note that this is even more significant if we only consider terminal combinations, meaning we exclude the streak days (concentrated in the upper left of the chart below) that lead up to a move outside of +1%. Note that the 2^nd link at the top of the article explores 1% drops in the markets using that approach.

The focus however is on the fact that 88 days without a -1% move is a 2^nd highest vigintile (top 10%) streak as shown in it being highlighted in the second lowest row out of 20.  But the 48 days without a -1% move is a highest vigintile (top 5%) streak as shown in it being highlighted in the right most column out of 20.  And while each joint partition should represent 0.25% (5%*5%), or 42 days (0.25% of ~17k days), instead we see a much higher copula (concordance in joint tail risk) with color counts that are essentially yellow.  For more on this probability  risk theory, please see here and here.

The next topic is what happens next when we arrive at a state where the combined streak of curbed volatility is 136 or more.  And the answer is commonly not much.  We see in the chart below that the following day’s trading is principally a constricted +0.5% (and centered near 0.0%).  On a typical day otherwise, the next day’s trading is usually a few basis points drift upwards but with nearly twice the standard deviation, at +0.9%.