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In this note we explore the statistical convolution between major market decline periods, and daily market declines. All the statistics shown are for the closing level of the S&P 500 (NYSEARCA:SPY). A major market decline is defined as one from a major market peak, to a major market bottom. So if there is intermediate market volatility, before the market makes a lower low from a prior high, then that decline would just be subsumed by the context of the broader drop. Similarly, if there are multiple market highs that equal one another, before the lowest future low, then only the most recent high is used to time the duration of the decline.

There have been over 16,000 trading days since early 1950 when we began tracking S&P 500 data. Of those, nearly 1,600 (or 10%) of those trading days saw a decline of 1% or more. And the distribution of these nearly 1,600 trading days is shown in the chart below. All declines, whether daily or for an entire decline period, are minimally rounded for this study. So we use the convention that would make a -2.3% value become a -2, or a -1.7% value becoming a -1.

(click to enlarge)

Also there were 165 periods, qualifying by the definition above, which saw a major market decline of 1% or more. We can see the distribution of these 165 decline periods in the chart below.

(click to enlarge)

To understand how these two charts above relate to one another, let's go through a few examples. Of the nearly 1,600 qualifying daily drop days, we can see 1,250 (or 79%) are at -1. And of the 165 decline periods, we see 53 (or 32%) at -1. Now for a decline of -5 instead, this was only 1% of the daily drops, but we see it makes up 7% of the decline periods. And for a larger decline of -10, we see it never occurs in a single day, but we see it makes up 1% of the qualifying decline periods. This probability would be scaled by about 1/3 if we included market drops of up to 1%, instead of beyond 1% in this study, with the scale slightly smaller for the daily market drops and slightly larger for the period market drops. We are actually in the middle of one of these truncated cases right now, as the S&P 500 closed 4 trading days ago at less than 1% higher at a record close of 1848.

So using the definition at the start of this note, we see in the chart above that since 1950 there was only 1 major market decline of -10 (i.e., from -10% to -11%), which occurred in the autumn of 1962. We also know this period lasted 43 trading days, so the daily pace of decline is -0.2 (-10/43).

Would the daily pace of market declines be faster or slower for a market period decline of -5 versus a market period decline of -10? We just showed that for a market period decline of -10, the daily pace works out to -0.2. It turns out that for a market period decline of -5, the daily pace is actually significantly greater. See the distribution count of the 165 market drop periods, by both its level of market drop (right axis) as well as by the duration of the market drop period (left axis). Note that the durations are not on an equal interval after 56 days (left axis), and this simply reflects the exceptionally larger durations of period market drops, particularly for drops of more than 20% (which again is the area to the lower left of -20 on the chart below or the left of -20 on the chart above).

(click to enlarge)

As noted earlier, there were 53 market decline periods of -1. But over the history of this study, all of the -1 complete market decline periods have lasted between 1 and 11 trading days, typically at 2 days. And the daily pace of drop comes to -0.4 on a period weighted average. This -0.4 daily pace of market drop was slightly faster than the -0.2 pace seen by the larger market drop period of -10.

But the 12 (or 7% of 165) market decline periods of -5 have all been fairly equally distributed between 1 and 26 trading days. And the daily pace of drop comes to -0.5 on a period weighted average. So this daily pace of drop of -0.5 is much more rapid than the -0.4 and -0.2 daily pace shown for either the smaller or the larger market drop periods, respectively.

This actually describes the general non-linear convolution pattern we see across the entire historical data. Of the nearly 1,600 daily drops, of -1 or more, those in qualifying-period market drops tend to cluster in small decline periods or large decline periods. But the medium decline periods instead are more concentrated (and characterized by) a faster pace of daily volatility. This is also important to consider as these major qualifying decline periods are more likely to be a medium drop period (7% are at a drop of -5) than a large drop period (only 1% are at a drop of -10).

Source: Market Decline Statistics For S&P 500