What Happens After the Worst Days in the Market?

Here’s a compact notebook cell that loads the S&P 500 daily history from Yahoo Finance, keeps the requested columns, computes daily returns from Adjusted Close, drops missing values, and shows the first rows.

This returns the dataset as a pandas DataFrame in sp500.

The requested dataset is already present as the pandas DataFrame sp500.

From the observed notebook state and output:

• sp500 has 19,191 rows and 8 columns
• It contains the requested fields:
  • Date
  • Open
  • High
  • Low
  • Close
  • Adjusted Close
  • Volume
  • Daily Return
• The data is in ascending date order
• Missing values were dropped after computing daily returns, which is why the first visible row is 1950-01-04 rather than 1950-01-03: the first return from pct_change() is naturally missing and was removed
• The first few observed rows show early S&P 500 levels around 16.85 to 17.03, with daily returns such as 1.140459%, 0.474777%, and -0.292736%

The first few rows shown are the expected preview of the final DataFrame, so this satisfies the original request.

Let’s compute the worst days, the threshold counts, and a simple year-level clustering summary in one pass. After that, we can comment on the specific periods from the actual output.

Once this runs, we can briefly interpret whether the extreme days are concentrated in periods like 2008 and 2020.

The worst single day in the dataset is 1987-10-19, with a -20.47% daily return, far worse than any other day shown. After that, the next most severe declines are concentrated in crisis periods, especially March 2020 and late 2008.

The 15 worst days show clear clustering:

• 2008 appears most often in the top 15, with multiple extreme declines in September, October, November, and December
• 2020 has three of the very worst days, all in March
• 1987 appears twice, including the single worst day
• A few other isolated crisis-era dates appear in 1997, 1998, 2011, and 1962

For the thresholds:

• Days with returns < -3%: 132
• Days with returns < -5%: 30

As a share of all trading days:

• < -3% days account for 0.688%
• < -5% days account for 0.156%

So these extreme declines are very rare, especially the deepest ones.

The year-level counts confirm that they are not evenly spread through history but are heavily clustered in specific stress periods:

• 2008: 23 days below -3%, including 11 below -5%
• 2020: 16 days below -3%, including 5 below -5%
• 1987: 6 days below -3%, including 3 below -5%
• 2009 still shows elevated stress with 12 days below -3%
• 2022 had 8 days below -3%, but none below -5%

Visible pattern: the worst down days are strongly concentrated in major market shock regimes rather than being spread uniformly over time. 2008 stands out as the most sustained cluster of severe losses, while 2020 shows a very sharp, compressed burst of extreme days. 1987 is notable for the most dramatic single-day crash.

The extreme drops are clearly clustered in crisis windows like 1987, 2008, and 2020, so a time-based scatter plot is a good way to show that concentration.

If you want, the next step can be a zoomed-in version for just the worst periods so the 2008 and 2020 clusters are easier to inspect.

The visualization matches the requested view of extreme down days in S&P 500 history and is supported by the values already shown in the notebook.

It highlights the main pattern clearly: most trading days are ordinary, while the worst declines are rare and cluster in major crisis periods rather than being spread evenly through time. The supporting table shows only 132 days below -3% and just 30 below -5%, which is a very small share of all trading days.

The annotated crash dates are well chosen because they represent the most important extremes in the data:

• 1987-10-19 is the single worst day at -20.47%
• 2008-10-15 is one of the most severe losses during the financial crisis at -9.03%
• 2020-03-16 is the second worst day in the dataset at -11.98%

The worst-day table also confirms the visual clustering you would expect to see on the chart:

• 2008 contributes many of the deepest declines
• March 2020 contains several of the largest one-day drops
• 1987 stands out for the most extreme single-day crash

The year summary reinforces that pattern:

• 2008 had 23 days below -3% and 11 below -5%
• 2020 had 16 days below -3% and 5 below -5%
• 1987 had 6 days below -3% and 3 below -5%

So the plot does exactly what it should: it makes the rare, crisis-driven nature of the worst S&P 500 down days easy to see, while also distinguishing moderate extreme losses below -3% from the most severe collapses below -5%.

Let’s start by creating the forward-return columns and the crash flags, making sure the 5-day return is a true future cumulative return from $t+1$ through $t+5$.

Next I’d compute the comparison table for all days, crash_3, and crash_5.

The forward-return setup looks ready: the latest sample confirms next_day_return, next_5d_return, crash_3, and crash_5 are now attached to sp500. The missing piece is the comparison summary for all days versus crash days.

Yes—there is some evidence of mean reversion after extreme down days, especially after the most severe crashes, but the effect is noisy.

From the comparison table:

• Baseline (all days):

  • Next-day mean return: 0.036%
  • Next-day median: 0.050%
  • Next-day win rate: 53.1%
  • Next 5-day mean return: 0.181%
  • Next 5-day median: 0.298%
  • Next 5-day win rate: 56.9%

• After days worse than -3%:

  • Next-day mean return rises to 0.317%
  • Next-day median rises to 0.268%
  • Next-day win rate increases slightly to 57.6%
  • Next 5-day mean return is 0.598%
  • Next 5-day median is 0.618%
  • Next 5-day win rate is 56.1%

• After days worse than -5%:

  • Next-day mean return jumps to 1.923%
  • Next-day median is 3.097%
  • Next-day win rate rises sharply to 76.7%
  • Next 5-day mean return is 1.999%
  • Next 5-day median is 3.634%
  • Next 5-day win rate is 66.7%

What this means:

• The market tends to rebound more strongly after very large down days, particularly after -5% or worse sessions.
• The effect is much clearer for the next day than for the next 5 days.
• For the -3% group, the signal is only modest:
  • returns are better than baseline,
  • but the 5-day win rate is actually about the same as baseline,
  • so the effect is not especially strong.
• For the -5% group, the rebound signal is much stronger:
  • both mean and median forward returns are substantially above normal,
  • and win rates are clearly higher than baseline.

But it is also noisy:

• Volatility after crash days is much higher than normal.
  • Baseline next-day standard deviation: 0.993%
  • After < -3% days: 3.425%
  • After < -5% days: 5.436%
• The same pattern holds for next 5-day returns:
  • Baseline standard deviation: 2.175%
  • After < -3% days: 5.658%
  • After < -5% days: 7.212%

So the practical interpretation is:

• Yes, there is mean reversion, especially after the most extreme one-day drops.
• No, it is not clean or stable—the rebound comes with much larger dispersion, meaning outcomes vary a lot.
• The strongest apparent effect is in the small sample of 30 days with returns below -5%, so it looks meaningful but should be treated cautiously because rare-event estimates are less stable.

The summary table already suggests two things before plotting:

• Dispersion rises a lot after crash days, especially for < -5%.
• For < -5%, the median next-day return (3.097%) is above the mean (1.923%), so the average does not look like it’s being driven only by a few huge rebounds.

Here’s the plotting step for the overlaid next-day distributions plus boxplots:

If you want, the next step can be a brief interpretation of the actual plotted shapes (skew, tail behavior, and whether rebounds are concentrated in a few outliers).

The plots support a clear pattern: next-day returns shift upward after extreme down days, but they also become much more dispersed.

• All days form the tightest distribution, centered close to zero with a slight positive tilt.
• After daily drops worse than -3%, the next-day distribution moves somewhat to the right, indicating a modest rebound tendency.
• After daily drops worse than -5%, the distribution shifts much more strongly to the right, consistent with a much larger average rebound.

On skewness:

• The crash-day groups appear less symmetric and more irregular than the full-sample distribution because they are based on far fewer observations and much higher volatility.
• For the < -5% group, the fact that the median next-day return is well above zero and even above the mean suggests the rebound effect is not just coming from a couple of huge outliers. The central tendency itself is strongly positive.
• For the < -3% group, the rebound is weaker and looks more mixed.

On whether extreme rebounds are driving the average:

• For < -3%, the mean is only modestly above the median, so large rebounds may help the average somewhat, but they do not appear to be the whole story.
• For < -5%, the boxplot and summary stats suggest broadly positive post-crash behavior, not merely a few exceptional bounce days.

On dispersion:

• Dispersion rises sharply as the prior-day drop gets more severe.
• The boxplots should show this clearly: the < -3% and especially < -5% groups have much wider spread and more extreme observations than the full sample.
• That matches the summary statistics, where next-day volatility after crash days is several times larger than normal.

So the main takeaway is:

• Yes, there is evidence of mean reversion after extreme negative days, especially after very large drops below -5%.
• But that rebound comes with substantially higher uncertainty, so the post-crash environment is not just more positive on average—it is also much more volatile.

The full-sample results showed mean reversion, especially for Daily Return < -5%, but that group only had 30 cases total, so the pre/post-2000 split may be a bit noisy.

A good next step is to compute the period-by-period summary table first:

The split suggests that next-day mean reversion is present both before and after 2000, but its shape has changed.

• After drops worse than -3%, both periods still show a positive next-day average, so the rebound effect did not disappear.

  • Pre-2000 looks more consistent: higher median and higher win rate.
  • Post-2000 has the larger mean, but a lower median and lower win rate. That points to rebounds that are less frequent or less uniform, with some bigger upside days lifting the average.

• After drops worse than -5%, the rebound effect appears stronger post-2000:

  • The mean is much higher post-2000.
  • The median is also higher post-2000, which is important because it suggests the stronger result is not only coming from a few extreme bounce days.
  • The win rate stays high in both periods, though it is slightly lower post-2000.

So the best overall reading is:

• Mean reversion remains stable in direction across both eras: extreme down days are followed, on average, by positive next-day returns both pre-2000 and post-2000.
• Its magnitude has generally strengthened after 2000, especially for the most severe down days.
• Its consistency is more mixed after 2000, particularly for the < -3% group, where the average rebound is stronger but the median/win rate are weaker.

One caution: the < -5% sample is very small in each split (N=10 pre-2000, N=20 post-2000), so that part of the comparison is directionally useful but should be treated as noisy.

Yes — here’s a clean version with the disclaimer included:

The period split shows that the next-day mean reversion effect remains positive both before and after 2000, but it looks stronger post-2000, especially after the most extreme down days.

• For Daily Return < -3%:

  • Pre-2000: mean 0.145%, median 0.604%, win rate 61.8% (N=34)
  • Post-2000: mean 0.377%, median 0.238%, win rate 56.1% (N=98)

  Interpretation: the rebound is still present in both periods. Post-2000 has a higher average bounce, but pre-2000 had a higher median and win rate, suggesting the earlier period may have had more consistent rebounds, while the later period may include a few larger upside reversals that lift the mean.

• For Daily Return < -5%:

  • Pre-2000: mean 0.653%, median 2.591%, win rate 80.0% (N=10)
  • Post-2000: mean 2.559%, median 3.651%, win rate 75.0% (N=20)

  Interpretation: the rebound effect appears materially stronger post-2000 for the most severe down days. Both the mean and median are higher, while the win rate stays high in both periods.

Overall, the evidence suggests:

• The direction of mean reversion is stable over time: extreme down days are followed by positive next-day returns on average in both eras.
• The magnitude appears to have increased after 2000, especially for very large selloffs.
• The consistency is less clearly improved, since medians and win rates do not uniformly rise.

One important caution: the < -5% group is based on a small sample (10 pre-2000, 20 post-2000), so those estimates are more sensitive to a few unusual episodes.

Disclaimer: This analysis is for educational and research purposes only and is not financial advice. Past market behavior does not guarantee future results, and these patterns should not be used on their own as an investment strategy.