Equity Sell-Off : Looking Back

Histogram of S&P 500 one-month (20 days) move following a 3% or more sell-off, since 1960s. This shows historical probabilities of a recovery or a worsening sell-off during the next month, conditional on a 3% or worse sell-off today. Index is scaled to start at 100 after the first down move on day 1.

The worst 5 recoveries are all in 2008 Sep to Oct, except once in 1987 flash crash. The best 5 recoveries are mixed across time.

The cumulative probability of continued sell-off is 37.5%, Cumulative probability of 5% or more recovery is approx 40%. Median move is 1.9% rally. On cases we had further sell-off, the median sell-off is 6.6%, The median for rally case is 5.6% (so the distribution is skewed, as obvious from above). However, this skew disappear if you take out the tumultuous period of 2008 following the Lehman Brother failure. In that case the moves are slightly positively skewed, 4.6% sell-off vs. 5.4% rally. Also the cumulative sell-off probability drop is around 30%

But with all hard numbers, it is hard to keep calm when everyone else is in panic mode.