After a negative 7-sigma two-day drop last week in the S&P 500 index, yesterday there was a positive 9-sigma rally. These tail events are rare and have historically occurred during large corrections and bear markets.
After a two-day 10.5% drop on April 4, 2025, which was a negative 7-sigma event based on historical data since 1945, on April 9, 2025, the index rallied 9.5% to deliver an extra rare positive 9-sigma event.
The S&P 500 index has only gained more than 9% on a single day six times in the past, as shown below.
In all previous cases of a rare 9-sigma daily event, the index was well below its 200-day moving average. Tail events, positive or negative, have mostly occurred during periods of high uncertainty. Usually, a bull market is a “dull market.”
For example, if we look at positive 5-sigma events (gains of more than 5% since the standard deviation of daily returns is about 1%) below or above the 200-day moving average, we find out that only one out of 24 has occurred above the average.
Finally, note that the forward path of the market after such extreme events is highly uncertain, as some occur along the downtrend, others occur near a bottom, and some occur while the market is recovering but is still below the 200-day moving average. 2025 is definitively “the year of the tails.”
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