Investors got to go on a wild roller-coaster ride of volatility during the last two weeks. The U.S. stock market has not just been swinging wildly from highs to lows during the course of daily trading.

Whether you're just an observer, an investor, or an analyst, it's certainly an exciting time. To help put today's volatility into some historical context, we've updated our long-term chart of the percentage change the S&P 500 and its aggregated market capitalization-weighted component stocks have gone through over the index' history.

Or rather, for each trading day for which we have data for the index and its predecessor indices and components from 3 January 1950 through 11 April 2025, which spans the modern era for the U.S. stock market. The chart condenses that 75 years of day-to-day trading activity into a statistical control chart-style presentation, which identifies several distinct thresholds for measuring the market's daily behavior. Here's the chart:

Over the past 18,940 trading days covered in this chart, the average day-to-day change in the S&P 500 rounds up to +0.04%. We can also see that the index has changed from its previous trading day's closing value by 0.99% (one standard deviation) or less on 79.1% of all the trading days from 3 January 1950 through 1 March 2024.

This concentration of day-to-day changes in its value that fall within one standard deviation of the mean is important. If the day-to-day variation of the index were accurately described by a normal Gaussian distribution, we would expect to see around 68.2% of all changes within that range. Instead, there are far more small changes than would be expected if that hypothesis held. At the same time, there are more "large" changes that would be expected if a normal distribution applied, which is what market analysts mean when they describe stock prices as having "fat tails".

These aspects are characteristics of a Lévy distribution, which is another class of stable distribution about a central trend. As we've discovered however, there's some overlap with a standard Gaussian distribution, which makes some of the tools used to analyze these "normal" distributions useful in analyzing daily stock price variation.

That overlap occurs at the plus-and-minus two standard deviation thresholds, which is we use to define an "interesting" day for the S&P 500. The standard deviation of the day-to-day change in the S&P 500 is just under one percent. Since 95% of these changes are within two standard deviations of the mean trend line, any change of two percent or more is relatively rare, which makes it interesting by this definition.

As the chart illustrates, these rare events are not evenly distributed. They occur in clusters with both unusually large positive changes and negative changes taking place in close proximity to each other.

That brings us to the newest volatility cluster, which got underway with President Donald Trump's announcement of global tariffs being imposed on the imports of all nations to the U.S. after the market closed on Wednesday, 2 April 2025. Starting from that date, the day-to-day percentage change in the S&P 500 index has exceeded the 2% threshold on four of seven trading days through Friday, 11 April 2025.

That's somewhat deceptive because the intraday swings from highs to lows and back again in the index during some of the days that had little overall change have been truly impressive.

Take what happened on 9 April 2025 when President Trump paused the reciprocal tariffs announced for all nations but China a week earlier. The day-to-day change was +9.52%, which now ranks as the third-highest ever daily gain for the index in the modern era. But if not for what appears to be late-day profit taking, it could have been bigger and maybe even the biggest.

The two bigger daily gains both occurred in the volatility cluster of October 2008, coinciding with the near-collapse of the U.S. auto industry and the 2008 Financial Crisis.

Which brings us to our final point. That kind of outsized daily gain typically occurs only during periods of great volatility and tends to follow substantial losses. Because it does, it qualifies as a bear market rally.

Bear market rallies tend to be temporary events. Perhaps this time is different given the artificial nature of how the latest volatility cluster began. Market history and logic argues against it.

The magnitude of the tariff event is such that we expect high volatility to continue because it exposed previously hidden weaknesses in the market that can no longer be glossed over by investors. Reckonings will now happen because they must, they can no longer be avoided. Whole new sets of winners and losers within the market will emerge because of it.

Are you ready to keep riding the roller coaster?

References

Yahoo! Finance. S&P 500 Historical Data. [Online Database]. Accessed 11 April 2025.

Volker Ziemann. Bubbles, Crashes, Fat Tails and Lévy-Stable Distributions. Physics and Finance. pp 113-143. DOI: 10.1007/978-3-030-63643-2_9. 19 January 2021.

Takumi Fukunaga and Ken Umeno. Universal Lévy’s stable law of stock market and its characterization. [ArXiv Preprint: PDF Document.] 20 February 2018.