Severity of this week's stock market downturn
Sigma Analysis
Dear readers,
As we are all aware and closely monitoring, global stock markets are currently experiencing significant turmoil.
You likely have seen numerous interpretations of what occurred and what might happen next.
We firmly believe that to fully grasp the current events, it is essential to understand our position from a historical perspective and evaluate how this week's crash compares to other major market downturns in the past.
In this post, we utilize sigma analysis to address the question: "How severe was this week's crash?"
This week's two-day stock market crash, spanning April 3-4, 2025, was one of the most severe in U.S. financial history.
On Friday, 98% of the stocks in the S&P 500 ended the day in negative territory, an exceptionally rare occurrence. The market might have seen all 500 stocks in the red if not for mid-day news about Vietnam removing tariffs, which caused a brief spike in apparel and footwear companies like Nike, Lululemon, and Skechers.
Sigma analysis in finance refers to the use of standard deviation (denoted by the Greek letter sigma, σ) to measure the variability or dispersion of investment returns around their mean. It is a critical tool for assessing risk and volatility in financial markets.
A 1-sigma"event refers to a market movement or an asset's return that deviates by 1 standard deviation from its mean, either above or below. Similarly:
A 2-sigma event represents a deviation of 2 standard deviations from the mean.
A 3-sigma event corresponds to a deviation of 3 standard deviations from the mean. This pattern continues for higher sigma levels.
There is an inverse relationship between sigma and the likelihood of an event occurring. This means that as sigma increases, the likelihood of the event decreases.
In a normal distribution:
Around 68.3% of the data lies within 1 sigma (one standard deviation) of the mean.
Approximately 95.4% falls within 2 sigmas.
Roughly 99.7% is contained within 3 sigmas.
We recognize that the returns of the S&P 500 do not follow a normal distribution. Instead, they display features such as fat tails and high kurtosis, which signify deviations from the characteristics of a normal distribution. This means extreme events (large gains or losses) occur more frequently than a normal distribution would predict. In financial markets, "Six Sigma" refers to extremely rare occurrences, such as daily market drops exceeding 9.5%. These events theoretically happen once every 796 years but occur more frequently in practice due to non-normal distributions. However,