One in a Quadrillion

The best investment lesson from the year, 2025?

The day, April 9th.

The stock market reacted to tariff surprises in late-February-early-April. It was a hellish couple months, with the S&P 500 down nearly 20%.

In a data set that's normally distributed, where outcomes cluster around an average (e.g. human heights, shoe sizes, ACT scores), by definition 68% of outcomes fall within one standard deviation ("one sigma" or "1σ") .

So if the average height is 70 inches with a standard deviation of 3 inches, 68% of people are between 67 and 73 inches. And 76 inches would be "2σ" above average.

April 9th was an eight sigma event.

Basically just after the hellish downturn, the market delivered +9.5%...a year's-worth of average returns, in a single day. 8σ above the average daily return.

Some "normal" distribution context:

• 1σ = 68% of outcomes fall within

• 2σ = 95% of outcomes fall within

• 4σ = 99.9937% of outcomes fall within

• 8σ= 99.99999999999994% of outcomes fall within

In a normal data distribution, an 8σ event is a 1 in 1.6 quadrillion event.

It's borderline mythical. The stock market moving +/- 9% in a single day seems like it should never, ever happen in your lifetime.

Except it has, and it does.

• 1987-10-19: −20.47%

• 1987-10-21: +9.10%

• 2008-10-13: +11.58%

• 2008-10-15: −9.03%

• 2008-10-28: +10.79%

• 2008-12-01: −9.47%

• 2020-03-12: −9.51%

• 2020-03-13: +9.29%

• 2020-03-16: −11.98%

• 2020-03-24: +9.38%

• 2025-04-09: +9.52%

And probably will again.

Rare? Yes.

Impossible? No.

1 in 1.6 quadrillion? No.

Stock market returns are not normally distributed. Daily outcomes do not cluster around a "daily average" — instead we observe (and expect) super weird, outsized, fringe outliers.

Similarly, the average annual return of the S&P 500 is between 8%-10%.

But we hardly ever get the average. Only 4 years since the 1950's. Said another way, historical stock market averages can inform an educated guess at a long-term expected average for the future. Yet at the same time, we should expect to be wrong every year.

And the abnormal distribution of stock market returns means nothing happens for a long time, then 1 in 1.6 quadrillion days happen. Sometimes, like in March, 2020...three times in the same a week.

In the stock market, statistical oddities cluster. Averages don't.

Calibrate your investment journey accordingly.

The historical average of the stock market is positive. We also know it gets unexpectedly zonked sometimes, both upward and downward. Critically, we can't guess when.

So if we want to engineer future outcomes as best possible, we must resolve to simply not miss 8σ days. The good ones and the bad ones. Can't risk investing any other way. Can't hijack the long-term average from ourselves by trying to forecast the unforecastable.

Lose 9%+ of your stock portfolio in a single day. That's what great investors do.

End.