A 50% loss needs a 100% gain to get back to even
Not a rule of thumb. Arithmetic: what is lost is measured against what you had, and what is needed is measured against what is left. The second base is smaller, so the second number is always bigger.
| Loss | Gain required | At 7% a year |
|---|---|---|
| 5% | 5% | 0.8 years |
| 10% | 11% | 1.6 years |
| 15% | 18% | 2.4 years |
| 20% | 25% | 3.3 years |
| 25% | 33% | 4.3 years |
| 30% | 43% | 5.3 years |
| 33% | 49% | 5.9 years |
| 40% | 67% | 7.6 years |
| 50% | 100% | 10.2 years |
| 60% | 150% | 13.5 years |
| 70% | 233% | 17.8 years |
| 75% | 300% | 20.5 years |
| 80% | 400% | 23.8 years |
| 90% | 900% | 34.0 years |
| 95% | 1,900% | 44.3 years |
Why it matters
Because this is the mechanism that turns a temporary loss into a permanent one. The arithmetic is not the problem; almost nobody sells because they miscalculated. They sell because the number recovery requires is so much larger than the number they lost that waiting for it stops feeling reasonable. A 33% loss needs a 50% gain. A 50% loss needs 100%. A 75% loss needs 300%, and at seven percent a year that is twenty years, which is a working life. Most of the people in the Reckonings who ended badly did not end badly on the way down. They ended badly on the way back, when the size of the climb became clear.
Show it
The gain required is loss ÷ (100 − loss). At small losses the two numbers are nearly equal — a 5% fall needs 5.3% back — and the curve is almost flat. It steepens without limit as the loss approaches 100%, because the base you are growing from is approaching zero. The honest calculator shows this on real holdings: the same page that says a stake became six figures also says how far it fell first, and the second number is why the first was hard to collect.
Context
This is also why volatility costs money even when the average return looks fine. A holding that gains 30% then loses 30% is not back to even; it is down 9%. Alternating +50% and −50% loses a quarter of the money each round trip. Arithmetic averages describe a series of returns; what you actually end up with is the product of them, and every loss in the sequence pulls the product below the average. See volatility is not risk for why that is not the same thing as danger, and drawdowns for how to read a fall while it is happening.
One question
What is the largest loss you have sat through without selling — and what did you tell yourself at the bottom that made it possible?