WarrenCo

The Asymmetry of Loss.

Buffett’s first rule of investing is “don’t lose money.” The second rule is “don’t forget the first rule.” Both rules come from one piece of math, and the math doesn’t care how good your story is. A 50% loss requires a 100% gain just to break even. Everything else on this site — margin of safety, the pre-buy gates, the drawdown map — is a defense against the chart below.

Chart 1 · The recovery ladder

A loss of x requires a gain of x ÷ (1 − x) to break even.

Every 10% deeper you fall, the climb back doesn’t add 10% — it multiplies. The slope of the curve is the whole reason discipline pays.

0% 50% 100% 200% 300% 400% Gain required to break even −10% +11% −20% +25% −30% +43% −40% +67% −50% +100% Buffett’s first rule. −60% +150% −70% +233% −80% +400% −90% +900% » off the chart

The math. If you lose a fraction x, your portfolio is worth (1 − x) of what it was. To get back to 1, you have to multiply by 1 ÷ (1 − x), which is a gain of x ÷ (1 − x). The function is convex: each 10% deeper you go, the required recovery grows faster than the loss did. By the time you’ve lost half, the climb is doubled. By the time you’ve lost nine-tenths, the climb is tenfold.

Chart 2 · Time to recover

At the long-run real return of the market, the climb back is measured in years.

Compounding at ~7% real (the S&P 500’s realized real total return over 150 years), this is how many years each level of loss costs you, assuming you neither add nor withdraw a dollar.

0 yr 5 10 15 20 25 30 35 Years at 7% real to break even −10% 1.6 yr −20% 3.3 yr −30% 5.3 yr −40% 7.6 yr −50% 10.2 yr a full decade out of the market. −60% 13.5 yr −70% 17.8 yr −80% 23.8 yr −90% 34.0 yr

What this means in a life. The average investor has perhaps 40 productive compounding years. A −50% loss eats a quarter of them. A −80% loss eats more than half. The wider point isn’t that you can’t recover — it’s that the years you spend recovering are years you don’t spend compounding. Most of the gap between great and average long-term records is not about the upside someone caught; it’s about the downside someone avoided.

Required-gain formula: g = x ÷ (1 − x), where x is the loss as a positive decimal. Time-to-recover formula: t = ln(1 ÷ (1 − x)) ÷ ln(1 + r), with r = 0.07 for long-run real total return on US equities (Shiller, 1871–2025). The model assumes no contributions or withdrawals during the recovery period and ignores taxes; both simplifications make the chart look better than reality, not worse.