The math of recovery: why a −50% doesn't come back with a +50%
3 min read by Opthest
Early in 2026 the S&P 500 ran a peak-to-trough drawdown of −9.1%; in mid-March, amid geopolitical tension and a spike in oil, the VIX pushed above 30 before settling back. Nothing dramatic in the numbers — yet it was enough to remind us of something the math has always known and instinct keeps ignoring: a loss and a gain of the same size do not cancel out. Lose 10%, then make 10%, and you are not back where you started. You are below it.
The table nobody shows you
The reason is arithmetic, not psychological. After a loss you start from a smaller base, so it takes a bigger percentage to climb back. The formula is simple — gain needed = loss ÷ (1 − loss) — but the table is brutal:
| Loss taken | Gain needed to break even |
|---|---|
| −10% | +11% |
| −20% | +25% |
| −30% | +43% |
| −40% | +67% |
| −50% | +100% |
| −70% | +233% |
| −90% | +900% |
Up to −20% the gap looks like a rounding detail. Then the curve goes wild: halfway down you need to double your money, and beyond two-thirds the recovery demands returns that, in practice, nobody earns in any reasonable time. It isn’t the loss that kills a portfolio — it’s its depth, because the cost of recovery grows far faster than the loss itself.
The “drag” is no mysterious force
This is where volatility drag comes from, one of those phrases that sound esoteric and aren’t at all. Take two years: +25%, then −20%. The arithmetic average is +2.5% a year, which sounds respectable. But 1.25 × 0.80 equals exactly 1: after two years you are right back where you began. The return you actually pocket — the geometric, compounded one — is zero, not +2.5%.
Drag is precisely that gap: the distance between the average you quote and the capital you keep. It is not a hidden tax or a force that steals returns; it is simply the way compounding punishes swings. And it has a famously handy rule of thumb: compounded return is roughly the average minus half the variance. At 20% annual volatility, that’s already two points a year the arithmetic average promises and the portfolio never delivers.
Why containing the downside beats chasing the upside
Put together, these two arithmetics say one thing, and a counter-intuitive one: at the same average return, the steadier portfolio finishes higher. Not because it is prudent by temperament, but because it avoids the deep holes whose recovery costs an outsized percentage, and because it pays less drag along the way. It is the same intuition behind the efficient frontier: at equal expected return, less swing isn’t just easier to stomach — it is mathematically richer at the finish.
That is why maximum drawdown is a metric at least as important as return, and why a portfolio is judged also by how low it took you, not only by how high. Chasing the best decile of return is seductive; containing the worst decile of loss is what, year after year, leaves the capital standing.
One honest caveat
It would be dishonest to sell drag as a magic shortcut: less volatility does not guarantee more return — it only guarantees that, at the same average, you keep more of it. You can perfectly well have a calm, mediocre portfolio and a turbulent, brilliant one: variance explains the gap between average and compounded, not which of the two average returns will be higher. And none of these lines tells you what to buy or sell — they describe an arithmetic, not a strategy. The decision, and the risk you knowingly choose to run, remain yours.
But one fact no opinion can soften: recovery is not symmetric with the fall. Keep that in mind and you stop asking only how much you might gain, and start asking how much you can afford to lose — which, in the long run, is the same question written the right way around.