Drawdown math: why −50% needs +100%

Lose 50%, then gain 50%, and you are not back to even — you are at 75 cents on the dollar, still down 25%. This is not a trick of wording. It is the central asymmetry of trading arithmetic: losses and gains of equal percentage are not equal forces, because every loss shrinks the base your recovery has to grow from. Most of risk management — small position sizes, diversification, stop placement, the entire previous four lessons — exists to keep you off the steep end of this curve.

This lesson makes the asymmetry concrete: the formula, the table worth memorizing, how to size your trading so the deep end stays theoretical, and why the order of your results matters as much as the results themselves.

The asymmetry, in one formula

The gain required to recover from a loss is the loss divided by what is left. Lose 20% and you must earn 20 divided by 80 — that is 25% — on the remaining capital just to revisit your old high-water mark. The denominator is what hurts you: as the loss grows, the surviving base shrinks, so the required recovery grows on both ends at once. Small losses are nearly symmetric. Large losses are catastrophically not.

The recovery table

Worth committing to memory — if not the numbers, then the shape:

1. −5% needs +5.3% to recover
2. −10% needs +11% to recover
3. −15% needs +18% to recover
4. −20% needs +25% to recover
5. −30% needs +43% to recover
6. −40% needs +67% to recover
7. −50% needs +100% to recover
8. −60% needs +150% to recover
9. −75% needs +300% to recover
10. −90% needs +900% to recover

Read it in two halves. Down to around −15%, the math is nearly symmetric: routine drawdowns, the unavoidable cost of doing business, repaired by the same ordinary trading that caused them. Somewhere past −30%, the curve turns vertical. Recovering from the deep end demands either a very long time or exactly the kind of outsized risk-taking that dug the hole — which is how one bad drawdown becomes two. The practical conclusion is blunt: the deep half of this table is not a region you trade your way out of. It is a region you arrange never to visit.

Sizing to your maximum tolerable drawdown

Most traders pick a risk per trade and discover their drawdown tolerance later, the hard way. Run it in the other direction. First, pick the maximum drawdown you could endure without quitting, panicking, or abandoning your system — the honest number, not the brave one. Then translate it into a per-trade risk using realistic streak math from the risk-per-trade lesson: losing streaks of seven to ten are normal, and a bad stretch is rarely one clean streak — it is streaks separated by failed recoveries. A sober planning figure for an active strategy is a worst stretch of 15 to 20 risk-units peak to trough.

• Pick the drawdown that would actually make you quit, then halve it — nearly everyone overestimates their tolerance by about that much.
• Budget a worst realistic stretch of 15–20 risk-units, not a single tidy streak.
• Divide tolerable drawdown by the stretch: 15% tolerance across 15 units points to 1% risk per trade. 2% risk with the same tolerance assumes your worst stretch never exceeds 7 units, which is optimism, not planning.

Sequence risk

Take a fixed set of monthly returns and shuffle their order. For a pure compounding account with no deposits or withdrawals, the endpoint is identical — multiplication does not care about order. Almost nothing else about the experience is. A −20% stretch in your first three months versus your last three months is the same arithmetic and a completely different life: one trader builds confidence and a sample before the storm, the other meets the storm with no cushion, no track record, and every incentive to conclude the whole approach is broken.

Sequence risk also stops being cosmetic the moment money moves in or out. Withdraw living expenses during an early drawdown and you are selling from a shrunken base — the recovery table steepens, because the gains must now come from even less capital. And for most traders, sequence risk bites through behavior: an early deep drawdown triggers the system abandonment, the doubled position sizes, the revenge arc. The returns may be order-independent. You are not.

Trading through a drawdown

Drawdowns are when plans earn their keep, because every instinct mid-drawdown is wrong. The urge is to size up and win it back fast; the table above is a list of reasons not to. The professional pattern runs the other way — risk shrinks as the hole deepens:

• Pre-commit a de-risking ladder: for example, at −10% from your high-water mark, halve the risk per trade; at −15%, halve it again or stop trading and review.
• Never size up to accelerate recovery. That is the martingale path, and the deep half of the table is where it leads.
• Use the drawdown to interrogate your journal: is this normal variance within a working system, or has something about the market regime actually changed? The two have identical first weeks and opposite remedies.
• Let recovery be slow. Fixed-fractional sizing means you were betting smaller all the way down, so the hole is shallower than your nerves report — and shallow holes need only shallow climbs.

Key takeaways

• Recovery required equals loss divided by what remains: −20% needs +25%, −50% needs +100%, −90% needs +900%.
• The curve has two halves — drawdowns under roughly 15% are routine, past 30% they become events you may not trade your way out of.
• Choose your maximum tolerable drawdown first and derive risk per trade from it, budgeting 15–20 risk-units for a worst stretch.
• Sequence matters: identical returns in a different order produce different behavior, and behavior is where accounts actually die.
• In a drawdown, cut size as the hole deepens — never raise it to recover faster.