Why a 50% Loss Needs a 100% Gain

Three bars

The whole idea fits in three bars. Start with a hundred. Lose fifty and the loss is half of what you had: fifty per cent. Now make the same fifty back. It is measured against what is left, which is fifty, so the gain is all of it: one hundred per cent. Nothing doubled and nothing halved; the same fifty dollars was measured against a hundred on the way down and against fifty on the way up. A loss and the gain that undoes it are never the same percentage, because they never share a base.

A real fall

Here is the sum on a real day. On 28 August 2026 a fifteen-hundred-dollar account holding two lots — 200,000 euros — of the euro against the dollar bought at the open was stopped out by the broker at 1.15896 with $233 left. The fall was $1,267, which against 1,500 is 84.5 per cent. To get back to 1,500 the account must make the same $1,267 — and against the 233 it now holds, that is 544 per cent: the account has to become more than six times what it is. The dollars are the same in both directions. The base is not.

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