Why Drawdowns Need More Than They Took

A ten per cent loss requires an eleven per cent gain to recover. A twenty per cent loss requires twenty-five per cent. A fifty per cent loss requires one hundred per cent - the account must double simply to return to where it started.

The reason is that the loss is measured against a larger balance and the recovery against a smaller one. After a fifty per cent loss, every percentage point of gain is worth half what a percentage point of loss was worth, because it is calculated on half the capital.

The required gain is the drawdown divided by one minus the drawdown. That expression rises slowly at first and then very steeply, which is why the difference between a fifteen per cent drawdown and a forty per cent one is far larger than the difference in the numbers suggests.

The percentage is only half the cost. If a strategy has an average return per trade, the number of trades needed to make up a deep drawdown scales with the size of the hole - and those trades have to be taken at the same expectancy that produced the drawdown in the first place.

That is a demanding assumption. Trading a damaged account tends to change behaviour: sizing up to recover faster, or sizing down out of caution, both of which change the distribution the recovery estimate assumed.

Where an account sits on this curve is decided by position sizing far more than by strategy selection. Risking a small fraction of capital per trade keeps a losing streak in the flat part of the curve, where recovery is close to symmetric.

Risking a large fraction moves the same losing streak into the steep part, where each additional loss requires disproportionately more to undo. The strategy did not change; only the sizing did.

This is the practical content of the arithmetic. A daily or weekly loss limit is a mechanism for keeping the account in the region where recovery is arithmetically plausible, and it works by capping the number of consecutive losses that can be taken before stopping.

Maximum drawdown is measured from the highest equity value reached, not from the starting balance. An account that doubled and then fell back to its starting point experienced a fifty per cent drawdown, even though it did not lose any of the original capital.

That definition is deliberate, because the peak is what the capital actually reached and what a withdrawal at that moment would have realised. Measuring from the start would report the same account as flat, which describes neither the risk taken nor the experience of it.