Drawdown arithmetic

Lose 20% and make 20% back, and you are still down 4%. The percentages refuse to cancel because they are percentages of different amounts - the fall was measured on the peak, the recovery on the trough.

Why does the required gain outrun the loss?

Divide instead of subtracting. After a fall of d percent, the account holds 100 minus d percent of its peak, and returning to the peak means multiplying what remains by enough to cover the gap. The required gain is the gap divided by the remainder - always larger than the fall, and growing without limit as the fall deepens. At 10% down the climb is 11%. At 20%, 25%. At 50%, 100%. At 90%, 900%.

The curve's steepening is the whole lesson. Shallow drawdowns cost roughly what they took. Deep ones cost multiples, and the multiple is set by arithmetic no method can negotiate with.

What connects the hole's depth to your risk fraction?

Losing runs happen to every method - module 5 will put numbers on how often. What the risk fraction from lesson 1 decides is how deep a given run digs. Eight consecutive losses at one fraction is a shallow dent; the same eight at four times the fraction is a hole from the steep end of the recovery curve. The market supplied the same run to both accounts. The fraction chose the depth.

Fixed-fractional sizing adds its quiet protection here: because each loss is a fraction of a shrinking balance, the falls decelerate in money terms as the run continues. Fixed-amount risking loses that brake.

Is a drawdown a verdict on the method?

The arithmetic cannot say - it only prices the hole. Module 5's measurement lessons separate an ordinary losing run from a method that has stopped working, and module 7 owns what to do while inside one. This lesson's job ends with the honest price list, and the price list is reason enough to choose the fraction with care.

What this means for you

Work the recovery arithmetic for a few depths until the asymmetry stops surprising you, then look back at your lesson 1 fraction and the losing-run lengths it makes survivable. The drawdown you can tolerate is a decision made now, at full balance, by that fraction - it will never again be as cheap to decide as it is today.