Loss recovery calculator

Why the gain is larger than the loss

After a loss, the recovery works from a smaller base. Lose 30% of $10,000 and $7,000 is left; winning back the missing $3,000 means earning 3,000 / 7,000 on what remains, or 42.86%. In general, gain needed = loss / (1 - loss). Small losses barely differ. A 5% loss needs 5.26%. The gap widens quickly as the loss grows, and at 50% the required gain reaches a full 100%, the point argued in a 50% loss needs a 100% gain. Run it the other way and the sum holds. A 42.86% gain followed by a 30% loss lands exactly where it began, which is why a big win and a big loss in quick succession can leave a year looking busy and flat.

Reading a sequence of returns

Returns compound, each one applied to whatever balance the last one left. The defaults run -10%, +5%, -20% and +15% on $10,000. Added up, they come to -10%. Compounded, they end at $8,694, a 13.06% loss, and getting back to $10,000 takes 15.02%. The table prints each step, with the running change from the starting balance in the last column, so you can see where the damage came from. Reordering the returns leaves the ending balance alone, since multiplication gives the same product in any order, while the lowest point along the way moves, and that low point is what a drawdown limit, a prop firm floor or a margin requirement reacts to. Maximum drawdown measures it.

What the arithmetic leaves out

The figures come before commissions, taxes and interest, and a margin account adds borrowing costs that push the required gain higher. Leverage deepens the drop for any given market move, so the recovery sum starts from a worse place. The formula also says nothing about time. A loss can arrive in a few bad weeks. Earning 42.86% back at an ordinary pace usually takes far longer, and the trades that do it tend to be sized smaller than the ones that lost it, because the account is smaller. The lesson on drawdown limits and the arithmetic of getting back to even turns these sums into a stopping rule, and how big a drawdown should make you stop trading sets the cutoff. The loss recovery math quiz tests the same ideas.