A 50% Loss Needs a 100% Gain, and That Should Change Your Rules

How much do you have to make back after losing a third of an account? The instinctive answer is a third, and it misses by a wide margin: a third lost needs 50% back. The gain is measured on what remains, and what remains is smaller than what you started with, so the percentage you need on the way up is always larger than the percentage you lost on the way down.

The formula is short. Recovery gain = loss / (1 - loss).

The table

Loss	Gain needed to get back to even
10%	11.1%
20%	25%
30%	42.9%
50%	100%
75%	300%

The top of the table barely bites. A 10% loss needs 11.1%, a difference you’d hardly notice in a year. By the middle the curve has turned: 30% needs 42.9%. At the bottom it is brutal. Half the account gone means doubling what’s left, and a 75% loss means making three times what remains, 300%, just to stand where you stood before. The loss recovery calculator gives the figure for any loss you type in.

A $50,000 account, 30% down

Put dollars on the middle row.

The dollars lost and the dollars needed are the same $15,000. What changes is the base doing the work. On the way down, $50,000 was exposed. On the way up, only $35,000 is, so each percentage point of gain earns less, and the account has to perform noticeably better than it did while falling, for longer, with a trader who is probably less calm than before.

Time makes it worse. Suppose, purely as a hypothetical, the account earns a steady 10% a year from here.

No account earns a steady anything. The point of the sum is the ratio: at the same assumed return, the deeper loss takes about twice as long to repair, and every one of those years is a year in which the account is only getting back to where it was, earning nothing new, while the next losing streak is free to arrive before the last one has been paid off.

The rule the arithmetic writes

If repairs cost more than damage, the cheap move is to limit damage. That means a maximum drawdown set before trading begins, with actions attached to it, so the decision is already made when the account is down and your judgment is at its worst.

A hypothetical plan on the $50,000 account might read like this:

• At -10% ($45,000), halve the risk per trade.
• At -20% ($40,000), stop trading and review every position and every rule.

Look at what each line protects. At -10% the account needs 11.1% to recover. At -20% it needs 25%. Stopping there keeps you out of the part of the table where the numbers turn ugly, and halving size at the first line slows the descent toward the second. Where you set the lines is your call. The answer on how big a drawdown should stop you goes through the trade-offs.

Leverage moves you down the table faster

Borrowing changes which row you land on. At 2:1, with half the position on margin, every move in the stock is doubled in your equity.

A 25% fall in the stock is a bad month. Your equity falling by half puts you on the row where the account has to double.

The stock itself only needs to climb back 33.3%, from $30,000 to $40,000, for the equity to double, which sounds gentler. That rebound helps only if you still hold the position when it comes, after a fall that may well have drawn a call from a broker with a house requirement above the FINRA floor, and after months of interest added to the loan. A leveraged account can be closed out before the rebound arrives. Leverage takes an ordinary decline and drops you straight onto the doubling row, and the interest on the loan keeps running while you try.

Where the ledger is kind, and where it stops applying

The concession is real. One small loss is easy to recover. A 5% loss needs about 5.3%, which is noise. Nobody should rebuild their rules around a single ordinary losing trade.

The arithmetic bites in two situations: a streak of losses that compounds into a deep drawdown, and a single large loss from an oversized position, a gap through a stop or borrowed money. Both are exactly the cases a drawdown limit is written for. Neither announces itself in advance.

The ledger also stops applying cleanly to an investor who keeps adding new money. Deposits raise the balance without any gain at all. A saver who adds $15,000 to a $35,000 account is back at $50,000 in dollars, and the portfolio’s own return is still down 30%. That’s different arithmetic, and it can hide a loss that a trader living on the account’s returns could never ignore.

Write the drawdown limit before the drawdown

The call is a rule, set in advance: decide the drawdown at which you cut size and the one at which you stop, and write both where you’ll see them on a bad day. You can test yourself on the arithmetic with the down fifty, up a hundred quiz. The table will not bend for anyone, so the rules have to.