Drawdown: why losses hit harder than gains

A drawdown is the fall of an account from its highest point so far to a later low, in percent of that highest point. It measures the pain a plan actually puts you through, which the final result hides.

drawdown = (peak − current value) ÷ peak

Example on a Pebble practice account: it grows to a peak of 12,000, then a bad stretch takes it to 10,200. The drawdown is (12,000 − 10,200) ÷ 12,000 = 15%, even though the account is still above its 10,000 start. The reference point is always the peak, not the starting balance.

Keeping track is simple: note the highest value the account has ever reached and how far below it the account is now. A plan with a fine total can hide a drawdown deep enough to make most people abandon it halfway, so the worst drawdown belongs next to the expectancy whenever you judge a plan.

After a loss, every gain is measured on a smaller base, so getting back takes a bigger percentage than the one you lost.

An account of 10,000 falls 50% to 5,000. Gaining 50% from there adds only 2,500 and leaves 7,500, still a quarter down. To return to 10,000 it needs another 5,000, which is 100% of 5,000.

The general rule, with the loss written as a fraction of the account:

gain needed to recover = loss ÷ (1 − loss)

For 50%: 0.5 ÷ 0.5 = 1, so +100%. For 10%: 0.1 ÷ 0.9 ≈ +11.1%. Small losses are cheap to repair; big ones are not. This is the arithmetic behind every rule that keeps the risk per trade small: the deeper the hole, the more of the future a plan has to spend climbing out of it.

Apply loss ÷ (1 − loss) to losses of different sizes and a pattern appears:

• 10% loss → +11.1% to recover
• 20% → +25%
• 33% → about +49%
• 50% → +100%
• 75% → +300%
• 90% → +900%

Up to about 20%, the gain needed is only a little bigger than the loss. Past about half, it runs away: a 75% loss needs the account to quadruple, and a 90% loss needs it to grow tenfold. For a plan that earns a few percent a month, that is years of work, or simply never.

That is why drawdowns are judged by their depth, not just by the fact that they happen. Every plan has losing stretches. The question is whether they stay in the shallow part of the curve, where recovery is ordinary arithmetic, or slide into the steep part, where it becomes a fantasy.

How deep a drawdown goes depends heavily on how much each trade risks. In the lesson's practice sequence, 40 trades from one plan each win 2 risk units or lose 1 (risk units as in Expectancy: the average trade): 15 wins and 25 losses, +0.125 units a trade on average. The same sequence runs twice on 10,000, risking 1% or 25% of the account at that moment.

Trades 7 to 13 are seven losses in a row. At 1% the account dips from 10,299.96 to 9,597.38, a 6.8% drawdown. At 25% it falls from a peak of 16,875.00 to 1,900.59: (16,875.00 − 1,900.59) ÷ 16,875.00 = 88.7%. Climbing back from there would take about +788%.

The bigger size also looked better at first: 16,875 after three trades. That early shine is what makes oversizing tempting, and it is exactly the stretch that tells you nothing.

When each trade risks a fixed percent of the account at that moment, losses and gains compound. A loss shrinks the base that every later trade is measured on.

At 25% risk, seven losses in a row leave 0.75⁷ ≈ 0.13 of the account, about 13% of where the run began. A win of +2 risk units then adds 50% of that small account, which can't rebuild what was lost. At 1% risk the same seven losses leave 0.99⁷ ≈ 0.93, a dip of under 7%, and the positive average has room to work.

Over all 40 trades the difference is stark: +4.7% at 1% and −67% at 25%, from identical trades with an average of +0.125 risk units. Nothing about the plan or the luck differed; only the size did.

So size is not a loudness knob that makes a good plan louder in both directions equally. Past a point, it lets the losses win.

Risk of ruin is the chance that a losing run takes an account so low that it can't realistically recover, or that the trader gives up. The account doesn't need to reach zero. After an 80% drawdown it needs +400% to get back (0.8 ÷ 0.2), which for most plans means never, and most people abandon a plan long before that, often at the worst moment.

Two things drive the risk: how long the losing runs are, and how much each trade risks. Losing runs come with every plan, even a positive one; in the lesson's sequence, seven losses in a row turned up within 40 trades. Size is the part you control. Halve the risk per trade and the same run costs roughly half as much, while the gain needed to recover shrinks even faster.

No size makes ruin impossible, and no formula here predicts your exact chance of it. The direction is reliable, though: bigger size, higher risk of ruin.

You can't choose when a losing run arrives, but the risk per trade decides how deep it digs. When each trade risks a fixed percent of the account at that moment, every loss leaves (1 − risk) of the account, so a run of n losses leaves (1 − risk)ⁿ.

Seven losses in a row at different sizes:

• 1%: 0.99⁷ ≈ 0.932, a 6.8% drawdown
• 2%: 0.98⁷ ≈ 0.868, 13.2%
• 5%: 0.95⁷ ≈ 0.698, 30.2%
• 25%: 0.75⁷ ≈ 0.133, 86.7%

At 1% and 2% the hole stays shallow, where the gain needed to recover is barely bigger than the loss. At 5% it already needs about +43% to repair, and at 25% the plan is effectively over.

This is the arithmetic behind keeping the risk per trade small (module 3). It also explains a rule many careful traders use, Marc included: when a drawdown reaches a set level, cut the risk per trade and review the journal, never raise it to win the money back.

A positive average result per trade is not enough on its own. The same 40 trades, averaging +0.125 risk units, ended at +4.7% when each risked 1% of the account and at −67% when each risked 25%, after an 88.7% drawdown. A good plan at a reckless size is a bad plan.

So every plan needs two answers, not one: is the expectancy positive after costs, and is the size small enough that its normal losing runs stay shallow? Marc writes down two numbers every Friday: his account's peak and how far below it he is now. If the drawdown reaches 10%, he halves his risk per trade and reviews the journal.

How it fits together: drawdown measures the fall from the peak, recovery needs more than the loss, and size decides how deep a losing run digs. The module's case, Case: compare two trade lists, puts expectancy, drawdown, sample size and steady risk to work on two journals.