Drawdown y las matemáticas de la recuperación: por qué una pérdida del 50% exige una ganancia del 100%

Losses and gains use the same units and behave like different animals. Lose 10% and a 10% gain does not repair it; lose half and the repair job is a double. This sheet derives that asymmetry once, so you never have to memorize it, then adds the second piece of mathematics every trader meets eventually: losing streaks of surprising length are a statistical certainty even for genuinely good methods. Put the two together and the case for small risk per trade stops being a personality trait and becomes arithmetic.

The recovery table — derived once, remembered forever

The asymmetry has nothing to do with markets; it is what percentages do. A loss shrinks the base that the recovery must be earned on. Drop a $10,000 account by 10% and $9,000 remains; the missing $1,000 is now 11.1% of the smaller base. The general rule follows in one line:

Read the table as two regimes. Down to roughly −20%, recovery costs only slightly more than was lost — a disciplined process can plausibly earn it back the same way it was lost, a percent at a time. Beyond −30% the curve turns vicious: the required gain grows faster than the drawdown, and the trader is asked to perform far better than they did before the damage, with a smaller account and worse morale. The practical lesson is not “recover harder”. It is that deep ▲drawdown must be priced as nearly irreversible — and prevented at the sizing stage, because no later stage can cheaply undo it.

Streak math: seven losses is not bad luck

Now the second piece. Take a method that genuinely wins 55% of the time — a strong result, better than most real records. The chance that any single trade loses is 45%, so the chance of seven consecutive losses starting at a given trade is 0.45⁷, about 0.37%. That sounds reassuring until you remember how many starting points a trading year contains. Computed exactly over a sequence of independent trades, the probability that at least one run of seven straight losses appears is:

A trader taking four trades a week reaches 200 trades inside a year — carrying a one-in-three chance of a seven-loss streak with a method that is working exactly as designed. Over a multi-year career the streak is close to certain. And seven is only the headline number: runs of five are routine, and the same arithmetic puts longer runs on the table for any realistic win rate. This is why interpreting a losing run as proof the method broke is usually wrong — the streak is what the method's own probabilities, working correctly, were always going to produce.

Sizing must therefore assume the streak in advance. At 1% risk per trade, seven losses cost about 6.8% of equity — the gentle end of the recovery table, repaired by a +7.3% run that the same method is equally capable of producing. At 5%, the identical streak costs about 30%, which the table prices at +43% to repair — the start of the vicious regime, now demanded from a trader who has just watched a third of the account disappear. Same method, same streak, same market. Only the sizing differed, and it was chosen before the first of the seven trades.

Risk-of-ruin: the concept, simplified

Risk-of-ruin asks the terminal question: what is the probability the account ever reaches a level it cannot continue from? The classical model is simplified — even-money payoffs, a fixed win rate, independent trades — but its shape is instructive. For a method winning 55% of even-money bets, ruin probability is approximately:

The model's numbers should not be quoted as precise — real trading violates all three of its assumptions, usually in the unfavourable direction. What is robust is the exponent. Ruin probability falls exponentially as risk per trade shrinks, because smaller risk means more units of capital between you and the floor. The 10% riser and the 1% riser can share an identical method and live in different statistical universes: one has a measurable chance of ending, the other's ruin probability has nine zeros after the decimal point. Nothing about forecasting skill appears anywhere in that calculation.

Equity vs balance: reading your own drawdown honestly

One bookkeeping habit decides whether you notice a drawdown while it is still in the gentle regime. ▲Balance is the result of closed trades only; it does not move while a losing position stays open. ▲Equity is balance plus ▲unrealized P/L — what the account is actually worth at this moment. A trader holding three losing positions “because they haven't lost until I close them” has a flat balance and a falling equity, and the falling number is the true one: it is what margin is measured against, and what a forced liquidation would crystallize.

Numbers make the gap concrete. An account with a $10,000 balance holds two open positions showing −$800 and −$700 of unrealized loss: the platform's balance field still reads $10,000, but equity reads $8,500 — a 15% drawdown that the comfortable number hides completely. The symmetry cuts both ways, of course: open profits push equity above balance just as silently, and counting those as banked is the mirror-image mistake. Whichever direction the gap runs, equity is the number telling the truth.

So measure drawdown the way an auditor would: from the highest equity the account has reached to its lowest point since — peak to trough, open positions included. Refusing to close a loser does not pause the drawdown; it only pauses the balance, while the real number quietly crosses from the recoverable rows of the table toward the vicious ones. The sheet on margin calls in this region shows where that road ends when leverage is involved.

The design conclusion: sizing is drawdown control

Assemble the three results. Recovery costs grow non-linearly, so drawdowns must be kept shallow. Streaks long enough to create deep drawdowns are statistically guaranteed, so “avoid losing streaks” is not an available strategy. And ruin probability is driven toward zero by one variable — the fraction of equity risked per trade. The only place a trader controls their future drawdown is at the sizing step, before any trade is taken. Choose 1% and the guaranteed bad stretch costs single digits and a manageable recovery. Choose 10% and the same mathematics, with the same method, writes a different ending. The forecast never enters into it.

A practical supplement, once the sizing is right: give the account a circuit breaker. A pre-committed pause point — stop trading for the week after, say, a 5% equity drawdown — costs nothing when things go well and interrupts the one behaviour the tables cannot model: a stressed trader raising risk mid-streak to force a recovery. The mathematics of this sheet keeps drawdowns shallow only while the risk fraction stays fixed. The circuit breaker is how it stays fixed.