The Cruel Arithmetic of Drawdown

Quick question, and be honest about your gut answer before reading on: if your account falls 50%, what gain do you need to get back to where you started?

Most people's gut says 50%. It's wrong, and the size of the error is the whole point of this chapter.

Do the arithmetic. Start with ₹1,00,000. Lose 50%: you have ₹50,000. To get back to ₹1,00,000 from ₹50,000, you don't need to gain 50% of your original capital — you need to gain 50,000 on a base of 50,000. That's a 100% gain, just to break even.

Look at the figure and let the full cruelty of the pattern sink in: lose 20%, you need +25% back. Lose 50%, you need +100%. Lose 80%, and you need a +400% gain just to be whole again. The relationship isn't a straight line — it's a curve that gets savagely steeper exactly as your account gets smaller, which is precisely the moment you have the least capital left to compound your way out.

RECOVERY NEEDED = LOSS % ÷ (100% − LOSS %)

Lose 50%: 50 ÷ 50 = 100% needed to recover

Lose 80%: 80 ÷ 20 = 400% needed to recover

This asymmetry is not a rare edge case. It's the mathematical law hiding underneath every single number you've met in this school so far, and it's the real reason Chapter 1's 1%-versus-10% choice matters as much as it does. A big loss doesn't just cost you money — it costs you exponentially more effort to earn back, at exactly the moment you're least equipped to provide that effort.

Now connect this to a number every trader underestimates: how many losses in a row is actually normal? Even a genuinely good strategy with a 55% win rate — a perfectly healthy edge — will, over enough trades, produce losing streaks far longer than intuition expects. Basic probability says a 55%-win-rate system will, somewhere across a few hundred trades, very plausibly produce 8, 9, even 10 consecutive losses — not because anything broke, but because that's what randomness does to a coin that's only slightly weighted in your favour. Traders who don't know this fact assume a 7-loss streak means the strategy stopped working, and abandon a perfectly good system at exactly the point (Chapter 4's expectancy, remember) where the averages were about to reassert themselves.

Put the two facts together — the asymmetric recovery curve, and the reality of long losing streaks — and you get the actual purpose of Chapter 2's position-sizing formula, stated properly for the first time:

Position size should be chosen so that your worst REALISTIC losing streak doesn't produce a drawdown you can't mathematically recover from.

Run the numbers at different risk-per-trade levels, ten losses in a row (a real, expectable event for many strategies, not a black swan):

At 1% risk per trade, ten straight losses costs roughly 10% of the account (slightly less, since each loss is 1% of a shrinking base) — painful, fully recoverable, requiring roughly an +11% gain to be whole.

At 5% risk per trade, ten straight losses costs roughly 40% of the account — requiring a +67% gain to recover.

At 10% risk per trade — Trader B's number from Chapter 1 — ten straight losses costs roughly 65% of the account, requiring nearly a +190% gain just to break even. This is not a hypothetical. This is the exact, ordinary mathematics of Chapter 1's story, now shown in full.

The number professionals actually watch, alongside individual position risk, is maximum portfolio drawdown — the worst peak-to-trough decline your entire account has experienced or is willing to tolerate. Many professional risk frameworks draw a hard line around 20% drawdown as the point where a strategy (or a trader) needs to stop, review, and potentially resize — not because 20% is unrecoverable (it needs +25%, manageable), but because the psychological damage of watching a fifth of your capital vanish tends to produce exactly the panic decisions the Psychology school warned you about, right when clear thinking matters most.

This is also where the phrase risk of ruin earns its place — the mathematical probability that a given strategy, at a given size, eventually loses so much capital that recovery becomes practically impossible (either the money's gone, or the psychological will to continue is). Every input you've met so far feeds it: win rate, average win/loss size (R and expectancy), and — the variable you actually control — position size. The honest, humbling conclusion of risk-of-ruin mathematics is the same conclusion Chapter 1 opened with: a strategy with real edge can still be sized into ruin, and a mediocre strategy sized conservatively can survive indefinitely. Sizing isn't secondary to edge. It's the variable that decides whether edge ever gets the chance to compound.

You now understand why 1–2% risk per trade isn't a cautious suggestion — it's the number that survives the losing streak your strategy will actually deal you, with room to keep compounding afterward. Chapter 6 adds the final multiplier that can undo all of this arithmetic in a single afternoon: leverage.