One table that should change how you think about position sizing forever:
| Drawdown | Gain needed to recover |
|---|---|
| 10% | 11% |
| 20% | 25% |
| 30% | 43% |
| 40% | 67% |
| 50% | 100% |
| 60% | 150% |
| 70% | 233% |
| 80% | 400% |
| 90% | 900% |
The math is straightforward. Lose 50% of your account, you have half left. Get back to even, you need to double what you have left. A 100% gain.
The asymmetry is brutal. It is the single most important fact in trading risk management. Most traders underestimate how much it matters until they experience it personally — usually once, often catastrophically.
Multiplication is not commutative with subtraction. Losing 50% then gaining 50% does not return you to where you started; it leaves you at 75% of original capital.
\`\`\`
$100 → lose 50% → $50 → gain 50% → $75
\`\`\`
Going from \$50 back to \$100 requires gaining \$50 on a \$50 base. That is a 100% return, not 50%.
Every consecutive return follows this logic. A 30% loss followed by a 30% gain leaves you at \$91, not \$100. Even small losses require slightly larger gains to recover.
Most strategies produce some losing months mixed with winning months. Consider monthly returns of:
\`\`\`
+10%, +10%, +10%, -20%
\`\`\`
Sum: +10%. Sounds great. Actual final balance starting from \$100:
\`\`\`
$100 × 1.10 × 1.10 × 1.10 × 0.80 = $106.48
\`\`\`
You made 6.48% over four months despite three winning months of 10% each, because the one losing month at 20% pulled the geometric average down hard.
The lesson: a strategy with high volatility (large up and down months) compounds worse than a strategy with the same average return but lower volatility. Smooth returns are mathematically superior at the same arithmetic average.
The fundamental insight: avoiding large drawdowns is mathematically more valuable than capturing large gains.
A trader who takes 10% positions and has a 30% loss on one ends with a 3% account drawdown. Easy to recover from.
The same trader at 50% positions has a 15% account drawdown. Harder.
At 100% positions, they are in serious trouble.
Position sizing implication: never have any single position large enough that its maximum reasonable loss would push your account into hard-to-recover territory.
What is "hard to recover"? Most experienced traders set their personal limit at 20% drawdown. Beyond that, the psychological cost of trading back to even — combined with the mathematical difficulty — leads many traders to abandon their strategy at exactly the wrong time.
If you set 20% as your maximum, position sizes should be calibrated so that even three or four bad trades in a row do not threaten that limit.
Sharpe ratio normalises returns by volatility, which sounds like it accounts for the drawdown asymmetry. It only partially does.
A Sharpe 1.5 strategy at 50% annualised volatility produces a different equity curve than a Sharpe 1.5 strategy at 10% annualised volatility. The high-vol version has much larger drawdowns and recoveries even if the long-term return is similar. The low-vol version is mathematically superior for compounding.
Calmar ratio (annualised return divided by max drawdown) is a better metric for this reason. Calmar 1.0 (you earn what you risk losing) is decent. Calmar 2.0 or higher is excellent. Most strategies that look great on Sharpe alone have mediocre Calmar.
Leverage amplifies both returns and drawdowns proportionally. A strategy with 2% expected monthly return and 5% monthly volatility at 1x becomes 4% expected return and 10% volatility at 2x. The Sharpe ratio is unchanged.
But the drawdown profile changes dramatically. Where 1x might have a 15% max drawdown over a year, 2x has 30%. And recovering from a 30% drawdown requires a 43% gain, not a 30% gain.
Honest take: most strategies that look attractive at 2-3x leverage are unattractive at 1x. Traders use leverage to make modest-return strategies look impressive. The mathematical reality is that the modest-return version at 1x compounds better over the long run, because the leveraged version's drawdowns make recovery harder.
Three rules emerge from the drawdown math:
**Never let any single trade matter that much.** If a single bad trade can put you in a 20%+ drawdown, your position size is too large. Reduce until single-trade risk is bounded.
**Prefer smooth returns to spiky returns.** A 1% per month with 2% volatility is better than 2% per month with 8% volatility, despite the higher arithmetic average of the latter. The geometric average — what you actually earn — favours the smoother one.
**Reduce leverage in losing periods.** Down 10% from peak, reduce sizes by 25%. Down 15%, reduce by 50%. Sounds defeatist but prevents the 50%-drawdown scenario that requires 100% to recover. Full size returns only when you have made back the losses.
Beyond the math, drawdowns have a psychological cost that compounds the mathematical one.
Most traders who hit a 50% drawdown abandon their strategy at exactly the wrong time. They switch strategies, reduce sizing dramatically, or quit entirely. Even if the original strategy would have recovered, the trader is no longer running it. The mathematical recovery does not happen because the human gave up.
Strategies need to be designed not just to be profitable, but to be psychologically tolerable through their worst expected drawdown. A theoretical 60% max drawdown is essentially untrade-able by most humans. The strategy's profitability is irrelevant if the human cannot stick with it through the bad periods.
Q: Is there any way to recover from a 90% drawdown other than the 900% return?
Mathematically, no. Practically, the only "recovery" from 90% is starting over with new capital. Which is why preventing extreme drawdowns matters far more than maximising returns. A strategy that could have made 30% but instead lost 70% on a tail event is a worse strategy than one that consistently makes 15% with 20% max drawdown.
Q: How do I know what my maximum realistic drawdown will be?
Take your backtest's worst drawdown and multiply by 1.5-2.0. Real drawdowns almost always exceed backtest drawdowns because reality includes events your backtest data did not contain. Backtest shows 20% max drawdown? Plan emotionally and financially for 30-40%.
Q: Should I add to losing positions to lower my average?
The classic martingale trap. Mostly no. Adding to losers feels rational ("the position will recover and I will have lowered my average") but mathematically amplifies your loss when the position keeps going against you. Size your trades initially and let them play out — do not throw good money after bad.
Q: Does dollar-cost averaging count as adding to losers?
Different concept, different math. DCA is buying a fixed amount on a schedule regardless of price, well-understood properties for long-term passive investing. Adding to a losing trading position is taking increased exposure to a position your thesis is already wrong about. First is investment discipline; second is martingale gambling.