The drawdown recovery table
Lesson 2 · about 7 min
A loss and the gain needed to undo it are not the same size. This is the single most under-appreciated fact in retail trading, and it is pure arithmetic.
Why a 50% loss needs a 100% gain
Start with $10,000. Lose 50%. You now have $5,000.
To get back to $10,000 you need to make $5,000. But $5,000 is not 50% of what you have now; it is 100% of it. You must double the account just to break even.
The general formula for the gain needed to recover from a loss of L (expressed as a fraction) is:
gain needed = L ÷ (1 − L)
Check it with the 50% case: 0.5 ÷ (1 − 0.5) = 0.5 ÷ 0.5 = 1.0, which is 100%.
Now the 10% case: 0.1 ÷ 0.9 = 0.111, which is 11.1%. Lose $1,000 from $10,000 and you have $9,000; $1,000 is 11.1% of $9,000.
The table
| Drawdown | Account left ($10,000 start) | Gain needed to break even |
|---|---|---|
| 5% | $9,500 | 5.3% |
| 10% | $9,000 | 11.1% |
| 15% | $8,500 | 17.6% |
| 20% | $8,000 | 25.0% |
| 25% | $7,500 | 33.3% |
| 30% | $7,000 | 42.9% |
| 40% | $6,000 | 66.7% |
| 50% | $5,000 | 100% |
| 60% | $4,000 | 150% |
| 75% | $2,500 | 300% |
| 90% | $1,000 | 900% |
Read down the third column. Up to about 20% the required gain is only slightly larger than the loss. Past 30% the curve bends hard. Past 50% you are in territory that most traders never climb out of, because the return needed exceeds anything a sensible risk plan produces in a year.
Key idea: Drawdowns get more expensive the deeper they go. The first 10% costs 11% to fix; the next 40% costs another 89% on top of that.
Recovery takes time, not just percentage
Percentages hide the calendar. Suppose you are a competent trader who averages a 2% gain per month after costs (this is an illustration, not a promise; many good traders do worse in a given year). How long does each recovery take?
months to recover = ln(1 + gain needed) ÷ ln(1.02)
| Drawdown | Gain needed | Months at 2% per month |
|---|---|---|
| 5% | 5.3% | 2.6 |
| 10% | 11.1% | 5.3 |
| 20% | 25% | 11.3 |
| 30% | 42.9% | 18.0 |
| 50% | 100% | 35.0 |
| 75% | 300% | 70.0 |
A 30% drawdown costs a year and a half of good trading just to get back to where you started. A 50% drawdown costs three years. Most people do not have three years of patience, which is why deep drawdowns so often end with the trader either quitting or "going big to get it back", which is how a 50% drawdown becomes a 90% one.
Worked example
Account: $8,000. A bad month leaves it at $6,000.
- Drawdown = (8,000 − 6,000) ÷ 8,000 = 0.25, or 25%.
- Gain needed = 0.25 ÷ 0.75 = 0.333, or 33.3%.
- Check: $6,000 × 1.333 = $8,000.
- At 2% per month: ln(1.333) ÷ ln(1.02) = 0.288 ÷ 0.0198 = 14.5 months.
Now redo it for a trader who lost the same number of trades but was risking half as much per trade. A 25% drawdown becomes roughly a 13% drawdown (not exactly half, because of compounding; 0.87^k versus 0.75^k for the same k). Gain needed = 0.13 ÷ 0.87 = 14.9%. Time at 2% per month = ln(1.149) ÷ ln(1.02) = 0.139 ÷ 0.0198 = 7.0 months.
Halving the size did not halve the pain. It cut the recovery time by more than half, because you never reached the steep part of the curve.
Try it: Look at the worst peak-to-trough drop your account (or your paper account) has had. Compute the gain you needed to recover using L ÷ (1 − L). If you have recovered, count how many months it actually took. If not, that number is the price of the sizing you were using.
Recap
- Gain needed to recover = loss ÷ (1 − loss). A 10% loss needs 11.1%; a 50% loss needs 100%.
- The curve is gentle to about 20% and steep after 30%.
- Time to recover grows even faster than the percentage: a 30% drawdown can cost a year and a half of good trading.
- Smaller size keeps you on the flat part of the curve, where recovery is quick and cheap.
- Everything in this course is designed to keep your drawdowns under the bend.
See it drawn
Original diagrams for the ideas on this page. Illustrative, not real market data.