Why losses and gains are asymmetric
A percentage loss and an equal percentage gain act on different starting balances. If $100 falls 20%, $80 remains. A 20% gain on $80 adds only $16, leaving $96. Returning from $80 to $100 requires $20, which is 25% of the reduced balance. The calculation is arithmetic, but its portfolio implication is important: preventing a deep drawdown is usually easier than earning the recovery that follows it.
required gain = [1 ÷ (1 − loss as a decimal)] − 1
loss offset by a gain = gain ÷ (1 + gain)
years at return r = ln[1 ÷ (1 − loss)] ÷ ln(1 + r)The inverse mode answers a different question: how large a prior loss could a known gain offset? A 25% gain takes a balance from 80 to 100, so it offsets a 20% loss. The time estimate assumes smooth annual compounding at a constant rate. Markets do not deliver smooth returns, so those years are scale markers rather than a promise or a retirement forecast.
Worked examples
A 50% drawdown leaves half the starting capital. Doubling that half is necessary to return to the original value, so the required gain is 100%. A 70% loss leaves 30 cents per original dollar; recovering the missing 70 cents requires a 233.3% gain on the remaining 30 cents. At a constant 10% annual compound rate, that 70% drawdown would take roughly 12.6 years to erase.
These figures also explain why averaging down does not remove risk. Adding capital can lower the average entry price, but it increases dollars exposed. The portfolio-level drawdown still determines the gain needed to restore the prior high-water mark. The right comparison is total equity before and after all cash flows, not the percentage move of a single lot.
Loss-to-recovery reference table
| Loss | Gain needed | Years at 7% | Years at 10% |
|---|---|---|---|
| 5% | 5.3% | 0.8 | 0.5 |
| 10% | 11.1% | 1.6 | 1.1 |
| 20% | 25.0% | 3.3 | 2.3 |
| 30% | 42.9% | 5.3 | 3.7 |
| 50% | 100.0% | 10.2 | 7.3 |
| 70% | 233.3% | 17.8 | 12.6 |
| 80% | 400.0% | 23.8 | 16.9 |
| 90% | 900.0% | 34.0 | 24.2 |
Using drawdown math in risk limits
Drawdown limits should be chosen before a difficult period, not improvised inside one. A trader can combine per-position sizing, portfolio concentration limits, and a maximum equity drawdown that forces de-risking or review. The position size calculator turns a per-trade risk budget into units. The recovery table then shows why several correlated 1% risks are not necessarily independent.
Recovery time is calendar-dependent as well as return-dependent; the days between dates calculator can measure an actual underwater period. Outside finance, use the TDEE calculator for formula-transparent calorie planning or the travel data calculator to add a quantified safety buffer to an eSIM plan.
Frequently asked questions
Why does a loss need a larger percentage gain to recover?
The gain is applied to the smaller balance that remains after the loss. After a 20% loss, only 80% remains, and the missing 20 is one quarter of 80. That changing denominator creates the asymmetry; it is not a fee, penalty, or forecasting assumption.
Why does a 50% loss require a 100% gain?
A 50% loss cuts the balance in half. Returning from one half to the original whole means doubling the remaining money, and a doubling is a 100% gain. Another 50% gain would restore only three quarters of the starting balance.
How should drawdown recovery affect position sizing?
It argues for controlling portfolio loss before it becomes nonlinear. Size each trade from a defined loss budget, account for correlation across positions, and reduce exposure when aggregate risk breaches a precommitted limit. Recovery math does not select trades; it shows the capital cost of poor risk containment.
Do deposits or withdrawals change the recovery calculation?
They change account value but are not investment return. For a clean performance drawdown, adjust the equity series for external cash flows or use a time-weighted return method. This calculator assumes no deposits or withdrawals between the peak, trough, and recovery.