Lose 50% and you need +100% to get back to where you started. This asymmetry is one of the most important ideas in investing and trading, and one of the least intuitive. Here's the formula, a full table and what it means for how you manage risk.
Percentage change formula
Percentage change = (New value − Old value) ÷ Old value × 100
Example: a position falls from $100 to $60: (60 − 100) ÷ 100 = −40%.
Gain needed to recover
To get from the new value back to the old value:
Gain needed = Old value ÷ New value − 1
or, from the loss percentage alone:
Gain needed = 1 ÷ (1 − Loss) − 1
From $60 back to $100: 100 ÷ 60 − 1 = +66.7%.
The gain is bigger than the loss because it's calculated on a smaller base. The $40 you lost was 40% of $100, but it's 66.7% of the $60 you have left.
Recovery table
| Loss | Gain needed to break even |
|---|---|
| −5% | +5.3% |
| −10% | +11.1% |
| −20% | +25.0% |
| −25% | +33.3% |
| −30% | +42.9% |
| −40% | +66.7% |
| −50% | +100% |
| −60% | +150% |
| −75% | +300% |
| −90% | +900% |
Small losses are almost symmetric. Big ones aren't: past about −30%, the required gain climbs very fast. A −90% loss needs the remaining money to grow ten times.
Calculate any change or recovery in the free percentage change & loss recovery calculator.
Multiple losses multiply
Consecutive percentage changes multiply rather than add:
- −20% then −20% → 0.8 × 0.8 = 0.64 → −36% total, needing +56.25% to recover
- +50% then −50% → 1.5 × 0.5 = 0.75 → −25% total, even though the percentages "cancel out"
- −50% then +50% → the same 0.75, order doesn't matter
This is why a volatile investment can have a positive average return and still lose money: the losses take a bigger bite than the same-sized gains give back.
Time to recover
Recovery also takes time. If a portfolio drops 40% and then grows at 7% a year, it needs ln(1.667) ÷ ln(1.07) ≈ 7.5 years just to get back to even, assuming no further losses and no new contributions. Regular contributions shorten that, which is one reason steady investing through downturns works.
What it means for traders
- Avoid large drawdowns, not just losing trades. A 10% drawdown is a speed bump. A 50% drawdown is a crisis that takes a doubling to fix.
- Keep risk per trade small. At 1% risk per trade, ten consecutive losses cost about 9.6%. At 10% per trade, they cost about 65%, which needs +187% to recover. The position sizing formula shows how to keep risk fixed.
- Don't double down to "get it back". Increasing size after losses means the next loss is bigger, from an already smaller account.
- Leverage magnifies the asymmetry. At 10x, a 5% adverse move is a 50% loss on margin. See how to calculate liquidation price.
Worked example: a portfolio drawdown
A $20,000 portfolio drops to $13,000, a −35% drawdown. Gain needed = 20,000 ÷ 13,000 − 1 = +53.8%. If you add $500 a month during the recovery, you need less investment growth, because new money also rebuilds the balance. Contributions are a recovery tool that doesn't depend on the market.
What it means for investors
- Diversification reduces the chance of a single holding causing a deep loss.
- Rebalancing trims what has run up and adds to what has fallen, keeping risk near your plan.
- Time horizon matters: money needed in two years shouldn't sit in something that can fall 50%.
Calculating percentage change correctly
A few mistakes to avoid:
- Wrong base: a change from 80 to 100 is +25%, but from 100 to 80 it's −20%. Always divide by the starting value.
- Percentage points vs percent: an interest rate going from 4% to 5% is +1 percentage point, but a 25% increase.
- Averaging percentages: the average of +50% and −50% is 0%, but the compounded result is −25%.
Frequently asked questions
Does the recovery math apply to crypto, stocks and businesses? Yes, to anything measured in percentage changes: portfolio values, prices, revenue or website traffic.
Is a drawdown the same as a loss? A drawdown is the decline from a peak to a later low, whether or not you sold. A realized loss is locked in when you close the position. The recovery math is the same for both.
Can averaging down speed up recovery? Buying more at a lower price lowers your average cost, so a smaller rebound gets you back to even. It also raises your exposure if the price keeps falling. Use the DCA calculator to see your average price, and set a risk limit first.
Why do index funds recover from crashes but some stocks don't? A broad index is diversified, so it reflects the whole market's recovery. An individual company can lose value permanently if the business fails. The recovery math is the same, but the likelihood of reaching break-even is very different.
Key takeaways
- Gain needed = 1 ÷ (1 − Loss) − 1.
- Small losses are nearly symmetric; big losses are not.
- Consecutive percentage changes multiply, they don't add.
- Keeping drawdowns small matters more than chasing big wins.
Track drawdowns in your journal
Knowing your maximum drawdown, and how long recoveries take, tells you far more about a strategy's risk than its best months do. The Crypto & Stock Trading Journal template tracks your equity curve, drawdowns and R-multiples from every logged trade.