A 20 percent loss takes a 25 percent gain to get back to even. Start at $10,000, lose 20 percent, and the balance is $8,000; returning to $10,000 means adding $2,000 to an $8,000 base, and $2,000 ÷ $8,000 is 25 percent. The required gain is G = L ÷ (1 − L), where L is the loss as a decimal. The condition that raises the answer further is cost: fees, spreads and taxes come out of the recovery, so the gain needed on a real account is larger than the formula's figure.
The second percentage runs on a smaller base
Start with a value of 1. A loss of fraction L leaves 1 − L. Getting back to 1 takes a gain G that satisfies (1 − L) × (1 + G) = 1, so 1 + G = 1 ÷ (1 − L) and G = L ÷ (1 − L).
Every term in that expression is the base problem. The loss is charged against the original value; the recovery is charged against the survivor. At L = 0.20 the loss costs 20 points out of 100, and the same 20 percent applied to the remaining 80 returns only 16 points. The gap widens as L grows, because the denominator 1 − L shrinks while the numerator L rises. At L = 1 the formula divides by zero, which is the arithmetic statement that nothing finite recovers a total loss.
The required gain climbs faster than the loss
The table applies G = L ÷ (1 − L) to five loss levels, on an illustrative $10,000 starting value because no public figure fixes an account balance. Percentages are rounded to two decimals; the dollar columns use the unrounded formula. No distributions, fees or taxes are included.
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| Loss | Value after loss | Required gain | Dollars needed back | Ending value |
|---|---|---|---|---|
| 10% | $9,000 | 11.11% | $1,000 | $10,000 |
| 20% | $8,000 | 25.00% | $2,000 | $10,000 |
| 33% | $6,700 | 49.25% | $3,300 | $10,000 |
| 50% | $5,000 | 100.00% | $5,000 | $10,000 |
| 75% | $2,500 | 300.00% | $7,500 | $10,000 |
Check two rows. At 33 percent, 0.33 ÷ 0.67 = 0.492537, or 49.25 percent, and 49.25 percent of $6,700 is $3,300. At 75 percent, 0.75 ÷ 0.25 = 3.00, so $2,500 has to quadruple, adding $7,500 to reach $10,000. A loss of 10 percent needs barely more than 10 percent back. A loss of 50 percent needs a doubling.
A 20 percent fall and a 20 percent rebound are not a round trip
The figure 20 percent appears in two separate rules, and neither one is symmetric. Investor.gov's bear market entry puts a bear market at a broad index falling 20 percent or more over at least a two-month period, and its bull market entry puts a bull market at a rise of 20 percent or more over the same minimum period. An index that meets the first and then meets the second is still 4 percent below where it started, because 20 percent of 80 is 16.
The SEC's investor bulletin on market-wide circuit breakers carries the same figure on a one-day clock: a 20 percent decline in the S&P 500 is a Level 3 halt and stops trading for the remainder of the day, with Level 1 at 7 percent and Level 2 at 13 percent each halting trading for 15 minutes before 3:25 p.m. A close 20 percent down needs a 25 percent rise from that close to get the index back to the prior day's level, and a 7 percent Level 1 decline needs 7.53 percent back, since 0.07 ÷ 0.93 = 0.0753.
The formula gives a size, not a schedule
G = L ÷ (1 − L) gives a magnitude, not a schedule. It says how large the gain has to be, never when or whether it arrives, and a path that reaches the required percentage can pass through lower prices on the way, which is the mechanism in a rising market can still be volatile. The two labels that go with the two percentages are separated in bull and bear markets, and the fields that make any two return figures comparable are listed in comparing market moves on the same basis.
Source references
Primary sources used for this guide. Follow the links for the original scope, definitions and conditions.
- Bear Market | Investor.govAccessed 2026-09-17
- Bull Market | Investor.govAccessed 2026-09-17
- Investor Bulletin: New Measures to Address Market Volatility | SEC.govAccessed 2026-09-17