Why a 30% Gain Does Not Recover a 30% Loss
After a loss, returns apply to a smaller amount, so recovering principal requires a larger percentage gain. Explore compounding, the illusion created by new deposits, and the impact of withdrawals.
The return needed after a loss equals the loss rate divided by one minus the loss rate. After a 30% decline, 70% of the original capital remains, so recovery requires a gain of approximately 42.86%. Declines and gains apply to different base amounts, so equal percentages do not offset each other.
Write down the amounts first to see the denominator
Losing 20 from an initial 100 leaves 80. You need to earn 20 again, but that 20 is 25% of the remaining 80. If the loss rate is expressed as decimal d, the recovery return is 1÷(1−d)−1, or d÷(1−d). As the loss grows, the denominator shrinks and the required recovery return rises steeply. At a 100% loss, the denominator becomes zero, so recovery cannot be described by a return on the remaining assets alone.
Distinguish the arithmetic average from the actual compounded result
If an investment rises 20% in one period and falls 20% in the next, the arithmetic average return is 0%, but the asset value becomes 1.2×0.8=0.96 times its starting value. Rather than adding period returns, multiply the factors obtained by adding each return to 1. With no deposits or withdrawals, reordering the same returns leaves the final product unchanged, but contributions or withdrawals along the way can change the resulting amounts. This is why cash flows must be considered when evaluating recovery.
Do not mistake additional deposits for investment performance
Adding money to a loss-making account until the balance returns to the initial capital does not mean the investment loss has been recovered. Separate existing funds from new contributions and examine returns adjusted for external cash flows. Increasing trade size because the required recovery return looks large does not guarantee recovery. Treat the higher recovery target and the risk level appropriate to current assets as separate questions.
Recovery calculations must also use consistent treatment of dividends and distributions. Even if the price remains below your purchase price, cash received along the way makes total return different from the price gain or loss. Dividends spent on living expenses no longer remain in the account balance, so assess balance recovery separately from recovery in total investment return. When citing a loss rate, specify whether it reflects price alone or includes cash income, so the required recovery return can be interpreted on the same basis.
Worked example
Hypothetical example: KRW 10 million falls 30% to KRW 7 million. A subsequent 30% gain brings it to KRW 9.1 million, still KRW 900,000 below the original capital. Recovery requires 300÷700≈42.86%. A 50% loss requires a 100% gain, and a 60% loss requires a 150% gain. If you withdraw KRW 1 million for living expenses from the KRW 7 million balance, KRW 6 million remains invested. Raising the account balance to KRW 10 million now requires a 66.67% gain, but treating the withdrawal as an investment loss would distort performance.
What to check
- Have you used post-loss assets as the denominator for the recovery return?
- Have you multiplied return factors rather than adding period returns?
- Have you shown additional deposits and withdrawals separately?
- Are you increasing your risk budget because of the recovery target?
Sources and primary materials
This is educational material about research methods. For an actual company decision, verify the filings and primary sources for the relevant period.