Hong Life CalculatorsUnderstanding the loss recovery calculator — concept and principle
When an investment falls, getting back to where you started takes a bigger percentage gain than the percentage you lost. This calculator shows the exact gain needed to break even after any loss, and how many years that recovery would take at an expected annual return. It is useful after a market drop, when judging a fund's drawdown, or when setting a stop-loss rule.
How it is calculated
Let L be the loss as a decimal (30% = 0.30). After the loss, each dollar is worth (1 − L).
- Gain needed: G = 1 ÷ (1 − L) − 1, which equals L ÷ (1 − L).
- Years to recover at annual return r: t = ln(1 ÷ (1 − L)) ÷ ln(1 + r).
- The loss must be below 100%; a total loss cannot be recovered.
The reference rows show common cases: a 10% loss needs 11.1%, a 50% loss needs 100%, and an 80% loss needs 400%.
The principle
Percentages are measured against a base, and a loss shrinks the base. After falling from 100 to 70, a 30-point rise is measured against 70, not 100, so it is a 42.9% gain. The deeper the loss, the faster the required gain grows: the curve L ÷ (1 − L) rises gently for small losses and explodes as L approaches 100%. This asymmetry is why avoiding large drawdowns matters more than chasing an occasional big win. The recovery time comes from compound growth: you need (1 + r)^t = 1 ÷ (1 − L), and taking logarithms solves for t.
Worked example
Default inputs: loss 30%, expected annual return 8%.
- Value left per dollar: 1 − 0.30 = 0.70.
- Gain needed = 1 ÷ 0.70 − 1 = 0.4286 = 42.9%.
- Years at 8%: ln(1 ÷ 0.70) ÷ ln(1.08) = 0.3567 ÷ 0.0770 = 4.6 years.
How to read the result
Losses up to about 10–15% need only slightly larger gains to recover. Beyond 30%, the required gain becomes large, and beyond 50% it is more than double the loss. Recovery time depends heavily on the return you assume: halving the expected return roughly doubles the time. Broad stock markets have had drawdowns of 50% or more in severe bear markets, and recovery has sometimes taken many years, so time horizon matters.
Common mistakes
- Thinking a 30% loss is undone by a 30% gain (it leaves you at 91% of the start).
- Averaging percentage returns: −50% then +50% averages 0% but leaves you 25% down.
- Assuming the expected return will arrive steadily every year.
- Forgetting that fees, taxes and withdrawals during the recovery make it slower.
Frequently asked questions
How much gain do I need after a 20% loss?
1 ÷ 0.8 − 1 = 25%.
Does adding money help me recover faster?
Your account balance recovers sooner because of the new money, but the original investment still needs the same percentage gain.
Why does a 50% loss need a 100% gain?
Half of the value is gone, so the remaining half has to double to get back to the start.
Sources: Bodie, Kane and Marcus, Investments (holding-period and compound returns)