The recovery gap
The asymmetry between a fall and its recovery is the useful output here:
| Fall | Rise needed to recover | | --- | --- | | −10% | +11.1% | | −20% | +25% | | −33% | +49.3% | | −50% | +100% | | −80% | +400% |
It grows quickly, which is why a large drawdown is much worse than it first sounds. This is a fact about arithmetic, not about markets.
Where a decrease is applied twice
A discount on a discount, an inflation-adjusted figure that is then discounted, a fee taken from an amount that already had a fee taken. Each reduction applies to what is left, so the total is never the sum of the parts.
Questions
Why does getting back cost more percent?+
Because the recovery is measured against the reduced number. Drop 1,000 by 20% and you have 800; getting from 800 back to 1,000 is a rise of 25%, not 20%. The base is smaller, so the same absolute amount is a larger share of it.
Can a decrease exceed 100%?+
Arithmetically yes, and it produces a negative result. That is meaningful for a balance or a temperature and nonsense for a price or a quantity — the tool computes it either way and leaves the interpretation to you.
Is a 50% discount the same as two 25% discounts?+
No. Two 25% discounts leave 56.25% of the price, so the effective discount is 43.75%, not 50%. Stacked discounts multiply. The [discount calculator](/t/discount-calculator) shows both figures side by side.
How does this differ from the percentage calculator?+
The [percentage calculator](/t/percentage-calculator) handles three general cases. This one focuses on a single decrease and adds the recovery figure, which is the part people get wrong.