A percentage change always uses a base. After a quantity changes, the next percentage usually applies to a new base. This fictional arithmetic example offers general learning context, not a market forecast or portfolio recommendation.
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Apply changes in sequence
A numerical index starts at 100 and falls by 20%, reaching 80. Increasing 80 by 20% gives 96, not 100, because the second increase is 16 rather than 20.
The combined growth factor is 0.8 × 1.2 = 0.96. Adding -20% and +20% ignores their different bases.
Calculate the recovery percentage
To move from 80 back to 100 requires an increase of 20 on a base of 80. The required percentage is 20/80 = 25%.
This is an arithmetic relationship. It does not tell us whether any actual asset, company measure or other quantity will recover, or how long a change would take.
Ask what the number represents
When reading a real chart, check its measure, units, starting date and whether adjustments have been made. A price change and a total-return measure may not be the same thing.
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Official information and further reading: Source 1
