Tools / Invest / Chapter 20 · Risk and Return in Practice
Losses and recovery
Percentages are not symmetrical. After a fall, the gain needed to get back is larger than the fall, which is why avoiding big losses matters more than chasing big gains.
1 · The idea
Gain needed to recover
If you lose a fraction of your money, what remains is (1 − loss). To get back to 1 it must be multiplied by 1 ÷ (1 − loss). At a steady return r, the time to recover is how long that multiplication takes.
The formula
Gain needed = 1 ÷ (1 − loss) − 1 Years to recover = ln(1 ÷ (1 − loss)) ÷ ln(1 + r)
- loss
- fall in value, as a decimal
- r
- annual return after the fall
2 · A worked example
A 50% fall needs a 100% gain. A 20% fall needs 25%. Gaining 50% then losing 50% does not return you to start: 75% is left.
3 · Now use your own numbers
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Illustrative, not personal advice. Inspired by Chapter 20 · Risk and Return in Practice of Money, Explained From the Inside. Your figures stay in this browser. Real products add terms, taxes and conditions that this simple model leaves out.
4 · Take care
What this tool can’t see
- Real markets do not recover at a steady rate, and some take many years or never fully return.
- The lesson is about sequence and size: risk you cannot stomach is risk you will not hold.
5 · Go further
Where this fits
See it in a life:
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Keep the thinking going. Checklists, questions and worksheets inspired by the book, for the next time money is on the table. Part of the Reader’s Letter: a few times a year, never more.
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