Questions / Quant trading, Numerical judgment
A round-trip percentage move
A price rises 20% and then falls 20%. What is its total percentage return?
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Answer: -4% (-1/25)
- Use an initial price of 100 without loss of generality. A 20% gain takes it to 120.
- A 20% loss is measured from 120, so the next price is 120 × 0.8 = 96.
- Relative to the starting price, the return is (96 − 100)/100 = −4%.
Interview shortcut. Up x then down x always loses x²: 1.2 × 0.8 = 0.96.
Takeaway. Successive simple returns compound through growth factors.
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