Up 12%, then down 12%, the exact damage

Question

A stock rises 12\%, then falls 12\%. Solve in your head. What is the exact net change? Aim: under 10 seconds.

Accepted Answer

The multipliers are (1 + x)(1 - x) = 1 - x^2 with x = 0.12: 1.12 	imes 0.88 = 1 - 0.12^2 = 1 - 0.0144 = 0.9856, a net loss of exactly 1.44\%. The order doesn't matter, down-then-up gives the same product. Takeaway. Symmetric round trips always lose x^2, the difference-of-squares identity wearing a finance costume. This is volatility drag in miniature: an asset that swings \pm x repeatedly loses about x^2 per round trip, which is why high-volatility assets underperform their average arithmetic return over time.

Up 12%, then down 12%, the exact damage

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