Up 20%, then down 20%, the exact loss

Question

A stock rises 20\%, then falls 20\%. 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 = 0.20: 1.20 	imes 0.80 = 1 - 0.20^2 = 1 - 0.04 = 0.96, a net loss of exactly 4\%. Order does not matter: down-then-up gives the same product. Takeaway. A symmetric \pm x round trip always loses x^2: here 0.20^2 = 0.04, so 4\%. This is volatility drag, the bigger the swing, the more a round trip costs, which is why volatile assets lag their average return.

Up 20%, then down 20%, the exact loss

Your answer

More Mental Math questions