Up 8%, then down 8%, the exact shortfall

Question

A stock rises 8\%, then falls 8\%. 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 = 0.08: 1.08 	imes 0.92 = 1 - 0.08^2 = 1 - 0.0064 = 0.9936, a net loss of exactly 0.64\%. Takeaway. The loss is the square of the swing, so small moves cost very little: 0.08^2 = 0.0064, just 0.64\%. Because the drag grows with the square, doubling the swing quadruples the round-trip loss.

Up 8%, then down 8%, the exact shortfall

Your answer

More Mental Math questions