Equal but Opposite Percentage Changes Do Not Cancel

percent

10

order

decrease  increase

increase  decrease

100. 90. 99.

Equal percentage increases and decreases do not cancel. The resulting change,

(1-p)(p+1)

, is always less than the initial value. For example, if you make 50% on an investment and then lose 50%, the result is a loss of 25%:

(1+1/2)(1-1/2)=3/2×1/2=3/4

. Going the other way, to make up for a loss of 50%, you need to make 100%, not just 50%.