Stock gains and losses

If a stock initially has a value of $1 and it gains 20%, then it has value $1.20. If it then loses 20% of its value, it now has a value of 0.8 x 1.20 = $0.96. You might expect that a 20% gain and a 20% loss average out, but they do not. Consider an extreme case: if a stock gains 100% and then loses 100%, it has value zero.

For more, read about the arithmetic-geometric mean inequality and figure out how it is relevant.