Why +50% then −50% leaves you poorer than you started

Say you put $100 into a fund. It jumps 50% to $150 — great. Then next year it falls 50%. You might expect to be back at $100. But 50% of $150 is $75, so you're actually down 25%. The gain and the loss don't cancel, because the loss is applied to a bigger number than the gain was.

This gap is called volatility drag: the more a portfolio's returns swing up and down, the more its actual compounded result falls short of its simple average return. In the example, the average of +50% and −50% is 0%, but the real outcome is −25%. Bigger swings mean a bigger drag.

It's why a smoother, steadier 7% a year can beat a jumpy investment that averages 7% but lurches wildly along the way. It also explains the brutal math of deep losses: a 50% drop needs a 100% gain just to break even, not another 50%. Protecting against large drawdowns matters as much as chasing big gains.