Why volatility ≠ risk

Volatility measures how spread out returns are, not the chance of losing money. Why that difference matters in finance.

Play with it

Volatility is not risk. Two assets, same destination, very different rides. And a calm one that quietly sinks.

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Volatility of the erratic asset35% a year

Where both end up after 5 years+50%

Steady asset volatility3.3%

Erratic asset volatility30.5%

Best month+32.1%

Worst month-29.9%

Volatility from up monthsfrom down months

49%51%

The erratic asset's 60 monthly returns

Both assets turn $1,000 into $1,500. The erratic one is 9.3× as volatile, and 49% of that volatility comes from months that went better than average. Volatility measures the spread, not the direction.

Try this

Drag the erratic asset's volatility up. The destination never moves, only the ride does.
Look at the split bar: big gains raise volatility just as much as big losses.
Run it again a few times. Is the erratic asset ever ahead of the steady one halfway through?

The math

\sigma = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(r_i - \bar r\right)^2}

$\sigma$: volatility, the standard deviation of returns
$r_i$: return in period i
$\bar r$: average return
$(r_i - \bar r)^2$: squared, so gains and losses count the same

Quick check

Two questions to see if it clicked. Answers explain themselves.

Mathematically, volatility is the…

Can a low-volatility asset steadily lose value?