Standard deviation

Standard deviation measures the typical distance between individual returns and their average. When applied to portfolio returns it's usually called volatility. A portfolio with 15% annualized standard deviation has roughly two-thirds of its monthly returns land within ±15%/√12 of the monthly average; the remaining third fall further out.

The units matter: it's conventional to annualize (monthly standard deviation × √12, daily × √252) for comparison. Mixing frequencies without annualizing is a classic source of misleading comparisons.

Standard deviation captures dispersion but ignores direction. A portfolio that went up steadily every month and one that oscillated wildly with the same average can have comparable standard deviations but very different investor experiences — which is why downside-only measures (downside deviation, max drawdown) complement rather than replace it.

A second assumption baked into using standard deviation is that returns follow something close to a normal distribution. In reality, equity returns have fatter tails — large moves happen more often than a normal distribution predicts. Risk measures built on standard deviation systematically understate the frequency of extreme events.