Standard Deviation
A dispersion statistic for a selected sample—not a complete measure of loss, liquidity, tail, or path-dependent risk.
Standard deviation measures the dispersion of observations around their mean for a specified sample or assumed distribution. In investing it is often used as a volatility estimate, but it treats upside and downside deviations symmetrically and does not capture every economically relevant risk.
Frequently Asked Questions
Does higher standard deviation always mean a worse investment?
No. It indicates greater measured dispersion under the chosen method, not whether expected return, downside, liquidity, drawdown, leverage, or investor objectives justify the exposure.
Can the 68% and 95% rules be applied to returns?
Only as a normal-distribution approximation. Financial returns can be skewed, fat-tailed, autocorrelated, and regime-dependent, so realized frequencies may differ materially.
How should standard deviation be annualized?
Multiplying periodic volatility by the square root of periods assumes conditions such as independent and identically distributed returns. Serial correlation, irregular spacing, changing volatility, and nontrading periods can invalidate the approximation.
Is historical standard deviation a forecast?
No. It is an estimate from a chosen sample. Future volatility can differ because of regime shifts, leverage, liquidity, events, or structural changes.