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The canonical measure of dispersion. Foundation of Modern Portfolio Theory.
Standard deviation is the square root of the variance of returns — the canonical measure of dispersion around the mean. Used as a proxy for total risk in Modern Portfolio Theory. Intuitive and easy to compute, but a poor measure of risk for non-normal distributions with fat tails or negative skew.
σ = sqrt(E[(R − μ)²])σ = sqrt(E[(R − μ)2])Compute the mean, subtract from each observation, square, average, take the square root. The result is in the same units as the original returns.
Standard deviation is the bedrock of mean-variance analysis (Markowitz 1952). It is mathematically convenient but treats upside and downside identically — which is its main critique.
Daily returns: 1%, −2%, 0.5%, 1.5%, −1%. Mean = 0%. Squared deviations: 0.0001, 0.0004, 0.000025, 0.000225, 0.0001. Mean = 0.000175. sqrt = 1.32%.
Daily standard deviation: 1.32%. Annualized volatility: 1.32% · sqrt(252) = 21%.
Standard deviation is in the same units as the underlying return series. For comparison across assets, use the annualized version (volatility).
Variance is the average squared deviation; standard deviation is its square root. Standard deviation has the same units as the original data, which makes it more intuitive.
Sample (n−1 denominator) is standard for return series — historical returns are samples of an unknown underlying distribution.
Standard deviation includes upside and downside dispersion equally. Downside deviation includes only returns below a target.
Yes — as the denominator of Sharpe and the basis for annualized volatility. The metrics engine computes flow-adjusted daily standard deviation.
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