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Portfolio & Risk

Standard Deviation (Volatility)

Dispersion of returns around the mean

What is Standard Deviation (Volatility)?

Standard deviation (in finance, used interchangeably with volatility) measures the dispersion of returns around their mean. A higher standard deviation means more variable returns, both up and down. Annualised standard deviation is the primary measure of investment risk. It is computed from a series of periodic returns (daily, weekly, or monthly) and then scaled to an annual figure by multiplying by the square root of the number of periods per year (√252 for daily, √52 for weekly, √12 for monthly). Standard deviation is symmetrical: it captures both good and bad volatility, which is the basis of the Sortino Ratio's improvement on the Sharpe Ratio.

Formula

σ = √[ Σ(r_i − r̄)² / (n−1) ]

Annualised σ = Period σ × √(Periods per year)

r_i = return in period i

r̄ = mean return

n = number of observations

√252 for daily → annual; √12 for monthly → annual

Calculator

How to Use

  1. 1
    Enter a return series: At least 12 observations recommended. Monthly returns over 3+ years produce a reliable estimate.
  2. 2
    Compute mean: Sum all returns and divide by n.
  3. 3
    Compute squared deviations: For each return, subtract the mean, square the result, sum them, divide by (n−1).
  4. 4
    Take the square root: This gives the period standard deviation. Annualise by multiplying by √(periods/year).

Worked Example

Example: Monthly returns for a year

Monthly StdDev

3.5%

Annualisation

×√12

Annualised σ = 3.5% × √12 = 3.5% × 3.464 = 12.1%. This is a typical annualised volatility for a diversified equity portfolio, comparable to the long-run S&P 500 volatility of 15-18%. Individual stocks typically range from 20% to 60%+ annualised volatility.