Volatility — standard deviation, annualisation, sample effects

The formula

σannual = √[Σ(Ri − R̄)² / (n − 1)] × √12

where:
  Ri  = monthly return for month i
  R̄  = sample mean of monthly returns over the window
  n   = number of observations (36 for 3-year monthly)
  √12 = annualisation factor (assumes uncorrelated monthly returns)

The (n−1) denominator gives "sample" standard deviation (Bessel's correction)
— appropriate when the 36 months are treated as a sample of the underlying
return distribution, not the entire population.

Why "sample" std dev (n−1) not "population" (n)

This is a subtle but important point. Two flavours of standard deviation:

• Population std dev (n denominator): appropriate if your 36 months ARE the entire population you care about.
• Sample std dev (n−1 denominator): appropriate if your 36 months are a sample drawn from a larger underlying distribution.

For ETF analysis, we're treating the 36 months as a sample — the underlying distribution is all possible monthly returns this ETF could have generated. We want to estimate the population std dev from the sample. The (n−1) denominator (Bessel's correction) gives an unbiased estimator.

In Excel/Sheets: STDEV.S uses (n−1) — correct for ETF analysis. STDEV.P uses (n) — wrong for our purposes. The difference for n=36: ~1.4% relative error.

Annualisation — the √12 factor

Returns over different time periods aren't directly comparable until annualised. The √n rule for variance:

Variance scales linearly with time (if uncorrelated): Varannual = 12 × Varmonthly
Standard deviation scales with √time:                  σannual   = √12 × σmonthly

For daily returns:                                     σannual   = √252 × σdaily
For weekly returns:                                    σannual   = √52 × σweekly

The assumption: monthly returns are independent (uncorrelated month-to-month). For most ETFs this is roughly true. For very trend-following or mean-reverting strategies, it's less true — and annualisation can over/underestimate.

Inputs we use

Worked example — VWRL volatility

Vanguard FTSE All-World UCITS ETF (VWRL), 3 years ending April 2026, monthly GBP TR returns.

VWRL's annualised volatility of ~14.8% is typical for broad global equity. This means:

• Roughly 68% of annual returns expected within ±14.8% of the mean.
• Roughly 95% within ±29.6% (2 standard deviations).
• Roughly 99.7% within ±44.4% (3 standard deviations).

Real-world ETF returns have fatter tails than this normal-distribution assumption suggests — extreme months are slightly more common than ±3σ would predict.

Typical volatility ranges by asset class

Sample-period effects

Volatility can vary dramatically across windows:

• 2017-2019 calm period: VWRL annualised vol ~10%.
• 2018-2020 including March 2020 crash: ~17%.
• 2020-2022 mixed: ~16%.
• 2021-2023 including 2022 bear market: ~17%.
• 2023-2025 recent calm: ~12%.

The 3-year window we use is a deliberate compromise:

• Long enough for statistical stability (36 observations).
• Short enough to reflect the current regime.
• Captures one full mini-cycle in most periods.

If you compare an ETF's volatility today to its volatility 5 years ago, both numbers are correct — but they describe different sample periods.

What volatility does NOT tell you

• Volatility doesn't measure tail risk. Returns are fat-tailed — extreme events more common than normal predicts.
• Volatility ignores skew. Two ETFs can have the same volatility but very different return shapes (one with occasional big down months, one with smooth declines).
• Annualised vol assumes independence. If returns are autocorrelated (trending or mean-reverting), √12 annualisation is biased.
• Volatility is not "risk". A bond ETF with 6% vol and a bond ETF with 8% vol aren't ranked by risk-of-loss alone — credit risk, duration risk, currency risk also matter.

How to reproduce this yourself

1. Get 36 months of total return GBP prices for your ETF.
2. Calculate monthly returns: =(P_t/P_t-1) − 1.
3. In Excel: =STDEV.S(returns) for monthly standard deviation.
4. Multiply by SQRT(12) for annualised volatility.

Cross-check against issuer factsheets — most publish "standard deviation" or "annualised volatility" using this same methodology. Your number should be within ~5%.

Sources and methodology

Volatility methodology follows standard portfolio theory (Markowitz, Sharpe). Annualisation factor √12 assumes uncorrelated monthly returns. Sample standard deviation (Bessel correction) appropriate for sample-based estimation. See the ETF Data Methodology for full data sources. The site methodology documents the broader review process.

Related metric pages

• Sharpe ratio (uses volatility as denominator)
• Sortino ratio (downside volatility only)
• Beta (relative volatility to benchmark)
• Max drawdown (worst-case loss)
• Tracking error (volatility of relative returns)
• Metrics transparency hub