Observed Return Volatility Calculator
Convert ordered prices into simple or log returns and calculate N−1 sample volatility with optional user-entered annualisation.
Enter equal-frequency prices
Keep the sampling interval, source, symbol and applied-price basis consistent.
No default is assumed. Enter only a factor matching the row frequency.
One row per line: price alone, or optional label then price. Commas, semicolons or tabs are accepted.
Entered-sample return dispersion
Entered Price Statistics 1.0.0.
| Label | Entered price | One-period return |
|---|
How observed return volatility is calculated
Log return = ln(Current price ÷ Previous price)
Sample volatility = √[Σ(return − mean)² ÷ (m − 1)]
The selected return transform is applied between adjacent entered prices. Sample standard deviation uses one fewer degree of freedom than the number of returns.
Annualisation is omitted unless you enter a periods-per-year factor. When supplied, the tool multiplies sample volatility by the square root of that factor.
Worked example from the audited fixture
How to interpret the result
The annualized figure is a scaling of this two-return sample, not a forecast. It assumes the entered period definition and square-root-of-time convention are appropriate. The same endpoints have a −1% start-to-end change, showing why path dispersion and net change are different measures.
Assumptions and limits
- Prices must be positive, ordered and equally spaced in the time unit you intend to describe.
- The page does not detect missing intervals, market closures, outliers or stale observations.
- Sample standard deviation can be strongly affected by extreme returns and heavy tails.
- Square-root-of-time annualisation is an assumption-based scaling convention, not a persistence forecast.
- The result contains no confidence interval, probability, VaR, target or recommendation.
Frequently asked questions
- Enter at least three positive ordered equal-frequency prices from one consistent source and applied-price basis.
- It is the current price divided by the previous price minus one.
- It is the natural logarithm of the current price divided by the previous price.
- The sample return deviation divides the squared-deviation total by the return count minus one.
- Only when a periods-per-year factor is entered, sample volatility is multiplied by the square root of that factor.
- The page cannot infer whether entered rows are daily, hourly or another frequency, so the factor remains user-defined.
- Yes. Standard deviation gives squared weight to deviations and can be strongly affected by heavy tails and outliers.
- No. It describes the entered sample under explicit spacing assumptions and contains no forecast or probability.
Sources and methodology
- NIST/SEMATECH — Standard deviation — N−1 sample standard-deviation formula.
- NIST/SEMATECH — Measures of Scale — Standard-deviation interpretation and heavy-tail limitations.
- MetaQuotes Code Base — Standard Deviation — Official contrast with the N-divisor price-deviation convention used by Bollinger Bands.
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Compare the chart feed and trading terms
Use one consistent broker feed for every entered observation and verify the symbol's price precision, spread and trading conditions before using any measurement in a plan.
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