Gold Realized Volatility: Calculate the Statistic and Audit Its Assumptions
Calculate sample volatility from gold returns, distinguish it from ATR, and understand why annualization is a convention rather than a forecast.
Define the object before calculating it
Volatility is not a single universal number attached to gold. A daily close-to-close return series, an intraday return series and a broker’s high-low range measure different aspects of movement. Specify the exact instrument, price field, sampling interval, session boundary, observation window and return convention. Simple returns use new price divided by old price minus one; logarithmic returns use the natural logarithm of that price ratio. Neither is an account return unless the exposure and cash-flow assumptions make it one. This lesson uses simple daily returns and a sample standard deviation, with no claim that the chosen window describes the future.
Build a reproducible four-return example
Use invented daily returns of +1%, −1%, +2% and −2%. Their arithmetic mean is zero. Expressed in percentage points, their squared deviations from the mean are 1, 1, 4 and 4, totaling 10. Divide by n minus one, here 3, for sample variance of 3.3333 percentage-points squared. Its square root is approximately 1.8257% daily volatility. Dividing by n instead would produce a population-style estimate of 1.5811%, answering a different estimation convention. Preserve that denominator in the worksheet. Four returns are deliberately small enough to calculate by hand; they are not sufficient evidence for a dependable market-risk estimate.
Annualize only after naming the scaling rule
Under an illustrative 252-session convention, multiply the daily standard deviation by the square root of 252. The example becomes approximately 28.98% annualized volatility. This is a scaling of the daily statistic, not an expected 28.98% gain, a guaranteed annual range or an observed year of data. Square-root scaling corresponds to assumptions about how return variance aggregates across time; serial dependence and changing volatility can undermine its use as a forward estimate. A different session convention changes the number. Do not multiply a daily percentage by 252, and do not apply square-root scaling to an average return as though the two operations were interchangeable.
| Step | Calculation | Result |
|---|---|---|
| Mean | (1−1+2−2) / 4 | 0% |
| Squared deviations | 1 + 1 + 4 + 4 | 10 (% points)² |
| Sample variance | 10 / (4−1) | 3.3333 (% points)² |
| Daily deviation | sqrt(3.3333) | 1.8257% |
| Annualized convention | 1.8257% × sqrt(252) | 28.98% |
Distinguish the statistic from ATR and price limits
ATR averages true ranges in price units, including gaps relative to the previous close. Return standard deviation measures dispersion around a mean in return units. Two gold paths can have similar close-to-close returns but different intraday ranges. Neither measurement establishes a maximum future loss or a stop distance guaranteed to contain price. A one-standard-deviation label also does not automatically describe a 68% coverage interval: that familiar interpretation requires distributional assumptions absent from a generic volatility calculation. Keep gap behavior, execution and leverage separate from the descriptive statistic instead of concealing them inside a precise-looking annual percentage.
Audit the observations that enter the window
A stale close repeated across several dates creates artificial zero returns. Mixing settlement prices with last trades can create non-comparable transitions. A futures contract roll can introduce a price-level jump unrelated to an investor’s actual same-contract P&L. Missing dates should be investigated, not silently filled with invented quiet sessions. Compare short and long windows using a rule set in advance, and report the number of usable returns. If a single extreme observation changes the estimate sharply, preserve and explain it rather than deleting it because it looks inconvenient. Data cleaning is a documented judgment, not a method for making the result calmer.
Practice task: submit a volatility audit
Reproduce the four-return calculation in a spreadsheet, including mean, squared deviations, sample variance, daily standard deviation and the stated annualization factor. Then add a fifth invented return of zero and recalculate; explain why the estimate changes even though the earlier observations remain unchanged. Write a second paragraph distinguishing your statistic from ATR, a forecast and account risk. A complete answer includes the source convention, window, missing-data policy and a reason why this small demonstration cannot justify live sizing. Continue to correlation only after the paired returns are defined with equally careful timestamps.
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Lesson sources and further study
MCX: Annualised Actual Volatility methodology
Core course references
CME Group: Gold Product Overview. Investor.gov: Types of Orders explains order concepts for stocks; check the execution rules of your specific gold instrument.
Gabriel Nicolaev — CyGuru · Published 6 November 2026. Educational material. Illustrative prices are not current quotes or trade recommendations.