Square-root-of-time rule
How can you scale a week's volatility up to a year, and when does that shortcut mislead?
In plain words
The square-root-of-time rule says volatility grows with the square root of elapsed time. Annual volatility equals weekly volatility multiplied by roughly the square root of the weeks in a year, so a longer period is wilder, but far less than proportionally.
Why it matters
Traders use it to compare a week's noise with a year's risk, to set margin buffers and to convert short-horizon risk into annual figures. It assumes price moves are independent over time. When moves cluster into episodes, the scaled figure understates what a long period can contain.
In a real week: BTC, week of 25 January 2021
For the week of 25 January 2021, BTC's realised annualised volatility was 138.1%, implying roughly 19% a week by the rule. Yet the week's high-to-low range was 31.77%, a single hour moved 12.32%, while the net weekly return was only 2.58%. The same week therefore looks very different depending on whether one compares the path or the endpoint.
A common mistake
Treating the scaled number as a ceiling. It describes average swing size, so one week or one hour can be far larger, and clustered moves make a period riskier than its annualised average implies.