Volatility: align return frequency and standard-deviation conventions

Financial volatility commonly refers to the standard deviation of returns. This article uses simple daily returns between adjacent observations. Price-level dispersion can be dominated by differences in price scale.

Standard deviation counts positive and negative deviations from the mean. It does not measure only losses or establish a future loss limit.

Four fictional returns are −1%, +1%, −1%, +1%. Their mean is zero and their squared deviations sum to 0.0004 in decimal units. With ddof=0, divide by four and take the square root: daily volatility is 1%.

With ddof=1, divide by three instead, giving about 1.155%. The variance correction does not make the standard deviation itself exactly unbiased.

Under a convention of 252 observations per year, 1% multiplied by sqrt(252) is about 15.87%. The observation count is an explicit assumption.

Square-root scaling relies on conditions including stable variance and absence of serial correlation. It is not exactly the standard deviation of compounded annual simple returns.

Do not silently replace missing returns with zero. A return across a date gap may cover more than one session. Report the frequency and actual observation count.

Dividend treatment, splits, currency and valuation timing affect the series. Matching formulas alone does not ensure matching risk definitions.

KabuForge’s course explains portfolio paths and benchmark price conventions. Check dates, costs and dividend treatment before calculating dispersion; this article does not certify a GUI ddof or annualization count.

Read Sharpe ratio, maximum drawdown and price and total return.

Concept references: NumPy standard deviation and ddof documentation. Additional reference: SciPy sample standard deviation and ddof. Software workflow and limitations: KabuForge public GUI research course. Reviewed October 6, 2026. The fictional examples are teaching calculations, not course execution results.

The public course is research-only and does not certify historical information availability. A concept explanation does not establish that every method is implemented in the software. This article recommends no securities, trades or settings. Read the disclaimer.

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