Risk & volatility

Daily volatility

Daily volatility is the estimated standard deviation of a stock’s returns over one trading day, usually expressed as a percentage of its price.

Calculate it: Value at Risk (VaR) Calculator for a Stock Position →

What it means

A stock can move by different amounts from one trading day to the next. Daily volatility summarizes how widely its one-day returns have varied, or are estimated to vary, around an average. It is usually expressed as a percentage per trading day, not as a dollar change or a prediction of tomorrow’s return.

A daily volatility estimate of 2% describes the scale of typical variation under the chosen model and data period. It does not mean the stock will move exactly 2%, that every move will stay within 2%, or that up and down moves are equally likely.

How it is calculated

One straightforward historical method calculates the sample standard deviation of daily returns:

r_t = (P_t / P_(t-1)) - 1; r̄ = (Σ r_t) / n; σ_daily = √[Σ(r_t - r̄)² / (n - 1)]

  • P_t is the stock’s adjusted closing price on trading day t; P_(t-1) is its adjusted closing price on the preceding trading day. Adjustment helps account for events such as stock splits.
  • r_t is that day’s close-to-close return, in decimal form. Multiply by 100 to express it as a percentage.
  • n is the number of daily returns in the sample; at least two are needed for this sample formula.
  • r̄ is the arithmetic average of those returns.
  • Σ means add the indicated values across all n returns. Squaring each deviation prevents positive and negative deviations from canceling.
  • σ_daily is the sample standard deviation of daily returns, in decimal units per trading day. Multiply by 100 for a percentage.

The lookback period matters: using a different set of days can change the estimate. Close-to-close returns include the change between consecutive closes, including any overnight price move. Other estimators use additional price information or model how volatility changes over time; their results need not match this formula.

Worked example

Suppose a hypothetical stock has four consecutive daily returns of +2%, −2%, +2%, and −2%. These are invented round numbers, not observed market data.

  1. The average return is (2% - 2% + 2% - 2%) / 4 = 0%.
  2. Each return differs from that average by 2 percentage points in magnitude. The sum of squared deviations is 4 × (2 percentage points)² = 16 squared percentage points.
  3. For a sample standard deviation, divide by n - 1 = 3, then take the square root: √(16 / 3) ≈ 2.31%.

The estimated daily volatility for this four-return sample is approximately 2.31% per trading day. The calculation measures dispersion, not whether the stock was profitable: these four returns average 0%, but they still vary substantially.

Why it matters before you trade

Daily volatility provides context for the size of an ordinary one-day price change relative to a proposed position. For a hypothetical position worth US$1,000, a 2% price move corresponds to US$20 before trading costs. That conversion does not set a maximum loss: a larger move is possible, and losses can exceed a one-standard-deviation illustration.

Volatility also affects risk estimates such as one-day value at risk (VaR). A VaR figure depends on its assumptions and confidence level; it is not a loss limit. Before placing an order, it is useful to distinguish price-movement risk from execution costs such as the bid-ask spread and market impact. A volatile stock may also have changing liquidity, but volatility alone does not measure liquidity or predict execution quality.

How PreTrAIde uses it

PreTrAIde’s pre-trade analysis includes a daily volatility estimate in its deterministic quantitative layer. It blends the Parkinson, close-to-close, and Yang-Zhang estimators with a simplified GARCH(1,1) estimator. The platform also calculates one-day 95% VaR and 0–100 volatility scores for each stock and the basket; its estimated bid-ask spread includes a volatility uplift.

Users enter a basket with sides, quantities, and execution conditions before placing orders themselves. PreTrAIde uses its quantitative results alongside other inputs to support a GO, NO-GO, or MODIFY verdict with a risk assessment and plain-language reasoning. These verdicts are decision support, not recommendations or guarantees.

Common mistakes

  • Treating volatility as direction. A high estimate does not say whether the next move will be up or down.
  • Treating one standard deviation as a cap. Prices can move farther, especially around events or market gaps.
  • Mixing time scales. Daily and annualized volatility are different units; neither should be labeled as the other.
  • Ignoring the method and lookback. Two valid estimators, or two sample periods, can produce different numbers.
  • Confusing volatility with trading cost. A percentage describing return dispersion is not a quoted spread, a commission, or a guaranteed fill price.

Frequently asked questions

Is daily volatility the same as the daily percentage change?

No. A daily percentage change is one day’s return. Daily volatility estimates how much one-day returns vary across a sample or under a model.

How do you convert annualized volatility to daily volatility?

Under a square-root-of-time approximation, divide annualized volatility by the square root of the assumed number of trading days per year. For example, using 252 days, 20% annualized volatility corresponds to about 1.26% daily volatility; the approximation can fail when volatility changes or returns are dependent.

Does 2% daily volatility mean a stock cannot fall more than 2% in a day?

No. Volatility is a measure of dispersion, not a maximum move or a loss limit. An individual day’s return can be much larger in magnitude.

Related terms

Historical volatility Historical volatility is a measure of how widely a stock’s returns varied over a past period, usually expressed as the standard deviation of returns at a specified daily or annualized frequency. Annualized volatility Annualized volatility is the standard deviation of returns expressed on a one-year scale, commonly calculated by multiplying daily return volatility by the square root of 252 trading days. Parkinson volatility estimator Parkinson volatility estimator is a measure of historical price variability that uses a stock’s daily highs and lows, rather than its closing prices, to estimate volatility. Yang-Zhang volatility estimator Yang-Zhang volatility estimator is a measure of historical price variability that combines overnight opening gaps with intraday open-to-close and high-low movements. GARCH model GARCH model is a statistical method for estimating changing volatility by using past return shocks and past estimates of volatility. Value at risk (VaR) Value at risk (VaR) is an estimate of the loss threshold that a position or portfolio is expected to exceed with a specified probability over a specified time horizon.

Risk & volatility

Volatility Implied volatility Expected shortfall (CVaR) Standard deviation Beta Alpha Drawdown Maximum drawdown All glossary terms →

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Educational content, not investment advice. PreTrAIde is analysis software, not a broker: it never executes orders, and its verdicts are decision support, not recommendations to buy or sell.