# 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.

## 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.

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Source: https://pretraide.com/glossary/daily-volatility