# 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.

## What it means

A daily volatility estimate describes how widely a stock’s daily returns have varied; annualizing it puts that variability on a one-year scale. The result is usually expressed as a percentage, such as 20% per year. It measures the scale of return fluctuations, not whether returns will be positive or negative.

Annualized volatility is not the return an investor expects to earn or lose over a year. Nor is it a maximum possible loss. A historical estimate summarizes a chosen period of past returns; future conditions can differ.

## How it is calculated

For a conventional estimate based on daily closing prices, first calculate each daily return and its sample standard deviation. Then apply square-root-of-time scaling:

`σ_annual = σ_daily × √N`

- `σ_annual` is annualized volatility, expressed as a percentage or decimal return per year.
- `σ_daily` is the standard deviation of daily returns over the selected observation window, expressed as a percentage or decimal return per trading day.
- `N` is the assumed number of trading days in a year, commonly 252 for stocks. It is a count, not a dollar amount.

For daily close-to-close returns, one possible input is `r_t = (P_t / P_(t−1)) − 1`, where `P_t` is today’s closing price and `P_(t−1)` is the previous trading day’s closing price. With `n` observed daily returns, their sample standard deviation is `σ_daily = √[Σ(r_t − r̄)² / (n − 1)]`; `r̄` is their arithmetic mean.

Multiplying by `√N` is the standard convention when daily returns are treated as having roughly stable variance and little relevant serial correlation. If volatility changes or returns are correlated across days, the square-root rule may not accurately describe variability over longer periods. Specify the return window and trading-day convention when comparing estimates.

## Worked example

Suppose, hypothetically, that a stock’s daily returns over a selected period have a sample standard deviation of 1.00% per trading day. Assume 252 trading days per year.

1. Express daily volatility as a decimal: `σ_daily = 0.0100`.
2. Calculate the time-scaling factor: `√252 ≈ 15.87`.
3. Annualize: `0.0100 × 15.87 ≈ 0.1587`, or **15.87% per year**.

This does not mean the stock will move 15.87% in the next year. It means the selected daily variability, scaled under the stated assumptions, corresponds to an annualized standard deviation of about 15.87%.

## Why it matters before you trade

Annualized volatility lets you compare return variability across stocks or observation windows on a common time scale. A stock with a larger estimate has exhibited wider returns under the chosen method; that can affect how a prospective position fits a risk budget. The estimate alone says nothing about valuation, direction, or whether an order can be filled at a particular price.

For near-term execution, daily volatility may be more directly relevant. Spread, order size relative to trading volume, and market impact address different questions about potential trading costs. An annualized figure does not replace those checks, and changing market conditions can quickly make a historical figure less representative.

## How PreTrAIde uses it

PreTrAIde’s pre-trade analysis estimates **daily** volatility using a blend of Parkinson, close-to-close, Yang–Zhang, and simplified GARCH(1,1) estimators. Its quantitative layer also calculates 1-day 95% value at risk and produces volatility scores for each stock and the basket. The product facts do not specify that PreTrAIde displays or uses an annualized volatility figure.

An annualized figure can provide context for a pre-trade check, but it should not be confused with PreTrAIde’s daily estimates. PreTrAIde’s GO, NO-GO, and MODIFY verdicts are decision support, not recommendations; users place any trades themselves through their own broker.

## Common mistakes

- **Treating volatility as a price forecast.** It describes variability, not the direction or size of a particular future move.
- **Confusing annualized volatility with annual return.** One is a standard deviation; the other is a gain or loss over a period.
- **Multiplying daily volatility by 252.** Standard-deviation scaling uses `√252`; multiplying *variance* by 252 is the corresponding variance rule under the same assumptions.
- **Comparing inconsistent inputs.** Different observation windows, return definitions, adjustments for corporate actions, or annualization conventions can produce different figures.
- **Assuming normal conditions or a loss ceiling.** Jumps, overnight gaps, and unusually large moves are possible, and an annualized estimate does not cap losses.

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