# How to Calculate Annualized Standard Deviation

A stock trader will generally have access to daily, weekly, monthly, or quarterly price data for a stock or a stock portfolio. Using this data he can calculate corresponding returns from the stock (daily, weekly, monthly, quarterly returns). He can use this data to calculate the standard deviation of the stock returns. The standard deviation so calculated will also be the standard deviation for that period. For example, using daily returns, we will calculate the standard deviation of daily returns. However, when we talk about volatility, we are most likely talking about annual standard deviation. Therefore, we will have to annualize the standard deviation calculated using the periodic data.

The annualized standard deviation of daily returns is calculated as follows:

Annualized Standard Deviation = Standard Deviation of Daily Returns * Square Root (250)

Here, we assumed that there were 250 trading days in the year. Depending on weekends and public holidays, this number will vary between 250 and 260.

So, if standard deviation of daily returns were 2%, the annualized volatility will be = 2%*Sqrt(250) = 31.6%

Similarly, we can calculate the annualized standard deviation using any periodic data.

For weekly returns, Annualized Standard Deviation = Standard Deviation of Weekly Returns * Sqrt(52).

For monthly returns, Annualized Standard Deviation = Standard Deviation of Monthly Returns * Sqrt(12).

For quarterly returns, Annualized Standard Deviation = Standard Deviation of Quarterly Returns * Sqrt(4).