How to convert volatility from annual to daily, weekly or monthly?

Converting volatility (standard deviation) from annual to daily is pretty simple. The thumb rule for calculation is that the volatility is proportional to the square root of time, and not to time itself.

For example you have average of 256 days trading days in a year and you find that implied volatility of a particular option is 25% then daily volatility is calculated as under

Square root of 256 is 16

25%/16= 1.56%.  Consequently we get the daily variance as 1.56%

This is because volatility, and more generally standard deviation, is the square root of variance and because variance is proportional to time.

Volatility rule of 16:

In the above example if we take average of 252 trading days instead of 256 days, the square root of 252 is 15.87 and 25% / 15.87 = 1.57%

Since the variance between 1.56 and 1.57 is insignificant, Traders often round the square root of the number of trading days per year to 16 when trading days are 252.  It allows quicker and easier calculation and is still accurate enough for most purposes.   This rule is referred as the ‘volatility rule of 16’ which is used for observing it in a trading platform or calculating it from the option’s price.

Weekly or monthly volatility:

Implied volatility, either in the form of volatility index (such as BSE/NSE , S&P500 index etc.) or implied volatility for a single option is normally expressed as annualized standard deviation of the underlying asset’s returns (price changes).

In case you need to find monthly volatility from the annualized volatility divide it by √12 (because12 months in a year).  Similarly, in the case of converting monthly to annual volatility multiply it by √12. Same way you can calculate weekly volatility from annualized volatility by dividing annualized volatility by √52 (Because there are 52 weeks in a year) or for weekly volatility to annual volatility multiply it by √52.