Volatility Rule of 16

Why Do You Multiply or Divide Volatility by 16?

You might have heard or seen traders multiplying volatility by 16 when calculating annualized volatility. Or you have heard traders dividing annual volatility by 16 when transforming it into daily volatility. Why 16?

The reason is very simple:

16 is approximately the square root of the number of trading days per year.

Number of Trading Days per Year

The number of trading days per year is slightly different in different countries and even for different securities, because different exchanges observe different holidays. Nevertheless, mostly it is somewhere around 250 trading days per year. For US stocks and options, the number of trading days per year has been about 252 in the recent years.

Why 16 and Why Not 15.87?

The square root of 252 is 15.87.

Or 15.8745079 to be more precise.

The obvious reason why a trader multiplies by 16 rather than by 15.8745079 is that with the 16 it is relatively quick and easy to calculate in your head. Time is often scarce when trading.

Furthermore, the rounding does not result in a particularly big error. For example, if you have daily volatility of 1.5% and annualize it, you get 24% if you multiply it by 16 (and it is very easy to do in your head) and you get 23.81% if you open Excel and multiply it by the exact square root of 252. Not much difference and the exact one takes 10x longer to calculate.

Why the Square Root?

Volatility is proportional to the square root of time and not to time directly. You can find full explanation of this here:

Why Is Volatility Proportional to the Square Root of Time?