Aug 26, 2010

Simple Trick to Convert Volatility

My boss came to me today with "how do I convert this monthly vol to annual?". This is by far not the first time someone asked me to convert x-period volatility to y-period volatility. If you're having troubles doing this, here is a simple trick to remember: figure out the multiplier as if scaling were linear, and take the square root of that multiplier. For example, returns scale linearly with time. If someone gives you a monthly returns to convert to annual, you would simply multiply it by 12. So, in the case of converting monthly to annual volatility multiply it by √12. If someone gives you annual returns and asks you to calculate daily returns you would divide it by 252. To convert annual volatility to daily volatility divide it by √252.

P.S. √252≈16, which is the reason for "rule of 16" for converting daily to annual volatility.
P.P.S. To convert:

             Daily to weekly      --- multiply by √5
             Daily to monthly    --- multiply by √21
             Daily to annual       --- multiply by √252

             Weekly to daily       --- divide by √5
             Weekly to monthly  --- multiply by √4  
             Weekly to annual    --- multiply by √50

             Monthly to daily     --- divide by √21
             Monthly to weekly  --- divide by √4  
             Monthly to annual   --- multiply by √12

             Annual to daily       --- divide by √252
             Annual to weekly    --- divide by √50  
             Annual to monthly  --- divide by √12


  1. Anonymous6/10/2015

    I have weekly volatilities over 370 weeks, I like to convert this into an annulized volatility..How does this work?

  2. Anonymous6/23/2015

    There are 52 weeks in a year, so divide the weekly volatility by √52.

  3. Anonymous10/30/2015

    multiply it by root 52, not divide

  4. Yes, anonymous, you're correct. From weekly to annual you need to multiply by √52

  5. Anonymous11/11/2015

    I have daily volatility. How can I convert it to monthly volatility? How about multiply it by root 30? Thank you for your help.

  6. Better multiply by sqrt(21) - approximate number of trading days in a month.