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.

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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 quarterly->multiply by √63
Daily to annual->multiply by √252
Weekly to daily->divide by √5
Weekly to monthly  ->multiply by √4  
Weekly to quarterly->multiply by √12.5
Weekly to annual    ->multiply by √50
Monthly to daily     ->divide by √21
Monthly to weekly  -> divide by √4  
Monthly to quarterly->multiply by √3
Monthly to annual   ->multiply by √12
Quarterly to daily     ->divide by √63
Quarterly to weekly  ->divide by √12.5
Quarterly to monthly->divide by √3
Quarterly to annual   ->multiply by √4
Annual to daily       ->divide by √252
Annual to weekly    -> divide by √50  
Annual to monthly  -> divide by √12
Annual to quarterly-> divide by √4

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  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.

    1. This is always a debatable issue
      that how much Days should use to
      convert Daily volatility to other specifice time period as
      (one week or month , year etc

      Because as India's Top exchange
      * NSE * Uses √365 to transform
      Daily Volty to annulized Volty

      But in US they use √252

      So my opinion is to follow the exchange in which one is trading

      Plz share your opinion

  7. Anonymous3/25/2016

    I have two questions.
    How can I convert monthly volatility to quarterly volatility?
    How can I convert daily volatility to quarterly volatility?

    Thank you in advance

  8. Anonymous4/29/2016

    I have daily volatility how can i convert it in hourly?

    1. Divide by sqrt(6.5). 6.5 represents number of trading hours.