## 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 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

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.

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?

8. 