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

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

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

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

ReplyDeletemultiply it by root 52, not divide

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

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

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

ReplyDelete