### Simple Trick to Convert Volatility

As I am sure all of you know Russia has began a full scale war against my home country Ukraine. Please make no mistake - Putin's goal in not to stop the expansion of NATO, not to install puppet government, and certainly not to bring peace. The goal is genocide of Ukrainian people.

When Ukraine was under Russian communist occupation, Russians started off with killing of political leaders, repression of Ukrainian language and traditions - including prohibiting people from celebrating Christmas, and then wide-scale murder of millions of Ukrainian civilians. We already starting to see this today:  Russians are targeting civilian hospitals, kindergartens, and bomb shelters.

If you are reading this make a phone call to your government representatives and ask to sanction Russian federation in absolutely any way possible, and provide military aid to Ukraine. Please just do this little thing to give us a chance to protect ourselves.

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 trouble doing this, here is a simple trick to remember: figure out the multiplier as if scaling was 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 volatility to annual, 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.

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

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. 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.

9. How is SPX minutes IV converted from daily IV?

For example, trading hours are 9:30 to 16:00. If the time is 13:00 and the daily IV = 3.60%, what is the IV based on the remaining three hours?

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