Three year annualized volatility

djc225's picture
Rank: Baboon | 144

im trying to calculate a three year annualized volatility. i understand that for a one year annualized volatility i will take the st dev and multiply it by SQRT ( 252). if im looking at three years worth of data and i need the three year volatility does that mean the annualization factor becomes Sqrt (252*3)?

if it helps im using three years worth of stock prices and for the st deviation. i just need to figure out how to calculate a three year volatility.

then if i use 5 years worth of stock prices how do i do a five year volatility?

would be the above be any different if i threw an annualization factor in there?

Comments (17)

Apr 15, 2010

I'm assuming your looking at the SD of daily returns?

Apr 15, 2010

No need to post in two forums, see the thread in IB.

Apr 15, 2010

sd of daily closing stock prices...im doing a stock options expense calculation

Apr 15, 2010

GARCH.

Apr 15, 2010

i need to stay somewhat consistent in my methodology so i cant use garch methods. just simple math....but obviously im missing something.

Apr 15, 2010

Aight, then you do this:

Annualized Vol = (Daily SD Returns)/SQRT(1/P)

Where P is the time period of the sample.

To get 3 year Vol = (Annualized Vol)SQRT(3)
To get 5 year Vol = (Annualized Vol)
SQRT(5)

Apr 15, 2010

is there any way i can run it with a calculation similar to what im using now?

im using the stdev function in excel with the cell range covering either 1, 3, or 5 years depending on the volatility im looking for?

one year vol = st dev(on years data) * SQRT (252 days)
three year vol = st dev( three years data) * SQRT (252 days) -

can you please explain what each step is doing, i dont understand why i need to divide by sqrt (1/p) if im multiplying by an annulization factor

Apr 15, 2010

annualized one year vol = st dev(on years data) * SQRT (1/252 days)

As for the second part, you are being sort of confusing. Are you looking for Annualized vol using 3 years of data or 3 year vol using 3 years of data?

Apr 15, 2010

can you actually show me the calculations for both so i can see the difference.....i am though looking for a 3 year volatility using 3 years of data

Apr 15, 2010

Ok so this is how it goes:

Vol for Period T = (Annualized Vol)*SQRT(T)

==> (Vol for Period T)/SQRT(T) = Annualized Vol
==> (Vol for Period T)*SQRT(1/T) = Annualized Vol

FOR 1 Year Data:
So for T = 252 days

Annualized Vol = (Vol for period T=252 days)*SQRT(1/252)
Where Vol for period T=252 days <==> ST Dev (One years daily data)

FOR 3 Years Data:
So for T=252*3=756 days

3 year Vol is simply = (Vol for period T=756 days) = ST Dev (Three years daily data)

If you need Annualized:
Annualized Vol = (Vol for period T=756 days)*SQRT(1/756 )
Where Vol for period T=756 days <==> ST Dev (Three years daily data)

Apr 15, 2010

i can't believe this post.

annualized volatility means volatility per year boys.pick up a stats text already.

ambition is a state of permanent dissatisfaction with the present.

Apr 15, 2010

ok now conceptually, if im looking at a stock options calc, which is more appropriate that i use? im assuming a simple 3 year volatility with three years of data make most sense, but it gives an unfavorable number....

what if any would be the arguments for using an annualized vol instead?

thanks for all of the help

Apr 15, 2010

I don't know what model you are using, but you almost always use annualized vol. I think your getting confused about what "Annualized Volatility" really is... it can be drawn from any period sample (1-year, 3-year, etc).

For example, 3 year Annualized Vol just means the sample is 3 years worth of data which is this calc above:

Annualized Vol = (Vol for period T=756 days)*SQRT(1/756 )
Where Vol for period T=756 days <==> ST Dev (Three years daily data)

That should be a fine one to use.

Apr 15, 2010

this is all assuming returns are serially independent. If so you can multiply by the sqrt factor and get the annualized volatility. if you have long enough dataset, try getting annualized returns and find the sd, you will see that that value can (but not necessariliy) differs from the value you get by using daily volatilities.

Apr 15, 2010

Revsly's doing a good job trying to explain this to you. But I fear you're misunderstanding a fundamental concept based on your original post.

First, you do not need 3 years of data to get a 3 year annualized vol, for the same reason you dont need 1 year of data to get a 1 year annualized vol.

For example, when calculating realized vol on the S&P 500 to compare it to the VIX, one ONLY uses the last 30 days of data and then annualizes it (by multiplying the stdev of returns over last 30 days by sqrt(252)).

I'm trying to be sure we're clear on this because you asked about using 5 years of data to get 5 year annualized vol (this is not necessary)

Confirm that you understand this.

CD~

Apr 15, 2010
creditderivatives:

Revsly's doing a good job trying to explain this to you. But I fear you're misunderstanding a fundamental concept based on your original post.

First, you do not need 3 years of data to get a 3 year annualized vol, for the same reason you dont need 1 year of data to get a 1 year annualized vol.

For example, when calculating realized vol on the S&P 500 to compare it to the VIX, one ONLY uses the last 30 days of data and then annualizes it (by multiplying the stdev of returns over last 30 days by sqrt(252)).

I'm trying to be sure we're clear on this because you asked about using 5 years of data to get 5 year annualized vol (this is not necessary)

Confirm that you understand this.

CD~

Exactly on the money what I was trying to explain, I think that's why he is confused.

Apr 15, 2010
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