rolling window realized volatility

[Saad Al]

Dear members,

I am working with panel data and would like to calculate a 5-day rolling window realized volatility for each firm. Here is a simulated data for illustration:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float Date str45 firm int firm_id float Logreturn
18536 "AAK" 1    0.0059992443
18539 "AAK" 1  -.002986188
18540 "AAK" 1    0.028037382
18541 "AAK" 1   .0.0090909088
18542 "AAK" 1   -0.029909907
18543 "AAK" 1    0.021545317
18546 "AAK" 1    0.002909088
18547 "AAK" 1   -0.0090645393
18548 "AAK" 1    0.021588003
18536 "BBA" 2   -0.015042983
18539 "BBA" 2    0.0061818208
18540 "BBA" 2   -0.018070113
18541 "BBA" 2    0.0095238099
18542 "BBA" 2   -0.006256904
18543 "BBA" 2   -0.018518519
18546 "BBA" 2    0.0094339624
18547 "BBA" 2   -0.02168224
18548 "BBA" 2    0.0030569325

end

I tried using different codes with no luck. I keep getting errors for codes such as:

gen squared_return = Logreturn^2
bysort firm_id (Date): egen realized_volatility = mean(squared_return), window(5)

and also

by firm_id: gen vola5 = sqrt(rolling(sum) squared_return, window(5))

I even tried a loop with no luck:

levelsof firm_id, local(firms)
foreach firm of local firms {
by firm_id: egen mean_squared_return = mean(squared_return)
by firm_id: egen volat5_firm = sqrt(5 * mean_squared_return)
replace volat5 = volat5_firm if firm_id == `firm'
drop mean_squared_return volat5_firm
}

then i revered to the asrol code with no luck:

gen volat5 =.
levelsof firm_id, local(firms)
foreach firm of local firms {
by firm_id: asrol volat5_firm = squared_return, window(5) start(Date) keep(firm_id)
replace volat5 = volat5_firm if firm_id == `firm'
drop volat5_firm
}

I then ran a simple code that worked:

bysort firm_id (Date): gen rvol5=sqrt(5*sum( Logreturn^2))

but the does not produce the same realized volatility as if you would do it on excel:

Date	firm	firm_id	L. Return	Realized Vol
30-Sep	AAK	1	0.005999244
1-Oct	AAK	1	-0.002981734
4-Oct	AAK	1	0.028037382	0.02764528
5-Oct	AAK	1	0.009090909	0.027082311
6-Oct	AAK	1	-0.029909907	0.051175779
7-Oct	AAK	1	0.021545317	0.046496322
8-Oct	AAK	1	0.002909088	0.045122254
11-Oct	AAK	1	-0.009064539	0.026717411
12-Oct	AAK	1	0.021588003	0.026756756
30-Sep	BBA	2	-0.015042983
1-Oct	BBA	2	0.006181821
4-Oct	BBA	2	-0.018070113	0.018688785
5-Oct	BBA	2	0.00952381	0.021297494
6-Oct	BBA	2	-0.006256904	0.019578963
7-Oct	BBA	2	-0.018518519	0.019880898
8-Oct	BBA	2	0.009433962	0.019814908
11-Oct	BBA	2	-0.02168224	0.024218233
12-Oct	BBA	2	0.003056933	0.023244435

I would appreciate any guidance

[Clyde Schechter]

The simplest way to calculate rolling statistics of any kind in Stata is with the -rangestat- command, by Robert Picard, Nick Cox, and Roberto Ferrer, available from SSC.

But I can't say anything more specific to your problem. I don't know what "realized volatility" means, and Google turns up nothing by that name for me. From the code you have attempted, it looks like you have some kind of standard deviation in mind, but I'm not sure what it's the standard deviation of, and I can't tell whether you want your rolling window to start at the given observation, end there, or be centered around it, or related to the current observation in some other way. If you can't figure out how to get what you want with -rangestat-, please post back with a clear explanation of what "realized volatility" is in statistical terms and I'll try to help.

[Saad Al]

My apologies for not explaining the realized volatility at the beginning. The realized volatility (RV) of an equity is nothing but the annualized standard deviation. So, for a one year (trading days) realized volatility, we begin by calculating the daily standard deviation as follows:

Where X is the log return per firm and X bar is the average/mean log returns per firm. If we multiply the daily standard deviation "S " by the square root of the window (say 252 trading days), we get the realized volatility of the stock for the past 252 days.

In my case, my window is only 5 days, so we are multiplying the standard deviation of the first five observations of each firm by the square root of 5 and should get something similar to this:

Date	firm	firm_id	L. Return	Realized Vol
30-Sep	AAK	1	0.005999244
1-Oct	AAK	1	-0.002981734
4-Oct	AAK	1	0.028037382
5-Oct	AAK	1	0.009090909
6-Oct	AAK	1	-0.029909907	0.04726612
7-Oct	AAK	1	0.021545317	0.051277327
8-Oct	AAK	1	0.002909088	0.050440216
11-Oct	AAK	1	-0.009064539	0.043677532
12-Oct	AAK	1	0.021588003	0.048804233
30-Sep	BBA	2	-0.015042983
1-Oct	BBA	2	0.006181821
4-Oct	BBA	2	-0.018070113
5-Oct	BBA	2	0.00952381
6-Oct	BBA	2	-0.006256904	0.027588189
7-Oct	BBA	2	-0.018518519	0.029372954
8-Oct	BBA	2	0.009433962	0.031108498
11-Oct	BBA	2	-0.02168224	0.03317864
12-Oct	BBA	2	0.003056933	0.029995836

Obviously, I won't be able to have any realized volatilities for the first 5 observations of each firm since I need the first 5 observation to get the window rolling to calculate the standard deviation and thus, the realized volatility.
I hope this helps.

[Saad Al]

I would appreciate any help in calculating the rolling window realized volatility.
Thank you

[Attaullah Shah]

Check ssc install asrol.

[Clyde Schechter]

I am not an -asrol- user, but since its author, Ataullah Shah is a professor of finance, there is a good chance that it is designed specifically to calculate financial indices like yours. That said, if it does not serve your purposes, the standard deviation over a 5 day rolling lagging-interval for lreturn can be gotten from -rangestat- with

rangestat (sd) lreturn, by(firm_id) interval(date -5 -1)

That said, these results do not match your variable realizedvol, even after multiplying them by sqrt(5). So there is some difference between what you describe and what you have calculated that I cannot pin down.

I should also point out that your date variable does not mention any year. To use -rangestat- (and I would bet to use -asrol-, too) you need a full date variable, not just day and month.

Correction: I see what you're doing. My calculation differs from yours in two ways. You are defining your five day lagging window as including the current date and extending back 4 days. Moreover, you are counting only days that appear in your data set (presumably these are the trading days), not all calendar days. When I change that, I do match your results:

replace date = date + "-2022"
gen _date = daily(date, "DMY"), after(date)
assert missing(date) == missing(_date)
format _date %td
drop date
rename _date date
by firm_id (date), sort: gen seq = _n // CREATE A TRADING DATE SEQUENCE

rangestat (sd) lreturn, by(firm_id) interval(seq -4 0)
by firm_id (seq), sort: gen wanted = lreturn_sd*sqrt(5) if _n >= 5

Note: To work with your date variable, I assumed that the dates referred to 2022, for demonstration purposes. In your real data you will have to supply the correct calendar year in order to avoid problems with, for example, leap years.