How to code to calculate Buy-and-hold Abnormal Return (BHAR)

[xipei li]

We use the income from May of T+1 to April of T+2 as T annual income.BHAR is equal to the multiplier of each company's 12-month revenue in a year, and then subtracts the 12-month revenue multiplication of the market in a year.For example, A company's 2015 BHAR is equal to the company's monthly yield from May 2016 to April 2017, and then subtracted the yield from May 2016 to April 2017.This is too complicated, I really can't figure it out, so ask questions.IT is Individual income.MT is market income
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* Example generated by -dataex-. To install: ssc install dataex
clear
input str6 code str7 date double(IT MT)
"000002" "2009-01"  .091473  .157394
"000002" "2009-02"  .015625   .08893
"000002" "2009-03"  .158042  .223024
"000002" "2009-04"  .024155  .076364
"000002" "2009-05"  .148585  .071731
"000002" "2009-06"  .314909  .088737
"000002" "2009-07"  .047843  .148047
"000002" "2009-08" -.296407  -.15897
"000002" "2009-09"  .108511  .045235
"000002" "2009-10"  .104607  .120721
"000002" "2009-11"  .001738  .146828
"000002" "2009-12" -.062446  .025708
"000002" "2010-01" -.135985 -.032345
"000002" "2010-02"  .009636  .066523
"000002" "2010-03"  .007423  .042699
"000002" "2010-04" -.178947 -.070492
"000002" "2010-05" -.066826 -.085053
"000002" "2010-06" -.059639 -.092684
"000002" "2010-07"  .222714  .152968
"000002" "2010-08"  .015682  .091707
"000002" "2010-09" -.002375  .014685
"000002" "2010-10"  .154762  .092551
"000002" "2010-11" -.161856  .008053
"000002" "2010-12"   .01107   -.0194
"000002" "2011-01" -.002433 -.049277
"000002" "2011-02" -.004878  .097416
"000002" "2011-03"  .064951 -.005443
"000002" "2011-04" -.024166 -.029671
"000002" "2011-05" -.063769 -.073427
"000002" "2011-06"  .077806  .037579
"000002" "2011-07" -.035503  .021129
"000002" "2011-08"        0 -.028933
"000002" "2011-09" -.111656 -.117144
"000002" "2011-10"  .104972   .03965
"000002" "2011-11"   -.1175 -.044145
"000002" "2011-12"  .058074 -.155997
"000002" "2012-01"  .024096  .007288
"000002" "2012-02"  .082353  .130467
"000002" "2012-03"        0 -.072395
"000002" "2012-04"  .084541  .075331
"000002" "2012-05"  .030067  .020294
"000002" "2012-06" -.036757 -.064925
"000002" "2012-07"   .05041 -.092077
"000002" "2012-08" -.131094  .019197
"000002" "2012-09"  .051122   .01457
"000002" "2012-10" -.013049   .00558
"000002" "2012-11"  .051683 -.108443
"000002" "2012-12"  .156571  .166233
"000002" "2013-01"  .186759  .065083
"000002" "2013-02" -.000833  .043567
"000002" "2013-03" -.103333 -.033948
"000002" "2013-04"  .025093 -.032165
"000002" "2013-05"  .102837   .13469
"000002" "2013-06" -.177796 -.163374
"000002" "2013-07" -.033503  .062773
"000002" "2013-08" -.006303  .092286
"000002" "2013-09" -.034884  .048109
"000002" "2013-10"  .008762 -.020632
"000002" "2013-11"  -.04886  .071771
"000002" "2013-12" -.083333  -.03295
"000002" "2014-01" -.080946  .005079
"000002" "2014-02" -.089431  .043985
"000002" "2014-03"  .203869 -.017824
"000002" "2014-04" -.023486 -.012822
"000002" "2014-05"  .142649  .024008
"000002" "2014-06" -.032749  .040563
"000002" "2014-07"  .197098  .092952
"000002" "2014-08" -.078788  .060615
"000002" "2014-09"  .006579  .143076
"000002" "2014-10"  .023965  .023014
"000002" "2014-11"  .159574  .063455
"000002" "2014-12"  .275229 -.010609
"000002" "2015-01" -.056115  .072194
"000002" "2015-02" -.028201   .07249
"000002" "2015-03"  .083922  .224049
"000002" "2015-04"   .05644  .189475
"000002" "2015-05" -.017123  .270192
"000002" "2015-06"  .011847 -.076295
"000002" "2015-07"  .010236 -.166447
"000002" "2015-08" -.026798 -.131148
"000002" "2015-09" -.077536  -.05459
"000002" "2015-10"  .073841  .218789
"000002" "2015-11"  .102414  .108848
"000002" "2015-12"  .621102  .076944
"000002" "2016-07" -.268932  .010287
"000002" "2016-08"  .454492  .053706
"000002" "2016-09"  .049739 -.003338
"000002" "2016-10" -.047765   .04209
"000002" "2016-11"  .082665  .037181
"000002" "2016-12" -.238325 -.034747
"000002" "2017-01"  .006326 -.017722
"000002" "2017-02" -.007253  .052976
"000002" "2017-03"  .002435 -.015306
"000002" "2017-04" -.052478 -.056799
"000002" "2017-05"  .090256 -.076485
"000002" "2017-06"  .174506  .041879
"000002" "2017-07" -.064077  .003885
"000002" "2017-08"  .027624  .038274
"000002" "2017-09"  .130004  .010294
"000002" "2017-10"  .103238 -.010664
end

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[Attaullah Shah]

You have asked the same question in yesterday's post. I think the FAQs warns against doing so.

To get you going, you may be interested in reading the help file of asrol (downloadable from SSC) and its product function for finding products of values. The following steps might be helpful to you in solving the problem.

1. Download asrol from ssc

ssc install asrol

2. Create daily date, month variable, year variable and the forward year variable

gen mofd= mofd(date(date, "YM"))
gen month =  month(date(date, "YM"))
gen year = year(date(date, "YM"))
* Create a forward year variable, you have to figure out the logic of months and year here

3. use asrol

bys code fyear : asrol IT, stat(product) add(1)
bys code fyear : asrol MT,  stat(product) add(1)

* And then find the difference of the two variables created by asrol

[xipei li]

Thank you for pointing out my mistake. Thank you. Could you be more careful? Besides, I don't know how to do it even by multiplying.

[Andrew Pierce]

This is a very simple manual way to approach it and you should be able to follow the code.

1) Panel your data:

egen firm=group(companykey)
gen year=substr(date,1,4)
gen month=substr(date,6,2)
gen day="20" // Arbitrary day that works in any given month

gen tempdate = year + "/" + month + "/" day
gen date2 = date(temp,"YMD")
format date2 %td
drop year month day tempdate

gen month=mofd(date2)

xtset firm month

2) Assuming that IT is firm-specific and MT is the benchmark, create adjusted return and create compound buy-and-hold adjusted returns for the year ending each month in your data:

gen adj_it = it - mt
gen compound = (1 + adj_it) * (1 + l.adj_it)

forvalues i=2/11 {
      replace compound = compound * (1 + l`i'.adj_it)
}

gen bhar = compound - 1

drop compound

If you have breaks in your series (e.g., you're missing Feb and Sep in a given year) then you need to make a decision of how to deal with that because you lack sufficient data to compute BHARs for months that require lagged data from those periods. Hopefully the above code is helpful for you and demonstrates the simple approach to creating adjusted returns and compounding over a specific window of time

[xipei li]

This is a very simple manual way to approach it and you should be able to follow the code.

1) Panel your data:

egen firm=group(companykey)
gen year=substr(date,1,4)
gen month=substr(date,6,2)
gen day="20" // Arbitrary day that works in any given month

gen tempdate = year + "/" + month + "/" day
gen date2 = date(temp,"YMD")
format date2 %td
drop year month day tempdate

gen month=mofd(date2)

xtset firm month

2) Assuming that IT is firm-specific and MT is the benchmark, create adjusted return and create compound buy-and-hold adjusted returns for the year ending each month in your data:

gen adj_it = it - mt
gen compound = (1 + adj_it) * (1 + l.adj_it)

forvalues i=2/11 {
replace compound = compound * (1 + l`i'.adj_it)
}

gen bhar = compound - 1

drop compound

If you have breaks in your series (e.g., you're missing Feb and Sep in a given year) then you need to make a decision of how to deal with that because you lack sufficient data to compute BHARs for months that require lagged data from those periods. Hopefully the above code is helpful for you and demonstrates the simple approach to creating adjusted returns and compounding over a specific window of time

thank you so much！