Market adjusted buy and hold return calculation using monthly return data

[joon1]

Dear mkeniz,

I have difficulty to understand the generated output by sas program you advised. I would like to compute the following BHAR:

Buy and Hold Abnormal return= ((1+return(m1))(1+return(m2))----(1+return(m12)) - (1+marketreturn(m1)(1+marketreturn(m2))---(1+marketreturn(m12)), where m1=closemonth-11, m2=closemonth-10, m3=closemonth-9, m4=closemonth-8, m5=closemonth-7, --- m12=closemonth

As shown in the excel sheet, the computed values in three different ways  are different. 

computed value by original definition above: 0.052

computed value by log and exponential: 0.023

computed value by current sas program: 0.388

It will be highly appreciative if you can give an idea how to fix program to generate the closest computed value by original definition (0.052).

data c4;
** Generate 12-month rolling benchmark returns **
** Do this only once and save in an array **;
if _n_=1 then do until (end_of_benchmark);
set benchmark end=end_of_benchmark;
array bmrk_ret {1990:2019,1:12} _temporary_ ;
array logplusone {12} _temporary_;
y=year(date);
m=month(date);
logplusone{m}=log(1+vwretd);
if n(of logplusone{*})=12 then bmrk_ret{y,m}=exp(sum(of logplusone{*}));
end;
set ch2;
by permno;
if first.permno then call missing(of logplusone{*});
m=month(date);
y=year(date);
logplusone{m}=log(1+ret);
if closemonth^=.;
if n(of logplusone{*})=12 then bhar=exp(sum(of logplusone{*})- bmrk_ret{y,m});
run;

Thank you

Joon1

[ChrisNZ]

@mkeintz 

This might be a call to you?

[joon1]

Hi ChrisNZ,

Thanks for your comment

Could you please clarify your comment? I don't understand your comment.

Joon1

[ChrisNZ]

You start your question with:

Dear mkeniz,

which I assume means you directed your question to @mkeintz ?

[mkeintz · Accepted solution]

It looks like a misplaced close parens:

Instead of 

if n(of logplusone{*})=12 then bhar=exp(sum(of logplusone{*})- bmrk_ret{y,m});

bmrk_ret{y,m} was already exponentiated, so it should not be inside another EXP() function.  Try this:

if n(of logplusone{*})=12 then bhar=exp(sum(of logplusone{*}))- bmrk_ret{y,m};

I've been mostly offline lately, so apologies for the tardy response.

[joon1]

Thank you so much, mkeintz. I greatly appreciate for your kind advice. Your code works well.