Rolling beta estimation

[Dowon1]

Dear all,

I'm working on a regression with rolling beta.

My regression starts from 2004/01/31 to 2017/12/31.

Based on 60 monthly returns, estimated betas for each of the two stocks at the end of each year for the recent 10 years.

For example, 2004/01/31 to 2008/12/31, 2005/01/31 to 2009/12/31, 2006/01/31 to 2010/12/31, ...., 2013/01/31- 2017/12/31.

It is to obtain period beta for stock A and B by 10 periods.

Here are my expected results:

                                                                  beta (A)   beta (B)

period 1 (2004/01/31 ~ 2008/12/31)           x.xx          x.xx

period 2 (2005/01/31 ~ 2009/12/31)           x.xx          x.xx

                           :                                          :               :

period10 (2013/01/31 ~ 2017/12/31)          x.xx          x.xx

SAS code in my textbook is following. How should I fix it?

data aaa ;

   set beta.beta ;

   keep cusip date ret sprtrn ;

   format date yymmdd6. ;

   rename cusip=firm ret=r sprtrn=rm ;

run ;

proc sort data=aaa ;

   by firm date ;

run ;

data begin (keep=firm bgndate) end (keep=firm enddate) ;

   set aaa ;

   by firm ;

   if first.firm then do ;

     bgndate=date ;

      format bgndate yymmdd6. ;

      output begin ;

   end ;

   if last.firm then do ;

     enddate=date ;

      format enddate yymmdd6. ;

      output end ;

   end ;

run ;

data length ;

   merge begin end ;

   by firm ;

   * delete firms with too few return days ;

   if bgndate > mdy (01,31,13) then delete ;

   if enddate < mdy (12,31,08) then delete ;

   keep firm ;

run ;

data gooddata ;

   merge aaa length (in=a) ;

   by firm ;

   if a ;

   n + 1 ;

   if first.firm then n=1 ;

run ;

%macro estim ;

%do x = 50 %to 66 ;

       data temp ;

                   set gooddata ;

                        if &x - 49 <= n <= &x ;

                        per = &x ;

            proc reg data = temp outest = results ;

                   model r = rm ;

                        by firm per ;

                        quit ;

            proc append base = betas1 data = results ;

%end ;

%mend estim ;

%estim ;

run ;

Here is sample data(data=aaa).

   data            firm                   r                  rm

040130     45920010       0.070673       0.017276

040227     45920010      -0.025899       0.012209

040331     45920010      -0.048290      -0.016359

      :                  :                     :                     :

171229     45920010      -0.003572       0.009832

[PeterClemmensen]

Show us some example data?

[ballardw]

Being a sometimes lazy programmer I might be tempted to add 10 variable to you data, one for each period such that period1=1 when date is in the given interval and 0 otherwise.

Something like:

data aaa ;
   set beta.beta ;
   keep cusip date ret sprtrn ;
   format date yymmdd6. ;
   rename cusip=firm ret=r sprtrn=rm ;
   period1 = (2004 le year(date) le 2008 );
   period2 = (2005 le year(date) le 2009 );
  /* continue the obvious pattern*/
run ;

Then your regression could look like:

proc reg data = temp outest = results ;

   where period1=1;

                   model r = rm ;

                        by firm  ;

                        quit ;

which would lend itself to a do 1 to 10 macro loop with : where period&i = 1;

I would also be tempted not to prefilter the "too few return days" but capture the n actually used by the model by adding:

ods output Nobs = ObsUsed;

to the Proc reg (and accumulating that as well)

You might want to add a label to the model statement such as:

Period&i: model ....

to have some additional information about which regression things are coming from as that label will be in the OUTEST or other model related output sets.

I have to say this bit of code is not obvious as to purpose

%do x = 50 %to 66 ;

       data temp ;

                   set gooddata ;

                        if &x - 49 <= n <= &x ;

                        per = &x ;

lots of magic numbers.