I don't have the prettiest solution but it gets the job done without too much high level coding. One note your dates include impossiblities like 31-Feb which doesn't exist. See the below code:
By ordering the data and using SAS's first./last. and the retain statement you can build rolling statistis within groups.
proc sql;
create table one
(name char(1)
,period char(8)
,ret num);
insert into one
values('A', '20010131', 0.1)
values('A', '20011231', 0.12)
values('A', '20020228', 0.22)
values('A', '20021231', -0.33)
values('B', '20010131', 0.12)
values('B', '20011231', 0.15)
values('B', '20020228', 0.44)
values('B', '20021231', -0.06)
;
create table two as
select name, put(input(period,yymmdd10.),year4.) as year ,input(period,yymmdd10.) as period format=yymmdd10., ret
from one
order by 1,2;
quit;
data three;
set two;
by name year;
retain sum_product NO 0;
if first.year then do;
sum_product=1;
NO=0;
end;
NO+1;
sum_product=sum_product*ret;
if last.year;
run;