How to query for 'First showed up as'
My solution using SQL Server is as below. I could not test it in mysql as my ubuntu server is down. Also, I am not sure if mysql implements cte and window functions yet. In such case you may have to re-write the query as a stored procedure.

--Table definition

create table test
(f_date date,
trd int,
code varchar(10),
t_date date);

--Populate table

insert into test
values
 ('1-Jan-14',   1,          'B',                  '1-Nov-13'),
 ('1-Jan-14',   2,          'B',                  '3-Oct-13'),
 ('1-Jan-14',   2,          'B',                  '3-Oct-13'),
 ('2-Jan-14',   1,          'A',                  '1-Nov-13'),
 ('2-Jan-14',   2,          'A',                  '3-Oct-13'),
 ('2-Jan-14',   2,          'A',                  '3-Oct-13'),
 ('2-Jan-14',   3,          'A',                  '2-Jan-14'),
 ('3-Jan-14',   2,          'A',                  '3-Oct-13'),
 ('3-Jan-14',   2,          'A',                  '3-Oct-13'),
 ('3-Jan-14',   3,          'A',                  '2-Jan-14'),
 ('3-Jan-14',   4,          'C',                  '3-Jan-14');


--Quey code

 ; with cte as
 (select RANK()over(partition by trd order by f_date) as rank_no, trd, code, f_date
 from dbo.test) 
 select distinct test.f_date as 'Date', cte.trd as 'Trd', cte.code as 'First showed up as code',
 cte.f_date as 'In Date', test.t_date as 'T-Date'
 from test
 join
 cte on  test.trd = cte.trd
 where test.f_date = '20140103'
 and cte.rank_no = 1;

--Results

Date    Trd First showed up as code In Date T-Date
2014-01-03  2   B   2014-01-01  2013-10-03
2014-01-03  3   A   2014-01-02  2014-01-02
2014-01-03  4   C   2014-01-03  2014-01-03