Oh wow so strong! Congrats on your offers and thanks for sharing your status. Firstly as usual, forgive me to ask for that but please do help us in sharing as many interview experiences you had (esp with those you got offers from...) with us so that we can further help coming applicants via here 👉🏻👉🏻http://bit.ly/InterviewStatus! It is so crucial to us!!

Concerning your situation, really appreciate that you do have a clear sharing on what you ultimately want and can definitely tell you are quite familiar with the possible working environment and exposure of those offers on hand already. From our understanding, what you mentioned is basically correct. Bloomberg should be somehow "nearer" to what you wanna be in the future but not close enough. It is not impossible for you to jump into investment banks (emmm of course even further to S&T I guess you know that) but it may take you some more time and exposure before you get a chance for the leap. From the search results I can see, "Equity" or "Product" roles of Bloomberg will be much closer to investment bank future opportunities. Below shows some related examples (sort-of) that you may wish to take reference from:

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Source: LinkedIn

For HASE Global Banking, yes it is possible for you to jump into foreign big banks, but in much more scenarios I can see from the past would be getting a career leap to Citi / HSBC / SCB at first and possibly into other overseas banks in later stage. Below shows an example but definitely not a close one as (1) not as a HASE Management Trainee and (2) She/he starts her/his career with a French bank trainee offer, but yea:

To conclude, if you are more inclined toward the Global Banking side, I would say HASE MT may still give you a decent chance of great progression into both big and overseas banks: while Bloomberg can buy you an immediate "foreign" firm exposure but seems there is still quite some spaces between this and IB S&T. Though the working scope may be unique, actually the skills you learnt on Bloomberg terminal are something treasurable and you may even broaden your career exploration into other financial services providers eg Moody's / S&P / Factset etc too.

Hope the above helps.