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Hedge Fund/Prop Trading after MFinE for international?

Hello everyone!

I have a question regarding FinE programs that has entered almost every international student's mind.

In multiple forums it has been stated that it is extremely difficult, particularly for international students, to join a HF or a prop trading firm after a FinE Masters. However the reasons are not exactly clear

What I want to know is this:

1. Why is it particularly so hard for international students? If BB banks are happy hiring international students, why are HFs so reluctant?
2. It is said that a lot of the stocal and derivatives curriculum is imp only for the sell-side and buy-side firms are not really concerned about these. Some forums have mentioned that buy-side firms focus more on programming and data science skills and hence prefer CS, Math grads. What if the FinE student takes up these courses and has an undergrad degree in computer science or math? Would that give them a better chance at say Citadel, 2 Sigma, IMC etc?
3. What would be an ideal path, if one exists at all, for an international MFinE student to make it to a HF or prop trade shop

Thanks in advance!