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PhD vs Career; Oxford vs LSE?

...
1) Will having a PhD benefit my career down the line? Do most PMs have PhD themselves?
2) What is your opinion on the reputation of Oxford vs LSE (and possible vs Harvard)?
3) How hard do you think it would be to re-join the same HF after the PhD? Will I need to interview with them again like a fresh applicant?

My 2 cents

1) It might benefit or it might not. That's very hard to tell. It really doesn't matter if most PMs have PhD or not.

2) dk; dc

3) It could be really hard. Not only you will have to go through the same process, the best case scenario is that they don't remember you. If they remember you, they might not even give you a time because you reject them once. Just keep that in mind.
 
1) Impossible to tell.
2) At the end of the day reputation doesn't matter, what matters is what you do with your education. You can have all the PhDs in the world but if you can't make money.... My present concern with Oxford would be their connection with the Man Group which isn't doing so well at the moment. Not sure if that will have any impact now or later. Regarding Harvard, the question really is US vs UK? PhD from Harvard would be worth more in the US than Oxford/LSE (my guess only).
3) Once you're in the job, look around at the credentials of the people working there and if you really trust someone there, ask their opinion (I would be vague on time frame but ask if they think having a PhD is worthwhile in the long term).
 
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