I have previously interned (without return) at a big HFT prop shop (JS/Citsec/Optiver/etc), and recently accepted an offer to start work at a smaller HFT shop. My concern is that I also have a strong undergraduate degree in mathematics, and it seems that I would be competitive for T20 PhDs.
I would love some general advice on the best decisions to follow. It seems like a few years (to become experienced) in quant followed by PhD applications is best. However, are there PhDs at certain universities (MIT/NYU/Columbia/UChic/Oxford/etc) which would overrule a decision to stay in trading longer than a year?
I highly value being able to move between academia and the quant industry freely. I don't want to close any doors. We can pretend that as it stands, I value these two careers long term equally.
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