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Applied Math PhD or Quantitative Consulting

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Coming out of undergrad I have offers from top 50 applied math PhD programs but also a nice offer from a big 4 group that does consulting (heavily quantitative) mainly for financial institutions. Not really sure what my ultimate career goal is but I'd like to either end up at a quant fund or in pe (I know these are very different, I just have a diverse set of interests). I have a variety of connections in pe (and ib). Should I work for a few years and then pivot/go back to grad school or get my PhD and hope for the best? I'm mainly worried about the opportunity cost of a PhD.
 
If you have the talent for Maths, do a PhD. You'll always get a job later. On the other hand don't do a PhD (just) to get a job, this won't motivate you on this lonely road.

Do big 4 do quant or check others' models? In this regard the cutting edge is a bit further away..
 
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If you don't view it as a means to an end, do the PhD. If however you are sure you want to end up at a quant fund, and have been applying for jobs and not getting any replies, then your CV is probably weak and having a maths PhD would make you a more viable candidate. If you are getting interviews, but not offers, I don't think the PhD would help you much in jobhunting.

In the consulting gig you will probably, but I'm guessing here as I don't even have a job description to look at, be working in writing up model documentation or checking said models and documentation for a big sell side institution. The work is often very maths heavy, usually does not involve much programming (but it can), and is somewhat removed from the action.

Jumping to work at a bank then in a model validation capacity I would say should come naturally, but it is doubtful that this will get you any closer to a quant hedge fund, and I do not expect the funds to share their models with outside consultants anyway.
 
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