PhD & Tips For Portfolio Manager Career

(Forgive me. English is not my first language)

Soon I'll finish my MSc in Mathematics from a non-target Uni (top #5 for math and engineering in Italy according to qs ranking). In these months I'm an exchange student at a university in Paris, and I'm more and more convinced to apply for a PhD in applied mathematics at a top university here in Paris (there are excellent universities with strong math departments like Ecole Polytechnique, dauphine- PSL, centralesupelec, Paris-Saclay, Sorbonne, MarieCurie). I would like to start a PhD and delve into fields such as portfolio optimization, model and risk calibration, or even mathematical concepts on stochastic analysis; I am strongly interested in deepening these aspects (which I also saw in my master's degree) and I believe that a PhD gives a lot of freedom, in the sense that it gives you the freedom to apply and be considered in many different companies. 

In fact, my dream is to become a portfolio manager. This doesn't mean that during the doctorate I'll only think about working in companies and not being interested in academic life, on the contrary, I am very interested in the subjects mentioned above and I would like to deepen them, in fact, I know people will tell me that generally you don't need a phd to reach a position as pm, but I'm interested in doing it to broaden my knowledge and to do research in these fields.

Questions part: 

My concern is making mistakes and wasting time getting to a pm role.

Let me tell you that I don't think I'm interested purely in quantitative HFs, or in places where you are required to coding for most of the day and to produce technical algorithms.

So I ask you, what would you recommend? what is the most common and successful career to become a pm? what kind of asset management firm or HFs can I be interested in?

what would you recommend me to do after the phd? And also, do you have any books or articles or links that help me better understand the differences between the various job positions in the various HFs or in the various BBs or MMs?

thank you very much.