Quant Education

I am about to complete an a UK BSc in Economics and Econometrics. I want to become a Quantitative Analyst one day but I have never heard of quants coming from this sort of background. My questions are:

1.) Since I'm looking at applying for an MSc in Statistics and eventually going into a PhD in that field. Would this line of education be good enough to prepare someone for quant work? Of course I'm planning on toning up my programming skills over the years too.

2.) Or is it just too unrealistic a plan, is there no way an Econometrician can do quant work? Should I just start a completely new degree; earn a second Bachelors in Mathematics and Computer Science? I am serious about this and would willingly go to school for another decade.

3.) If anyone out there knows or any sort of postgraduate mathematics conversion diploma, that'd really help me out.

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