I tend to disagree a bit with the degree requirement. In general if you demonstrate impressive talent/research, firms will be interested. Firms that are stubborn and judge you just based on your on-paper degrees are likely firms you don't want to work for anyway. I would focus incredibly strongly on building your rigorous statistical knowledge, both in the specific tests, but more importantly in the general way a statistician looks at the world. Statisticians are like scientists and tend to constantly be looking for reasons to doubt claims: Why is this potentially not profitable? What biases could be causing this to falsely look good? Even Jim Simons of RenTech says that quant is really mainly statistics (https://www.youtube.com/watch?v=QNznD9hMEh0).
In order to rapidly iterate on statistical research you'll need to learn more programming. Both Python and R are very useful, but Python has a bit more momentum right now in industry and in my experience is generally far easier to use than R. Plus you can use Python for more applications, like full stack development or front end if you work in tech.
I want to shamelessly pitch our lecture series as it covers a lot of stats and coding. Folks I've talked to have said that having research done on Quantopian has helped them get jobs, as it's a way to display a portfolio just like an artist might. Quant firms will want to see interesting pieces of research more so than completed algorithms usually.
At the end of the day pick projects that are interesting to you. Google what you don't know and keep pushing forward. The thing is, if you develop some great skills in stats and programming, there are tons of jobs waiting to be filled right now, not just quant. So it's not an over-concentrated investment to learn these things.
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