However while the typical wall steeter used to be a liberal arts major, it has heavily shifted toward STEM. At most i-banks, something like a third of headcount are tech. Even many of the front office are engineers, though again moreso in trading/asset management. Nowadays a large part of the competitive advantage comes from better software - a classic example of 'software eating the world'.
Anecdotally some of the brightest people I've known were at BGI (now Blackrock), and they all had deep knowledge in finance, math, stats, tech and old school boys club company politics. [my old boss read math cambridge with stephen hawking and created the first and now biggest by AUM electronic portfolio management system for index funds, grinold & kahn literately [1] wrote the book on active portfolio management, etc]
[1] http://www.amazon.com/Active-Portfolio-Management-Quantitati...
[1] http://www.amazon.com/Active-Portfolio-Management-Quantitati...
A big part of algorithmic trading and stat arb is portfolio management, including deriving alpha, building risk models, etc.
The bible is: http://www.amazon.com/Active-Portfolio-Management-Quantitati...
To run a successful strategy requires strong signals (indicators that dictate what to buy/sell and when), execution (actual filling of orders on exchanges), risk management (which can include statistical risk modelling as well as draw-down controls), and infrastructure (the wrong type of bug can be costly enough to kill the whole operation!).
As mentioned earlier, there is overlap in the skills and experience required for these broad categories, but people in the quant hedge fund/asset management industry typically specialize in one. This is where larger shops have an advantage. The entire strategy is only as good as its weakest link. Its common for people who haven't worked in the space to focus mostly, or even exclusively, on the signals and infrastructure aspects.
If you were to group most of the successful quant funds out there by alpha time horizon you would see that funds within the same bucket are generally running very similar types of strategies using very similar signals (the general concepts behind successful signals/execution of varying time horizons are actually not that complicated, but just might take a while to explain). Again, that's not say its easy to do. With most of the equities and derivatives markets getting ever more efficient, tighter coordination and implementation of the entire strategy pipeline (signals, execution, risk mgmt, infrastructure) can lead to significant Sharpe/Information ratio improvements.
If you wanted to get a feel for how some successful people in the industry think about the problem, I would recommend reading through the following books in roughly the corresponding order:
1 - https://www.amazon.com/Efficiently-Inefficient-Invests-Marke...
2 - https://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3...
3 - https://www.amazon.com/Active-Equity-Management-Xinfeng-Zhou...
And I didn't personally like this one so much but its quite popular among the more "academic" types
4 - https://www.amazon.com/Active-Portfolio-Management-Quantitat...