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Probably 10 - 50 million. You will need 5 - 10 hard core programmers, a network engineer, a trader or three, a bunch of the fastest servers around, etc. etc. This is an insane idea, I would not recommend it! (The margins are being pushed to zero as more and more companies get into this.)

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I guess I meant excluding human labor (imagine that a bunch of programmers, etc. with the necessary skills wanted to do it). Would they need to rent a building next to the NYSE and put the machines there?

Yes they need to buy an office nearby to NYSE, to get fastest feeds(~ us).

Are there no hosting / cloud services for this sort of thing?

The network latency will kill you. You want to be in the same rack, not just the same colo, as the exchange's endpoints.

Are those slots in the same rack auctioned or something? How does having an office in a nearby building help?

Auctioned: I believe so.

I don't do HFT, but with what our company does, I've spoken to a few people who do. So take all of this with a pinch of salt, but as I understand it, your execution and autonomous trading systems live in the same rack as your exchange/dark-pool endpoints. Your slower strategies can be offsite, as is the Big Red Button to close down your positions. Still, faster's invariably going to be better, all else being equal...

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