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ThrustVectoring comments on Open Thread, June 2-15, 2013 - Less Wrong
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In a competitive and efficient market, he'll profit on average to the tune of the risk-free interest rate (~2% or so now) but higher since renting is not risk-free. So you could start by figuring out his risks in renting out to you.
There's also a non-obvious positive risk, too. Specifically, the appreciation of real estate prices. If the landlord owns a $120k house that they expect to increase in value 1%/year over their mortgage rate, then that's another $100/month that the landlord doesn't have to get in rent.
In other words, the landlord is holding an equity position in the real estate they are leasing to you. This equity position can appreciate, giving a non-rent-collection profit source that increases the price they are willing to pay for the real estate in the first place, lowering their profit as a percentage of capital invested.
But it can also fall, as we witnessed not too many years ago... Any speculation on real estate will already have been priced in and the expected profit from buying a house minimal.
To borrow your phrasing - in a competitive and efficient market, the expected profit from buying a house is equal to the risk-free interest rate. So my math actually was rather bogus - I should have talked about how the landlord should expect his $20k equity stake to appreciate at the risk-free interest rate (~2%), which would shave $400/year off the amount of collected rent needed to justify the house price in the first place.