Yeah I guess the main flaw is that the market is not totally efficient and the two are not 100% covariant so this will never be a perfect strategy.
But as a general hedge (say 70% or so covariance), and as a theory only, does it not work?
They have REITs that cover individual neighborhoods?
Neighbourhoods no, but countires yes.
If you live in a small enough country (UAE, Hong Kong, etc) the correlation would be higher, plus I would blindly assume that REITs, for the most part, hold property in urban areas not rural countryside, which should increase the correlation if you also live in a city.
What if that REIT owns more buildings across the country, and those fall in value? Suddenly your rent is rising as the REIT price is falling.
Even if your REIT only held the one building, you're assuming the market is perfectly efficient - i.e. the REIT value is 100% directed by the current income. However it's been shown that REITs tend to track the market. So market falls, REITs fall too. Your rent could be increasing though, as the stock market overall is falling.
I suppose the hedge is more against the systematic risk of rising prices, rather than the unsystematic individual properties.
Ah well, was mostly just a thought exercise that I hoped to try and stir up some discussion around.
I think it's cool to consider using financial tools such as derivatives and future options to hedge against real world costs of stuff, it helps understand a connection between Wall Street and Main Street.