Beta for Illiquid assets

Hi all! Today during class we were looking at the valuation of real estate and for the example given, the WACC was provided. I was just thinking that for the calculation of WACC, how do you estimate the beta? My understanding of beta estimation is that you will require a list of returns for both the asset and an index. Will it not prove difficult given that real estate is not a very liquid asset class and additionally, comps can be hard to find?

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