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Pension funds are investing in rental properties but it's mostly big assets for rental (i.e build to rent schemes) which will be debt financed to a set LTV (e.g. 60%). They probably do encourage supply as they often / usually buy new, or enter into forward funding to develop them out. But I think they probably on average have less time in the market than owner occupiers (where the average is probably pretty long as it includes all the "I bought my house in the 1970s" crowd) so I just didn't follow why they have some sort of resilience due to capital gains.
Don't get me wrong, I'm not saying the market is going to correct magically in a way that is great for homeowners, I'm just not sure I follow your arguments for why investors are necessarily better equipped to ride out turbulence.
Pension funds, banks buying properties and foreign investors are largely cash markets.
Those on BTL mortgages will pass on the increased costs to renters (further fucking anyone looking to buy a house) until that market goes pop too.
We're a long way off houses shrinking to affordable rates for the masses and getting there will crash the economy / fuck normal people for years first.