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Where is the money that is stuck in the house, that would hypothetically be able to be invested if not spent on the house? You have to pay to live somewhere, and if you're paying less to purchase than rent, that is money saved which is available to invest. Do you mean the up-front downpayment money needed to acquire a mortgage in the first place (typically 10-20% of the purchase cost), that could be invested in the market instead for a higher return than slowly building equity through principal payments?
Let me give you an overly simplified example. You are in a property market where rental yield is 3% (happens in some cities)
You could put a million dollar into buying a house and save $30k in rent every year
or
You could rent a million dollar house for $30k, and invest your million dollar in the market at 7%, returning $70k per year
Obviously this gets more complicated with mortgages, taxes, maintenance, interest rates, etc. but the gist of it is that owning your home always comes with an opportunity cost, every dollar of house equity is a dollar that isn't invested somewhere else. Depending on circumstances, renting might be the most economical choice.
This is interesting. I do get that if you have initial money to buy a house outright, there are better mostly safe things you can invest in, to get a higher return on investment than a house. If I got a 30 year mortgage in 1994 and paid $1M over that time to pay it off on say, a 5% fixed rate with no PMI or downpayment required, the purchase price was probably closer to $500K assuming 2.5% average annual inflation. And average housing inflation since then was more like 2.8%, so factoring in maintenance and taxes and insurance, guessing no real appreciation over that time. But the quality of life difference to an apartment of the same cost would I think in most cases more than make up for it.
I think where I'm stuck is, we're starting from the idea of having $1M in hand to start out with to buy a house outright or rent + invest, where a much more common situation is either: I have not got anything saved up, so I can neither invest nor get a mortgage without an initial downpayment; or else, I have enough saved up for a downpayment or PMI and hopefully a secure enough income to pay the mortgage every month.
In my case, mortgage + escrow + maintenance costs are still less than half what I was paying for my cheapest studio apt nearly a decade later, and a much better quality of life because of the extra savings. My neighbors are renting a nearly identical house, and it's criminal how much they have to pay to stay there. I wouldn't be able to afford rent here.