I made a spread sheet comparing renting to buying a few years ago. The premise was that I wanted to compare my investment in my home vs. paying less to rent and investing the difference in the stock market. The assumptions were something like a 3.5% mortgage rate (30y) and 4% appreciation on my home, vs. a 7% appreciation in the market.

What I found is that on a time horizon of ~7 years, it absolutely makes sense to buy a home. The reason is that when you have a mortgage, you're making a highly leveraged investment. If you buy a house for 100k and put 20k down, then you're 5x leveraged. If you're able to sell the house for 110k. The price has increased 10%, but your ROI is 50%.

There was a definite inflection point after 7 years, however, where the amount of leverage decreases to the point that the higher gains in the market begin to dominate the modest increase in home value.