According to a recent study the default rates for mortgages over one million dollars is nearly twice as high as the default rate for mortgages under one millions dollars (14.3% to 8.3%). A default on a mortgage essentially means that the home-owner stops making mortgage payments and the bank takes possession of the home.
There are a lot of interesting mathematical, sociological, and perhaps ethical questions here, but I wanted to point out that although the above probabilities are interesting, the number and total value of the mortgages in question are probably more relevant data to consider.
For example, if only 1/10 of all mortgages are over a million dollars, then this statistic might not be that important; on the other hand, if a good number of defaults are way over a million dollars, than this statistic isn’t telling the real story either, but in a different way.
As an aside, renting vs. owning is a general and interesting mathematical question to explore in a variety of different contexts.