Some of that search is of course coming from offshore. That’s a big part of how accommodative monetary policy works: by prompting substitution towards higher-risk assets; raising asset prices, which increases collateral values and makes credit extension more viable; improving the cash flows of debtors; and so on. All those things are quite normal parts of the so-called “monetary transmission mechanism”.
In some ways that term is a misnomer because while some of the “transmission” is somewhat mechanical, a lot of it isn’t. It depends on the behaviour and general frame of mind of the myriad households, businesses large and small, investors and financial market players and so on.