It seems that when you put money into the hands of the public broadly, they consume goods and services. When you put money into the hands of the top few %, they have much less need for additional goods and services, so instead they invest it, which drives yields down and (consequently) asset prices up. The real question, then, seems to be how do we get money into the hands of tens of millions of grasshoppers and not just a few ants.
If the Feds return to QE, stocks and real estate go up further. I think stocks do so first, and real estate a bit more slowly.
And I think that what the Fed wants to do is unwind QE reasonably quickly, without causing the economy to tank (the real economy, not just the stock market). The real question is, how rapidly can the Fed unwind QE without damaging the real economy? Or can it unwind it at all?