Paul Krugman is on the mark in his comments on quantitative easing and inequality. The policy has helped boost the economy and create jobs, it is almost certainly a net gainer from the standpoint of distribution. I would make three additional points, all going in the same direction.
First, when comparing the real value of the stock market to prior levels which we should expect an upward trend. The economy grows through time, as do profits, just assuming that profit share remains constant. The profit share has of course grown in recent years. This means that if the price to earnings ratio remains constant, then the value of the market should grow at roughly the same rate as the economy.
If we assume a 2.4 percent trend growth rate between 2007 and the present, the market should be roughly 17 percent higher in real terms today than in 2007, assuming no increase in trend profit shares. In other words, the market is pretty much in line with where we would expect it to be if there were no extraordinary monetary policy in place and the economy had followed it trend path. Crediting or blaming the Fed for the market's bounceback from the 2008-2009 lows is just silly.
The second point is that the impoverished masses with large interest incomes (that's a joke) also would benefit from the increase in asset prices, if they held any longer term bonds. When the interest rates on 10-year and 30-year bonds plummeted, the price of these bonds soared. This would have increased the wealth of middle income people who held these bonds. It's possible that they don't want to sell the bonds (after all, they can't get a high interest rate if they re-invest the money elsewhere), but this the same story for rich people who hold lots of stock. The high stock price doesn't do them any good unless they sell some stock.
Anyhow, the point is that in order for our middle income people to be hurt on net by the fall in interest rates, not only would it be necessary that all their money was in interest bearing assets (as opposed to stock), but it would have to be in short-term assets like savings accounts or certificates of deposits. This is a very small group of people. (I know everyone has an aunt who has $50k in a savings account -- sorry, someone is lying in that story.)
Finally, normal middle income people tend to be big net payers of interest because of something called a "mortgage." They may also have student loan debt. Lower interest rates have allowed tens of millions of people to have substantially lower mortgage and student loan payments. This is a huge plus on the distributional side. That doesn't mean that mortgage and student loan payments are not a major burden in many cases, but they would be a much bigger burden if the interest payments were 1-2 percentage points higher.
In short, the distributional effects of QE were almost certainly a net positive, in spite of the fact that everyone's aunt got hurt.