Will QE3 raise stock prices? My answer is yes, but the impact will be quite small at first, and will only become visible with the scale of its impact on the Monetary Base (the Fed's securities portfolio).
First of all, we need to recognize that the Fed's balance sheet has not grown since May of 2011, seventeen long months ago. There has been zero monetary stimulus for over a year. Second, we need to recognize that, although the Fed promised to start QE3 on September 13th, it has not yet started. Don't ask me why. I can imagine a number of (unsatisfactory) reasons why QE3 hasn't started, but it hasn't started. The Monetary Base is still the same size that it was in May, 2011. The Fed has provided no explanation for the one-month siesta.
Therefore, we can't make any empirical statements about the impact of QE3 on the Dow, because there is no QE3 yet. Assuming that Bernanke gets his act together, QE3 should get started by the end of this month. The Fed's announced schedule for QE3 was to buy $23B in September and $40B in October. That means they will need to buy $72B between now and the end of the month (since the MB has declined by $9B since the FOMC announcement). I'm not holding my breath; the Fed appears to be taking its public promises as very general guidance.
The amount, $72B, is peanuts, as it would represent an increment of only 3% on the Fed's balance sheet. This is why the impact of QE3 will only be felt cumulatively, as the little bits start to add up over the next six months. Six times $40B is $240B, which would represent a 9% growth in the Fed's balance sheet, which becomes more significant--but that's next April. Even when QE3 gets started, it won't be an adrenaline injection; more like a cup of coffee.
If there has been no bond-buying by the end of this month, I will demand an explanation.