Interesting, we were just talking about that on a related thread, but the thing is that the fed does not buy common stock (much less derivatives/futures) so they can't move share prices. Loony leftists like to say the government's all powerful but in real life the Fed's small potatoes. Right now Fed banks got about $4T --mostly T-bills plus a few mortgages. Total corporate assets (from page 124 of the Flow of Funds) for non-financial businesses is $37T. The Fed --or any governmental agency for that matter-- couldn't control the free market even if it wanted to. Central planning is a lie --one that works great only for pundits and politicians.
The Fed and Central Banks in other countries buy futures contracts on broad market indexes and derivatives on the same. If you Google it, you will find plenty of information.
Certainly, the Fed has expanded its balance sheet with huge amounts of bond buying, forcing money into the stock market and making it attractive for companies to begin stock buy-backs with such low rates.
It goes beyond that though. I recently sold my investment management firm after 27 years of being involved. Every trader I know, who sits at a terminal every day and watches what is happening tells me that an unseen hand is stepping in at every dicey decline to save it from disaster.
Central banks around the world are buying stocks. When you have lots of money, the easiest way to get exposure is with futures on indexes - or other derivative contracts.
As a sample to save you time...
http://www.zerohedge.com/news/2014-08-30/its-settled-central-banks-trade-sp500-futures
http://nypost.com/2014/10/20/plunge-protection-behind-markets-sudden-recovery/
http://www.zerohedge.com/article/us-government-buying-stocks
http://business.time.com/2013/04/26/why-are-central-banks-suddenly-buying-stocks/
http://www.zerohedge.com/news/2015-03-11/how-boj-stepped-143-times-send-japanese-stocks-soaring