I write on this website about the Fed controlling interest rates, but I also write on part of it (see the Elliott wave section) that the Fed does not have any control over interest rates.
Let me explain. The issue is an indirect one. It is true - documentably proven (by the people at www.elliottwave.com) - that the Fed follows interest rates, rather than driving them. But most people don't know that - and so when the Fed says it is adjusting an interest rate, the people react accordingly in the economy and the stock market, since they think the Fed is in control all the time.
That is also why I claim that the Fed does have some control over the stock market, at least at times (probably basically ended in 2008, with that downturn - but the Wall Street traders do still have some control, for now).
The process in the stock market is simple - but indirect. People think the Fed has control all the time, so when the Fed makes an announcement, enthusiasm is increased and people buy into the stock market.
That is why the stock market could go exponential in the late 1990's (aside from the fact that the money the Fed pumped into the system in the 1990's was necessary for the stock market to be able to go so high in the first place and it is the fact of how the Kondratieff wave operates during this time, which was part of the plateau phase in our case due to the enforcement of the law against recessions during that time, that was the most basic reason why the people were motivated to put that money into the stock market in the first place) - and stayed up for as long as it did in the mid-2000's (because the enthusiasm of the plateau phase spilled over into the beginning of the depression phase, which started in 2000 in our case, due to the continued enforcement of the law against recessions, even though the law actually expired in the summer of 2000, a situation which was nominally just a coincidence relative to when the depression phase actually started).
The problem is that sooner or later, something is going to come along (guaranteed!) that perturbs the enthusiasm - and that's when the stock market goes back down. The higher it goes along the way, the further it has to fall - and that is our problem now.