The Fed's balance sheet has been expanding over the last few month due to QE3. When the Fed goes out to buy treasuries or MBS, it's taking those securities out of the market and exchanging them with cash (an increase in the monetary aggregates). Question is, if the central bank buys treasuries from the primary dealers, where does the primary dealer take the cash he just received from the Fed? Many are claiming that the rally in the SPX index is fueled by QE's easy cash, if so what data could be used to validate this story?
First of all Fed traders do not necessarily buy from primary dealers. In fact Fed buys most treasuries in the secondary market and that can include sell-side investment banks or even large fund houses that may not have primary dealer status.
Keeping this in mind, essentially anyone who has large chunks of treasuries to sell which the Fed might be fond of will use the money to either re-invest elsewhere or park with, guess who, the Fed. Yes, the sad truth is that a lot of the money the Fed intended to pump into the system gets parked in overnight or even term loans with the Fed, exactly where it came from for lack of investment opportunities. The rest will be invested in fresh bond series, equities, essentially anything that meets the investment guidelines and targets. Only money that banks cash out of selling bonds to the Fed off their own balance sheets can be put to work and lend out by a multiple through the fractional reserve banking system.
Now, the reason why equity markets are so bid is not really because of quantitative easing but it is due to a reason that also originally caused the Fed to act by buying government bonds: Unstable markets and a lack of growth. Hardly any company currently invests in capital expenditures, hardly any company shows interest in buying other companies (at least not to the tune of past deal data), hardly any company massively pays out dividends. Guess what that results in: Exorbitant earnings. Equity investors like nothing more than higher expected earnings and potentially juicy dividend payouts and that is why everyone chases equities.
That the Fed stepped in and still continues to pump money into the "system" (again system here is meant to be those who sell treasuries to the Fed) is an important psychological factor but in terms of distribution of money it hardly can even be compared to large fiscal packages that the government may shower upon its people and corporates (such as the Japanese government is doing without much success).
In summary, the biggest effect the Fed is having on equity markets is a signaling effect and a subordinate effect is that Fed is freeing bond holders off their investments and letting them switch into other asset classes, such as equities. Keep in mind that some of the largest bond powerhouses publicly announced they believe the bond rally has ended and that they have started to lighten up on their US government bond holdings. Of course a big reason for that is also the meager returns US treasuries provide vs, or example, emerging market bond yields. So, I do not believe the Fed directly pumps any money into equity markets. Remember that BOJ has run a zero interest policy (their own form of QE) for years and look where Nikkei has traded until recently. The large Nikkei rally can thus not be attributed to BOJ buying government bonds but almost entirely to the effect the buying has on the exchange rate and direct impact on Japan's export-centric industries. Similarly, US equity markets are fueled by other factors, which I mentioned above, rather than a direct effect that results from Fed purchases of US treasuries.