A lot of the money the Fed has spent to buy these assets has been deposited by banks back at the Federal Reserve as excess reserves.
Excess reserves now stand at over $2.5 trillion. Prior to the crisis, in January 2007, excess reserves were only $2.1 billion.
Excess reserves are cash balances that are not in the economy bidding up prices. We are in complete uncharted territory with these reserves. If they start to flow out of the Fed, the price inflation implications will be severe.