According to the Fed, QE's aim was to drive down interest rates to unattractive levels by purchasing bonds in the market, thus encouraging participants to purchase riskier (and higher-yielding) securities. As Cornerstone's Ronnie Spence notes, this risk-seeking behavior in theory boosts asset prices (and increases the 'wealth effect'). However, when one examines what has actually happened under QE, only stock prices have followed the QE theory.
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In fact interest rates have only declined in periods when the Fed stopped QE.
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Spence points out, that the drop in rates in response to QE likely results from the plunge in equity prices that has resulted when the Fed has looked to end their QE programs. Put another way, "Taper" is a false narrative for higher rates when in fact all the 'taper' risk is in stocks (and historically traders haven't priced it in until the money actually stops flowing).
(h/t @RonnieSpence)