Isn't that what FRS had been doing during QEs? The newly printed money went directly to financial markets, them hitting new highs. Did it contribute to the devaluation of the US dollar? If it did, then why is the USD index soaring? I guess in today's perverted world with the currency wars raging, it is not so straightforward as it had been in the good old days...
It might have a lag effect. Which is why the US is so concerned about inflation and ended QE.
Interest rates are going to go up some time this year too. This is a pre-emptive measure to prevent high inflation.
And there might never be a lag effect. Those too-simple-that-even-an-idiot-can-understand economy theories in economy books are only a very small subset of the giant central bank game. Central banks can make things works like those books described, but they can also change it when they see fit
They can print several trillion dollars and pump up the stock market and assets price, at the same time they tighten the loan condition so that majority of business and consumers are not qualified for a loan, then you have it: Increased money supply and deflation