Inflation always lags behind, though, and it’s pretty likely at this point that rising inflation indicators in the coming quarters force the fed to tighten. Opinions are very much divided on this, where many are convinced the fed needs to take drastic action to keep inflation from getting out of control with another financial crisis as a result. The other mainstream view is that we’re only seeing transitory inflation right now and as long as the real economy is healthy we shouldn’t expect inflation to persist and cause carnage.
I believe the situation is the same with stocks. They were criminally undervalued for decades (imo still are somewhat undervalued) so additional money supply causes the prices to increase (it's profitable to buy into great opportunity and pay back cheap loan later) but it's only because the assets were very cheap. If they weren't it wouldn't make sense to buy them no matter how much money is around (as you need to pay it back).
What may cause inflation though are programs when you just hand money to people (not as loans but as handouts) as then you just diluted everyone's else money.
Because another way to read the situation is that stocks are simply the asset of last resort. In a world with no interest, you can't park money in bonds (or CD's etc.) so you've basically got stocks, real-estate and commodities left as options.
Large-scale asset managers are not going to park billions of dollars under the mattress, so basically it has to go to stocks.