Consumer price inflation is not responsible for the increase in equity valuations, but quantitative easing and bond buybacks certainly do. QE reduces the yield of bonds, making stocks look more attractive and hence resulting in more money flowing into stocks.

It additionally devalues the dollar, which leads to assets to be worth bigger numbers. QE has been mainly flowing to investors and the financial sector, and ts been staying there, hence not translating to consumer price inflation.

So yes QE is responsible and QE caused inflation and inflation is also responsible. This inflation is confined to investment assets.