It still seems to me that velocity can vary depending on the underlying entity. So unless every asset has the same velocity measure as the items in the CPI basket, it seems that there has to be some amount of inflation somewhere like possibly US equities.
How this interacts with assets is in my opinion not super clear. Pricing of assets is supply and demand, unlike the CPI basket. The CPI basket is based on human need. There's no human need for AAPL shares. However, there's a ton of stimulus money, and folks who remember 2008's V-shaped recovery, and a bunch of people stuck at home day trading. I think that's much more likely to be driving asset prices than supply. After all supply is enacted by changing lending parameters.
To the extent asset prices don't put pressure on CPI, they reflect an increase in welfare, not an increase in inflation.
Not necessarily, no. The value of money is a function of supply and velocity. If the velocity went down and the supply went up 25% the fed can still nail its 2% target. [1, 2, 3] If the velocity increases next year the fed can shrink the supply commensurately to maintain its targets.
[1] https://www.investopedia.com/terms/v/velocity.asp
[2] https://www.stlouisfed.org/on-the-economy/2014/september/wha...
[3] https://www.investopedia.com/ask/answers/042015/how-does-mon...