Relationship between CPI inflation and asset price inflation

What is the relationship between consumer inflation and asset price inflation? Are these linked?

For example, Bond buying / general Fed balance sheet expansion in the 2010s led to rampant asset price inflation. And recently, direct cash injections to Americans has led to rampant consumer inflation.

It seems like wherever you have artificial cash injections, you see inflation, which makes sense. But is there any spillover effect, i.e. increase in consumer inflation should have a second-order effect on asset price inflation, or vice versa?

I don't have any academic business or economic training so would appreciate a nudge in the right direction with my thinking. Thanks in advance. 

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