2 major inflation phases in the recent history (blue chart above): first time between 2009-11, post crisis times (yellow marks). During this time Nasdaq actly ended up 12% higher, while SP500 rose around 15%. I believe the difference is because Nasdag is more heavily weighted towards growth companies, which apparently sucked back then during staples and other consumer sectors rose.
Then comes the similar trend in the second phase of the inflation (purple marks), which was between 2015 - 2017, the rate hike period of Yellen. This time Nasdaq goes up by almost 50%, while SP500 repeated the similar growth trend of 13% like before.
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