This was largely due to the supply glut of oil. Price of food went up by~3.5%.
Additionally CPI tends to be a lagging indicator. In other words it is a good way to determine if we have just seen massive inflation. The stock market is forward looking, meaning analysts are considering future risks in pricing the assets.
This is true, but various parties have been predicting a large increase in inflation in the US for years and years and they keep being wrong. I expect them to be wrong again this time too.
It's simply not true that they keep being wrong. Yes, hyper-inflationists were wrong. But "much larger inflation"-ists were not wrong.
Anything with inelastic supply has gotten more expensive by an average of about 3% every year for the last decade: health care [0], education [1], real estate [2]. That's 50% higher inflation than the 2% conventional target, and arguably after the revelations of 2008 one might justifiably expect even lower than 2% natural inflation.
Then there's the very rapid rise in the price of stocks which is itself a form of price inflation (it takes more money to buy the same share of the productive economy).
Anything rich people/institutions hold or supply in exchange for dollars from laborers has gotten more expensive at a substantially-higher-than-normal rate.
There will always be some subset of goods that rise in price faster than the rest of the basket especially when those goods have artificial constraints on supply. That doesn't mean that inflation is rising faster than the overall basket of goods.
When we talk about the rate of inflation we aren't talking about the cost of health care or education or real estate or really any other particular good. We're talking about the value of money.
You're just choosing a definition that is convenient for you, and I might mention convenient for the wealthy establishment. The things ordinary people most need to buy with money have gotten more expensive — not as a blip, but durably and steadily for a decade. If you want to die on the hill of "this is not how I choose to use the word 'inflation'" then that's fine, I just don't see it as very persuasive.
Stock market PE ratios are up a little bit over long run historical averages but hardly out of line with fundamentals. The same goes for price to rent ratio of most real estate.
Additionally CPI tends to be a lagging indicator. In other words it is a good way to determine if we have just seen massive inflation. The stock market is forward looking, meaning analysts are considering future risks in pricing the assets.