What risk exists if a portfolio is immunized?

CFA Level III
#1

The book says that if a portfolio is immunized against a change in the market yield at a given horizon by matching portfolio duration to horizon, the portfolio still faces the risk of a change in interest rates

Do they mean here that immunization only covers the risk of parallel shifts in the yield curve and not a change in the slope of the yield curve?

#2

Yes exactly that. Plus there is the default risk, which is ignored.

So there is the CFA curriculum and then there is real life. Two different things.