Hello all

In Fixed Income I under the section “Risk minimization for immunized portfolios” there is a paragraph starting with “Recall that the target value of an immunized portfolio is a lower bound on the terminal value of the portfolio at the investment horizon if yields on all maturities changes by the same amount.” 

What does it mean? If yield curve has a non parallel shift then why is the target value of immunized portfolio not the lower bound of possible terminal values? Maybe some one could give a detailed explanation?

Thank you.