Immunized Target Rate of Return Vs YTM

In the CFAI books it says

In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return. Conversely, a negative or downward-sloping yield curve will result in an immunization target rate of return greater than the yield to maturity because of the higher reinvestment return.

I am slightly confused. the YTM is the return on the portfolio over the investment horizon and the immunized target rate of return is the return needed to fund the liability? or is it the other way around?

Because I would have though with an upward sloping yield curve that the immunization target rate of return would be less than the YTM because of higher reinvestment return, because you can reinvest the assets at a high interest rate along the yeild curve which makes your YTM higher than the immunized rate of return. Can someone please clear this up for me

In case of upward-sloping yield curve the reinvestments rates will be lower than YTM since these rates come from the shorter end of the yield curve, so your final total return will be lower than YTM. Downward-sloping case is the oposite of above.

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91350124