Determining the Target return ( under the bond immunization topic)

[archived_user]

Hi everyone,
I was hoping if someone could help me understand this concept. It says in the CFAI reading that:
“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”
Why is the reinvestment return lower in upward sloping curve? Shouldn’t it be the opposite as the coupons that are being received now get reinvested at a higher rate?

 

[archived_user]

This has been discussed many times here; the search function may help locate the other threads.
In fact, the coupons are reinvested at a lower rate, not a higher rate.
Suppose that the yield curve is:

• 1-year (par) rate: 1%
• 2-year (par) rate: 2%
• 3-year (par) rate: 3%

To make things simple, imagine that the yield curve doesn’t change for the next 3 years.
If you own a 3-year bond, your YTM is 3%, but your actual yield will be lower. A coupon you receive today will be invested at 3%, but the coupons received next year and the year after that will be invested at, respectively, 2% and 1%.