Target immunization Return vs. YTM

CFA Level III Fixed Income
#1

All,

Can anyone clarify the relationship between Target Immunization Return vs YTM.

The book says that for a positively sloped yield curve: TIR < YTM and that cash flows will be reinvested for shorter periods at lower rates.

What is the link with the period length? I don’t get the relationship. Also, if yield curve is positively sloped, and future rates are higher than current, we would be reinvesting at HIGHER rates, no?

#2

There have been several threads on this question this Spring.

Suppose that the par yield curve is:

  • 1-year rate, 2%
  • 2-year rate, 4%
  • 3-year-rate, 5%

Further, assume that the par yield curve doesn’t change for the next three years, and that you’ve invested in an annual pay bond against a liability coming due in three years.

One year from today you get a coupon payment that you will reinvest for the remaining two years until the liability is due; you will therefore reinvest it at 4%, the prevailing 2-year par rate.

Two years from today you get a coupon payment that you will reinvest for the remaining year until the liability is due; you will therefore reinvest it at 2%, the prevailing 1-year par rate.

Your realized yield on the original 3-year bond will be less than 5%.

#3

Great explanation. Many thanks!

If you don’t mind, I’d very much appreciate if you could check my question on Classical Immunization. Hehe

Thanks s2000magician.