I don’t understand the following: “For an upward sloping yield curve, the immunization target rate of return will be less than the YTM because of lower rewinvestment return”. If the curve is upward sloping and higher yields at longer maturities, doesn’t that mean that the coupons over time will be reinvested at higher yields creating a higher reinvestment return? Lost on this…
If the Yield curve slopes upwards, interest rates decrease the closer you are to maturity. So each subsequent coupon you receive gets reinvested at a lower rate than the previous coupon each time. So reinvestment income is affected by lower and lower rates the closer you are to the end of the planning horizon.
YTM is the IRR which assumes reinvestment of coupons at the YTM at the start of the planning horizon. So reinvestment income would theoretically be invested at the same rate each time which is the YTM.
Due to the lower reinvestment income from an upward sloping yield curve, the rate you can lock in (immunized rate) based on the term structure is lower than the YTM.
The reason this is not intuitive is because you say we need less return to immunize while Also saying you will get a lower return from coupons.
it’s the opposite. say you have annual coupons and a 10 year horizon. at the end of year 1 you will invest the coupon at the 9 year rate, year 2 at 8 years, year 3 at 7 and so on. as time goes on you are reinvesting those coupons at lower yields (9 year > 7 year > 3 year)
the immunization rate is the rate that you can invest your ptf at so that the changes in reinvestment offset the changes in the ptf balance - hence immune to rate movements.
the immunization rate is less than the YTM because the target rate is fixed at inception it does not change. YTM is theoretical and is dependent on the maturity of the bond. because of this upward sloping yield curve you will not be able to reinvest at YTM. if the 10year treasury has a YTM of 6% and the curve is constant, you can reinvest at 6%, but because of the upward sloping nature you will not be able to reinvest the coupons at 6%, as the two year rate (for the coupon receive afte year 8) is < the 10 year rate (original YTM) for example
this is how I interpret it. so since you can’t earn this YTM your immunization rate is less than it.
thanks BayStreet…that example made a lot of sense. Was pounding my head on this today and now can move on and finish up studying before dinner!!! thanks!!!
Thanks BayStreet. That was something I didn’t understand intuitively either. You explained that more clearly that the textbook authors could ever write in their lifetimes combined. That’s not saying much but good job all the same.
Hi coolwasky - Can you please let me know which page you pulled the information with quotations from? Thank you SO much!
reading 23 page 28