If an option-free bond is trading at par, the bond’s maturity- matched rate (or the spot rate applicable to its maturity) is the only rate that affects the bond’s value. Its maturity key rate duration is the same as its effective duration, and all other key rate durations are zero.
I don’t understand why this is so. If we have a 5 yr bond trading at par, why is the only rate we care about the 5 year rate? If a shorter term interest rate fell, wouldn’t’ that affect the value of our 5 year bond?
thnx
The shorter term interest rates also affect the bond value, but a little. The 5yr spot rate would affect the most since the face value is on year 5.
While true, this doesn’t directly address the question at hand.
The fundamental understanding needed is that key rates are par rates, not spot rates. If the 2-year par rate changes but the 5-year par rate is unchanged, then the price of a 5-year bond is unchanged: the price is the present value of the bond’s cash flows discounted at the YTM, which is the 5-year par rate.
Here’s the article I wrote on key-rate duration; maybe it’ll help a bit: Key Rate Duration | Financial Exam Help 123
Yup, sorry what I meant to say was the par rate, you are totally right.
Thanks.