Key Rate Durations

[ayousaf]

I’m struggling to understand how key rate durations work. From my understanding, a change in the yield at a specific maturity will increase the discount rate at that particular maturity. However, discount rates at other maturities will fall (as an adjustment for the yield increase).
What I’m struggling to understand is why a par bond will have a price decrease as a result of yield changes at its maturity date? Surely the other yields (at other maturities) will fall allowing the par bond to remain at par?
Any help is appreciated. Thanks,

 

[S2000magician]

I’m not sure why you think that the bond’s price would remain unchanged. In fact, the point is that the price will change.
For modified duration, all yields are increased and decreased by some amount (say, 50 bp), and we observe the changes in the bond’s price. The percentage change in the bond’s price divided by the total change in yield (here, 100 bp) is the bond’s modified duration.
For key-rate duration, the yield at a specific maturity is increased and decreased by some amount (say, 50 bp), and we observe the changes in the bond’s price. The percentage change in the bond’s price divided by the total change in yield (here, 100 bp) is the bond’s key-rate duration for that maturity.

 

[ayousaf]

I think if we used an example it might be easier: suppose we have a 10-year 4% annual pay bond issued at par (suppose a flat yield curve of 4%).
The textbook states that:
If the yield at 2 years was increased by, say, 200 bps, there would be no change in the price.
If the yield at 5 years was increased by, say, 200 bps, there would be no change in the price.
However, if the yield at 10 years was increased by 200 bps, there would be a significant change (fall) in price.
This is what I don’t understand. Surely, the other yield changes should have an effect?
Thanks,

 

[S2000magician]

The yield curve they’re discussing is the par curve, not the spot curve. The only par yield that matters to a 10-year bond is the 10-year par yield.
You’d be correct if they were talking about changing the yields on the spot curve, because a change in a single spot rate will have an effect on the par rate for all maturities equal to or greater than the maturity of the spot rate change.