Key rate duration

CFA Level II Fixed Income
#1

Does anybody understand why a bond trading at a premium has a positive key rate duration while a discount bond has a negative key rate duration?

Based on my understanding, if you have a 10-yr discount bond & there is an increase in the 5-yr par rate, it will result in an increased 5-yr spot rate (since the YTM/par rate is the weighted avg. of spot rates). Since the remaining maturities on the par curve do NOT change, the subsequent spot rates must decrease and since the primary CFs are received at maturity, lower spot rates = increased value for the 10-yr discount bond, which results in negative key rate duration.

Am I missing something? If not, wouldn’t this same logic apply to bonds trading at a premium?

Thanks for any help or thoughts!

#2

You nailed it.

#3

But then why would premium bonds have a positive key rate duration? Wouldn’t the logic be the same, resulting in negative key rate duration?

#4

You have to work out the individual calculations; it depends on the magnitude of the individual spot rate changes compared to the magnitude of the cash flows (coupons, then coupon + principal).

I wrote an article on key rate duration here: http://www.financialexamhelp123.com/key-rate-duration/

I encourage you to use the tables of spot rates near the end, and use those to value a discount bond and a premium bond. You’ll see it immediately.

1 Like
#5

Got it, thank you!

#6

Did he hit the nail on the head?

Or hit his head on the nail?