# Key rate duration vs mod duration

This confusion is boiling my brain. Can anyone pls help

Modified duration measures the change in value of a bond due to change in bonds YTM? Correct

• if above is a correct then if i have a 5 year bond will its 5 year key rate duration equal its modified duration as well…? Since modified duration of 5 yr bind will also mean change in price of the bond due to change in 5 yr ytm … is that correct?

so will 5 year key rate duration for that bond and macaulay duration for a 5 year bond be same??

Yes, as long as the bond’s cash flows don’t change when its yield changes.

Only if the bond is selling at par.

If it is selling at a discount, then its 5-year key rate duration will be higher than its modified duration, and if it is selling at a premium, then its 5-year key-rate duration will be lower than its modified duration.

Only if it is a zero-coupon bond whose YTM is 0.0%.

In short, no.

if that is the case how will sum of all key rates durations equal macaulay duration as suggested by schweser… wouldn’t it sum to a greater number then? Or may be some key rate durations will be negative?

The sum of the key rate durations will be the modified (or effective) duration, not the Macaulay duration. If anyone told you that the sum is the Macaulay duration, they’re wrong.

Yes, key rate durations can be negative. It’s part of their charm.

Take a look at the article I wrote on key rate duration: http://finexamhelp123.wpengine.com/key-rate-duration/

In particular schweser says each (t) (w) is a key rate duration… is it correct to say that?

Oh sorry yes modified duration i mean

Inasmuch as I have no idea what a (t) (w) is, I cannot say for certain.

Thanks smagician your article was great particularly the change in spot rate from 6th year onwards was mind blowing…

For (t)(w)

t is time of cash flow

w is weight i.e pv of time t cashflow as %age of total PV

but i understand that is just contribution to maacaulay duration hence it cannot be key rate duration… i dont know why schweser is referring it as duration contribution

Hi, Nokia:
I am just reading this part of the Schweser notes too. And got confused by the statement that: each (t)(w) is the cash follow’s contribution to duration and a key rate duration.
Isn’t the (t) just a Macaulay duration? and another questiong follows: is a key rate duration a Macduration or Modduration? i found the definition of key rate duration=(p1-p2)/(2
0.01*p0). it should be a Modduruation, isn’t it?

Well . . . it’s the Macaulay duration for that one payment, but that’s really bastardizing the idea of Macaulay duration.