I dont get the generalizations of bond durations in the LOS 37.j
The Schweser notes say
If an option free bond is trading at par, the bond’s maturity key rate duration is the only rate that effects the bond’s value
Why is that so ? theoretically , if any of the key rates in which a coupon is received changes it SHOULD have an effect on the bond value as the discount factor changes
A bond with a low or zero coupon rate may have negative key rate duration for horizons other than its maturity
How ? what does a negative key rate duration even mean, that an increase in the rate would lead yo an increase in the price ?
Higher coupon bonds are more likely to be called
Doesn’t a higher coupon decrease duration which means a lower price sensitivity to a change in rates which means lower chance of being called ??
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If you’ve issued bonds paying a 1% coupon and rates are at 5%, are you likely to call those bonds?
If you’ve issued bonds paying a 10% coupon and rates are at 5%, are you likely to call those bonds?
Yes.
Yes.
No.
What does duration have to do with the probability of a bond being called?
Option free bond has the largest duration at the maturity date, which is when the coupon and principal is paid. The other coupons are tiny and dont matter as much but they do have some impacts if the bond is not trading at par. Shifting a par rate up or down at a particular maturity point, however, respectively increases or decreases the discount rate at that maturity point.
Higher coupons are likely to be called because rates are high and have distance to go down. For example, a 10% high yield bond can take a dive to 5% which is a huge move. Now a 2% callable bond has not much distance to go… it might go down to 1.75% so it is unlikely to be called.