Properties of Bond Duration
Duration has many unique properties. These properties are a function of the impact of coupon timing, coupon levels, and maturity. Duration of a bond decreases over time as the bond nears maturity. However, the periodic payment of coupons causes duration to be choppy over the coupon payment interval.
You can see the effect of each variable on duration by changing one variable and keeping the others the same. The results are generally the same for modified duration or Macaulay duration.
Which of the following would _not_ exhibit this duration pattern?
In summary:
[[summary]]
Incorrect.
Between interest payment dates, 6% coupon bonds have this duration pattern.
Incorrect.
Between interest payment dates, 8% coupon bonds have this duration pattern.
Correct!
This pattern of duration applies only to full-coupon bonds. A zero-coupon bond's duration declines in a linear manner as the bond matures.
Incorrect.
The zero-coupon bond would have the highest duration of the three.
Incorrect.
The 6.00% bonds would have duration in the middle of the other two.
Correct!
Duration is lowest for higher coupon bonds, other things equal. The zero-coupon bond would have the highest duration, followed by the 6.00% bonds and the 10.00% bonds.
The properties of duration as they relate to coupons and maturity can be seen by examining bonds with various coupons and maturities. Below is a figure that displays the duration on four very different bonds: a par bond, a premium bond, a discount bond, and a zero-coupon bond. All bonds are priced at a yield of 6.00%.
Assuming the same yield and maturity, which of the following would have the lowest duration?
For all bonds, duration gradually decreases over time as the bonds approach maturity. However, duration has an interesting property between coupon payments dates.
The figure below shows the duration of a 6.00% par bond computed monthly for two years. The bond pays coupons semiannually. You can see that duration declines over the six months approaching the coupon payment date and then spikes when the coupon is paid. Every six months it spikes to a lower level than the previous six-month level.
There are some important relationships in this figure. First, zero-coupon bonds have a duration that is linear in maturity. Second, as coupons increase, duration goes down. Finally, for coupon bonds, as maturity increases durations approach each other. In fact, if the maturity was further increased, the three coupon bonds would continue to converge.
6.00% bond
8.00% bond
Zero-coupon bond
Zero-coupon bond
6.00% full-coupon bond
10.00% full-coupon bond
Continue
Continue
Continue
Continue
