9.15 Duration: “The Hiccup”
Question
What happens to Duration on coupon payment date? (Hint: The coupon “glass” falls off and …)
Solution
This question can, perhaps, be best understood visually. Going back to the prior page, the glass to the extreme left represents the coupon which shall imminently be paid. Its water – or Present Value – is filled to the brim. The present and nominal values of the coupon, represented by the respective watermarks and heights of the glasses, are equal.
When the coupon is paid, the glass “falls off”; it is gone. At that very moment, in order to rebalance the fulcrum, the duration point will have to shift, momentarily, to the right. Duration, at that instant, increases. With time, Duration should decrease as does maturity. This movement is contrary to the other, natural movement of the fulcrum to the left due to “duration drift.”
Once the bond experiences this “hiccup,” immediately after which duration drift will resume its leftward movement, shortening the duration of the bond with the continuous passage of time, and the fulcrum will continue shifting to the left, once again.
Maturity Pull versus Duration Drift
Both Maturity Pull and Duration Drift are affected by the passage of time. As time goes on, a non-Par bond approaches Par, and Duration (for all bonds) decreases.
Maturity Pull refers to the movement of a non-Par bond’s price in the direction of Par as time moves on. A bond must mature at Par.
Duration Drift is the movement of a bond’s duration lower (or shorter) as time moves on. When a bond matures, its duration and maturity will be nil. There are only two occasions in which a bond’s duration will increase – when it either: 1. experiences a hiccup or 2. a decrease in market yield.
