Bond Duration and Convexity: Practical Application

Check out this graph: It shows how duration increases with maturity, depending on the size of the coupon. As you can see, the smaller the coupon, the longer the duration.

Got all that? Ready to become a bond trader? Not so fast. As a bond ages, its duration shortens. Every time the investor receives a coupon payment, one bucket gets taken away, and the extra plank gets sawed off. The fulcrum must move to the right from where it was, but because the plank is shorter, so is the duration.

Another complication: As a bond's price and yield fluctuate, so does its duration. As the yield drops, the duration lengthens; as the yield rises, the duration shortens. Here's why: Recall that yield is the rate used to discount the bond's future payments to calculate their present value. As the yield drops, the present value of the payments rises, with the value of the payments furthest in the future rising the most proportionally. So to rebalance the system, the fulcrum would move to the right, indicating a longer duration. Likewise, as the yield rises, the present value of the payments declines, with the value of those furthest in the future declining the most proportionally. To rebalance the system, the fulcrum would move to the left, indicating a shorter duration.

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