A portfolio manager owns $5 million par value of bond ABC. The bond is trading at 70 and has a modified duration of 6 . The portfolio manager is considering swapping out of bond ABC and into bond XYZ
The price of this bond is 85 and it has a modified duration of 3.5 .
What is the dollar duration of bond ABC per 100-basis-point change in yield?
The price of bond ABC is 70 with a modified duration of 6, and bond XYZ has a price of 85 with a modified duration of 3.5 . Because modified duration is the approximate percentage change per 100-basis-point change in yield, a 100-basis-point change in yield for bond ABC would change its price by about 6%. Based on a price of 70, its price will change by about 0.06(70) = $4.2 per $70 of market value. Thus, for bond ABC, its dollar duration for a 100-basis-point change in yield is $4.2 per $70 of market value.
Similarly, for bond XYZ, its dollar duration for a 100-basis-point change in yield per $85 of market value can be determined. In this case it is 0.035(85) = $2.975 . So if bonds ABC and XYZ are being considered as alternative investments in a strategy other than one based on anticipating interest-rate movements, the amount of each bond in the strategy should be such that they will both have the same dollar duration.
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