Original practice · fully worked
Original variant: duration inferred from an observed local price change
A bond priced at 1,000 falls to approximately 970 when its annual effective yield rises from 4.0% to 4.5%. Treat the price move as a first-order modified-duration change. Estimate the bond’s Macaulay duration at the original yield.
- A
5.62 years - B
5.93 years - C
6.24 years - D
6.55 years - E
6.86 years
Answer and calculation
Modified duration is 6.00, so Macaulay duration is 6.24 years. The estimated Macaulay duration is 6.24 years, selecting choice C.
Setup
Setup
Use the observed percentage price loss and the 50-basis-point yield increase to infer modified duration.
ΔP/P=−30/1000=−0.03,Δi=0.005 Model
Model
Convert modified duration back to Macaulay duration at the original 4% yield.
Dmod≈−ΔiΔP/P=6 Compute
Compute
Modified duration is 6.00, so Macaulay duration is 6.24 years.
DM=(1.04)Dmod=6.2400 Answer
Answer
The estimated Macaulay duration is 6.24 years, selecting choice C.
DM=6.24 years(C) 