Original practice · fully worked
Original variant: quantify a coupon-driven duration change
Two ten-year bonds share a 1,000 redemption value and a 7% annual effective yield. Bond L pays 4% annual coupons and Bond H pays 8% annual coupons. Which bond has the greater Macaulay duration, and by approximately how much?
- A
Bond H by 1.709 years - B
Bond H by 0.854 years - C
They have equal duration - D
Bond L by 0.427 years - E
Bond L by 0.854 years
Answer and calculation
The durations are 8.201 years for Bond L and 7.347 years for Bond H, so Bond L is longer by 0.854 years, choice E.
Setup
Setup
Discount both bonds at their common 7% yield and preserve the different coupon amounts.
DL=40a10∣+1000v10∑t=19t(40)vt+10(1040)v10=8.2011 Model
Model
Compute each present-value-weighted average payment time separately.
DH=80a10∣+1000v10∑t=19t(80)vt+10(1080)v10=7.3466 Compute
Compute
The lower-coupon bond retains more of its value in the maturity payment, increasing duration by 0.8545 years.
DL−DH=8.2011−7.3466=0.8545 Answer
Answer
Bond L has the greater duration by about 0.854 years, corresponding to choice E.
Bond L by 0.854 years(E) 