This Exam FM sample reference tests Duration and Convexity. Scaling face value scales every cash flow equally and leaves duration unchanged, while a higher coupon shifts value toward earlier payments and reduces duration; choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AFace scaling cancels from duration, and a larger coupon moves weight earlier rather than later.
BThe coupon direction is correct, but face value cannot change duration when all cash flows scale together.
CFace invariance is correct, but increasing coupons reduces rather than increases duration.
DCoupon changes alter the relative weight of early payments and therefore do change duration.
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
Variant answer in brief
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.
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