This Exam FM sample reference tests Modified Duration Approximation. The modified duration is 7.425 and the approximate new price is 940.60. The result agrees with the published answer key, choice A.
How to solve this Modified Duration Approximation question
Setup
Setup
Convert the quoted Macaulay duration to modified duration at the current 7.2% annual yield. Modified duration is the coefficient for the first-order percentage price change.
Dmod=7.959/1.072=7.425
Model
Model
The yield rises by 0.008. Apply the linear approximation P₁ ≈ P₀[1 − Dmod Δi] to the initial price 1,000.
P1≈1000[1−Dmod(0.080−0.072)]
Compute
Compute
The modified duration is 7.425 and the approximate new price is 940.60.
P1=940.60
Answer
Answer
The calculation gives 940.60 for modified duration approximation, matching published choice A.
P1=940.60(A)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B (942.88) does not match the checked modified duration approximation result (940.60); no distinct standard one-step error is identifiable.
CChoice C (944.56) does not match the checked modified duration approximation result (940.60); no distinct standard one-step error is identifiable.
DChoice D (947.03) does not match the checked modified duration approximation result (940.60); no distinct standard one-step error is identifiable.
EChoice E (948.47) does not match the checked modified duration approximation result (940.60); no distinct standard one-step error is identifiable.
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
Variant answer in brief
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.
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