This Exam FM sample reference tests Macaulay Duration from Price Sensitivity. Substitution gives −1.08(−700)/100 = 7.56 years. The result agrees with the published answer key, choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (7.00) does not match the checked macaulay duration from price sensitivity result (7.56); no distinct standard one-step error is identifiable.
BChoice B (7.49) does not match the checked macaulay duration from price sensitivity result (7.56); no distinct standard one-step error is identifiable.
DChoice D (7.69) does not match the checked macaulay duration from price sensitivity result (7.56); no distinct standard one-step error is identifiable.
EChoice E (8.00) does not match the checked macaulay duration from price sensitivity result (7.56); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: price derivative implied by a quoted duration
A bond is priced at 500 when its annual effective yield is 6%, and its Macaulay duration is 4.5 years. Calculate the derivative of price with respect to the annual yield at that point.
A -2,334.91
B -2,228.77
C -2,122.64
D -2,016.51
E -1,910.38
Variant answer in brief
The derivative is -2122.64 price units per unit change in yield. The required derivative is −2,122.64, selecting choice C.
Setup
Setup
Here duration is known and the local price derivative is the unknown, reversing the usual sensitivity calculation.
P=500,i=0.06,DM=4.5
Model
Model
Rearrange the Macaulay-duration identity to isolate the derivative.
P′(i)=−1+iDMP
Compute
Compute
The derivative is -2122.64 price units per unit change in yield.
P′(i)=−2122.641509
Answer
Answer
The required derivative is −2,122.64, selecting choice C.
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