This Exam FM sample reference tests Macaulay Price Approximation. Bond 1's observed approximation implies a current yield of 4.48841%. Applying the same 50-basis-point shift with Bond 2's Macaulay duration gives 21784.47, choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A applies Bond 1's shorter duration to Bond 2 after recovering the common yield.
BChoice B substitutes modified duration directly as the exponent in the Macaulay approximation.
CChoice C uses a simple linear 50-basis-point adjustment instead of the stated Macaulay rate-ratio form.
DChoice D converts Bond 2's duration with the new yield rather than today's yield used for the supplied duration.
Original practice · fully worked
Original variant: infer a yield change from a Macaulay estimate
A bond is worth 5,000 at an annual effective yield of 5% and has Macaulay duration 9 years. A Macaulay price approximation values it at 5,200 after an immediate yield change. Determine the new annual effective yield.
A 4.09%
B 4.32%
C 4.54%
D 4.77%
E 5.46%
Variant answer in brief
The approximation ratio is 1.04. Solving 1.04 = 1.05 divided by one plus the new yield, all raised to the ninth power, gives 4.5434%, choice C.
Setup
Setup
Write the Macaulay rate-ratio approximation using the known initial yield and duration.
5,0005,200=(1+i11.05)9
Model
Model
Take the ninth root and isolate the new accumulation factor.
1+i1=1.041/91.05
Compute
Compute
Evaluate the implied yield.
i1=0.04543421
Answer
Answer
The new annual effective yield is 4.54%, choice C.
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