Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The first-order Macaulay approximation scales par by (1.072/1.08)⁷·⁹⁵⁹, giving estimated price 942.54, choice B.
Independent solution
Setup
The bond begins at par, and the yield-factor approximation uses the ratio of old to new annual accumulation factors.
Model
Raise that ratio to the supplied Macaulay duration.
Compute
The factor is approximately 0.94254, so applying it to 1,000 gives 942.54.
Answer
The estimated bond price is 942.54, which is choice B.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A conservation note is worth 2,000 at 4% annual effective yield. Under the Macaulay yield-factor approximation, its estimated value at 4.5% is 1,943.27. Determine the Macaulay duration used.
Taking logarithms of the price ratio and yield-factor ratio gives Macaulay duration 6.0, choice C.
Setup
Divide the estimated new value by the original value to obtain the observed price factor.
Model
The Macaulay approximation raises the old-to-new yield factor to the unknown duration.
Compute
Taking logarithms isolates the exponent and gives 5.9999.
Answer
The Macaulay duration is 6.0 years, corresponding to choice C.
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These references share syllabus concepts or sit nearby in the official sequence. All 117 Exam FM general cash flows, portfolios, and asset liability management practice problems.
Drill the method: Exam FM Duration and Convexity problems
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