Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. Macaulay duration 11 at yield 10% corresponds to modified duration 10; a 0.25-point yield increase therefore changes price by approximately −10(0.0025) = −2.50%, choice C.
Independent solution
Setup
Convert the supplied Macaulay duration to modified duration at the original yield.
Model
The first-order modified-duration approximation multiplies the yield change in decimal form by negative modified duration.
Compute
A 25-basis-point increase is 0.0025, producing a proportional price change of negative 0.025.
Answer
The approximate decline is 2.50%, corresponding to choice C.
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 food-bank bond is priced at 5,000. After a 20-basis-point increase in yield, its first-order estimated price change is a decrease of 75. Determine the modified duration used in the estimate.
A 75 decline is 1.5% of price; dividing by the 0.002 yield increase gives modified duration 7.5, choice C.
Setup
Convert the dollar decline to a proportional price change and 20 basis points to 0.002.
Model
The first-order relation equates the magnitude of that proportional decline to duration times yield change.
Compute
Dividing 0.015 by 0.002 gives 7.5.
Answer
The inferred modified duration is 7.5, 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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