Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. Modified duration 5.76 must pair with Macaulay duration 6, giving one plus yield 6/5.76; applying the same factor to Macaulay duration 5 gives modified duration 4.800, choice B.
Independent solution
Setup
At a positive yield, modified duration is smaller than its corresponding Macaulay duration.
Model
Therefore 5.76 pairs with the six-year Macaulay measure and identifies the common yield factor.
Compute
Divide the other five-year Macaulay duration by that same factor.
Answer
The remaining modified duration is 4.800 years, corresponding to 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 municipal bond has Macaulay duration 6.00 years and modified duration 5.70 years. Determine its annual effective yield.
The ratio of Macaulay to modified duration is 1.05263, giving annual yield 5.26%, choice C.
Setup
Use the annual effective conversion between the two duration measures.
Model
Their ratio equals one plus the bond yield.
Compute
Subtracting one from 1.0526316 gives 0.0526316.
Answer
The annual effective yield is 5.26%, corresponding to choice C.
Keep practicing
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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