Worked solution · Exam FM
This Exam FM sample reference tests Cash-Flow and Risk Matching. Present values must be equal, price sensitivities must match rather than one exceed the other, and asset convexity must exceed liability convexity; therefore only statement I is necessary, choice A.
Independent solution
Setup
State the local balance conditions for a Redington-style immunization at the chosen yield.
Model
Equal first-order sensitivity requires equality, not a strictly larger asset sensitivity.
Compute
Positive second-order surplus curvature requires asset convexity to be greater, not less.
Answer
Among the statements given, only present-value equality is necessary, so choice A is correct.
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.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A liability portfolio has present value 1,000, modified duration 6.0, and convexity 50. Which candidate asset portfolio satisfies the local value, duration, and curvature conditions for immunization?
Only candidate C matches value and modified duration while retaining greater convexity, so choice C is correct.
Setup
Test each candidate first for value equality, because a value mismatch leaves an immediate surplus or deficit.
Model
Next require equal modified duration so that the first-order response to a small rate change cancels.
Compute
Candidate C also has convexity above 50, making the local second-order surplus positive.
Answer
Candidate C is the only locally immunizing portfolio.
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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.
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