Worked solution · Exam FM
This Exam FM sample reference tests Immunization Principles. Statement I overstates Redington protection, statement II reverses the duration equality, and statement III replaces the required asset-convexity excess with equality. None is true, so choice A is correct.
Independent solution
Setup
Redington immunization is local protection for small parallel yield changes, not arbitrary rate movements.
Model
Both Redington and full immunization require matched value and duration at the immunization yield.
Compute
The curvature condition requires asset convexity to exceed liability convexity.
Answer
No listed statement is true, which is choice A.
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
At a selected yield, an asset portfolio and a liability have equal present values and equal Macaulay durations. Asset convexity is 105 and liability convexity is 96. Which conclusion follows under Redington immunization?
Value and duration match, while asset convexity exceeds liability convexity. These are the Redington conditions for local protection against small parallel shifts, choice B.
Setup
The supplied equalities satisfy the zero-order and first-order conditions.
Model
Compare second-order curvature.
Compute
Positive curvature difference makes surplus locally convex at the matched yield.
Answer
The portfolio has local parallel-shift protection, choice B.
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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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