Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. Asset and liability values coincide, their modified durations also coincide, and asset convexity is greater. These are exactly the three local conditions for Redington immunization, so choice E applies.
Independent solution
Setup
Present-value matching eliminates the initial asset-liability surplus difference.
Model
Modified-duration matching eliminates the first-order sensitivity difference.
Compute
Greater asset convexity supplies the favorable second-order curvature condition.
Answer
These conditions define a Redington-immunized position, which is choice E.
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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
At a reference yield, an insurer's asset value equals its liability value and the two modified durations coincide, but asset convexity is lower than liability convexity. Which conclusion is correct about Redington immunization?
Value and duration matching remove the constant and first-order mismatch, but lower asset convexity makes the second-order surplus term unfavorable. The position is not Redington immunized, so choice D is correct.
Setup
The proposed position satisfies the value and first-order sensitivity conditions.
Model
Redington immunization additionally requires asset convexity to exceed liability convexity.
Compute
Here the supplied inequality is reversed, so the local second-order surplus condition fails.
Answer
The position is not Redington immunized for the stated reason, selecting choice D.
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