Verified solution · Exam FM

SOA Exam FM Sample Question #295 Solution

This Exam FM sample reference tests Immunization and Asset-Liability Management. Small-change immunization requires equal asset and liability values, equal modified durations, and greater asset convexity. Only Company V has matched duration and asset convexity 85 above liability convexity 80. Therefore statement II only is true, choice B.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

Read the solution Open official source

Independent solution

How to solve this Immunization and Asset-Liability Management question

Setup

Check present-value equality first; all three companies satisfy it.

A=L

Model

Then require modified-duration equality and asset convexity strictly above liability convexity.

D_A=D_L

C_A>C_L

Compute

Company U fails duration matching, Company V satisfies both remaining tests, and Company W has asset convexity below liability convexity.

V:\quad8.6=8.6,\qquad85>80

Answer

Only statement II is correct, so choice B is the answer.

\boxed{\text{II only}\quad\text{(B)}}

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AChoice A (I only) does not satisfy all three Redington conditions applied separately to each company; no distinct standard one-step error is identifiable.
CChoice C (III only) does not satisfy all three Redington conditions applied separately to each company; no distinct standard one-step error is identifiable.
DChoice D (I, II, and III) does not satisfy all three Redington conditions applied separately to each company; no distinct standard one-step error is identifiable.
EChoice E does not satisfy all three Redington conditions applied separately to each company; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: minimum asset convexity condition after value and duration matching

A liability portfolio has convexity 120. Its asset portfolio already has equal present value and equal modified duration at the reference yield. What condition on asset convexity is required for strict Redington immunization?

A
Asset convexity must be less than 120.
B
Asset convexity may take any value.
C
Asset convexity must equal 120.
D
Asset convexity must be at least 120.
E
Asset convexity must be greater than 120.

Variant answer in brief

Strict Redington immunization requires the asset value curve to have greater local curvature than the liability curve after value and duration are matched. Asset convexity must therefore exceed 120, so choice E is correct.

Setup

Value and modified-duration matching already satisfy the zero-order and first-order conditions.

A=L

D_A=D_L

Model

The strict second-order Redington condition requires greater asset convexity.

C_A>C_L

Compute

With liability convexity 120, substitute that threshold directly.

C_A>120

Answer

Asset convexity must be greater than 120, selecting choice E.

\boxed{C_A>120\quad\text{(E)}}

Keep practicing

Turn this solution into a complete study sequence

The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

See the Exam FM study manual PDF — $49 More Exam FM General Cash Flows, Portfolios, and Asset Liability Management practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #295 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Immunization and Asset-Liability Management question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: minimum asset convexity condition after value and duration matching

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution