Verified solution · Exam FM

SOA Exam FM Sample Question #103 Solution

This Exam FM sample reference tests Cash-Flow and Risk Matching. Only statement II is valid: either consistent duration measure can support immunization; yield-curve slope does not remove the need, and present-value matching alone is not exact matching, so 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.

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Independent solution

How to solve this Cash-Flow and Risk Matching question

Setup

Evaluate each assertion against the definitions of immunization and exact cash-flow matching.

\text{I: false}

Model

Macaulay and modified duration differ by the positive scale factor one plus yield, so either can be used consistently.

D_{mod}=\frac{D_M}{1+i}\Longrightarrow\text{II: true}

Compute

The current curve shape does not eliminate interest-rate risk, while equal present values alone do not guarantee identical dated payments.

PV_A=PV_L\ \not\Longrightarrow\ CF_{A,t}=CF_{L,t}\Longrightarrow\text{III: false}

Answer

Consequently only the second assertion survives, giving choice B.

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

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Error diagnosis

Why the other letters tempt

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

AStatement I is false because a downward-sloping curve does not remove exposure to later rate changes.
CStatement III confuses current present-value equality with exact equality of every dated cash flow.
DThis option includes both false statements I and III along with the one valid statement.
EChoice B states the valid subset exactly, so the catch-all alternative is unnecessary.

Original practice · fully worked

Original variant: deciding whether a museum reserve is exactly matched

A museum owes 500 in one year and 700 in two years. Portfolio R pays those exact amounts on those dates. Portfolio S merely has the same current value and duration. Which conclusion is necessarily true?

A
Both portfolios are exact matches.
B
Only Portfolio S is an exact match.
C
Only Portfolio R is an exact match.
D
Neither portfolio can be immunized.
E
Curve slope determines which is exact.

Variant answer in brief

Matching every liability date makes R an exact match; value and duration alone do not make S exact, so choice C.

Setup

Exact matching is a date-by-date statement, not merely an equality of summary risk measures.

CF_{R,1}=500=CF_{L,1}

Model

Portfolio R reproduces each required payment; Portfolio S is described only by present value and duration.

CF_{R,2}=700=CF_{L,2}

Compute

Those two moments can support an immunization strategy but permit many different underlying cash-flow patterns.

PV_S=PV_L,\ D_S=D_L\ \not\Longrightarrow\ CF_{S,t}=CF_{L,t}

Answer

Therefore R alone is guaranteed to be an exact cash-flow match, choice C.

\boxed{\text{Portfolio R only}\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #103 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Cash-Flow and Risk Matching question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: deciding whether a museum reserve is exactly matched

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution