Verified solution · Exam FM

SOA Exam FM Sample Question #154 Solution

This Exam FM sample reference tests Duration and Convexity. Modified duration 8 at yield 6.4% implies Macaulay duration 8.512; the Macaulay and modified estimates are 107,676 and 107,533, differing by 143, choice E.

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 Duration and Convexity question

Setup

Convert modified duration to Macaulay duration before using the yield-factor estimate.

D_M=8(1.064)=8.512

Model

Evaluate the Macaulay ratio estimate and the linear modified-duration estimate at the same 0.6-point yield increase.

E_{MAC}=112955(1.064/1.07)^{8.512}=107676

Compute

The two estimated prices are 107,676 and 107,533.

E_{MOD}=112955[1-8(0.006)]=107533

Answer

Their difference is 143, corresponding to choice E.

\boxed{E_{MAC}-E_{MOD}=143\quad\text{(E)}}

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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.

AChoice A is inconsistent with the paired Macaulay-ratio and modified-linear estimates; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the paired Macaulay-ratio and modified-linear estimates; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the paired Macaulay-ratio and modified-linear estimates; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the paired Macaulay-ratio and modified-linear estimates; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: comparing two duration estimates for a housing note

A housing note is worth 10,000 at 5% yield and has modified duration 4. Yield rises to 6%. Let M be the Macaulay-ratio estimate and L the modified-duration linear estimate. Calculate M − L.

A
−20.00
B
0.00
C
9.71
D
20.00
E
40.00

Variant answer in brief

Macaulay duration 4.2 gives M = 9,609.71 while L = 9,600; the difference is 9.71, choice C.

Setup

The ratio approximation requires Macaulay duration, obtained by multiplying the given modified duration by 1.05.

D_M=4(1.05)=4.2

Model

Evaluate both estimates at the same one-point increase before comparing them.

M=10000(1.05/1.06)^{4.2}=9609.7131

Compute

The ratio method gives 9,609.7131 and the linear method gives 9,600.

L=10000[1-4(0.01)]=9600

Answer

Their difference is 9.71, so choice C is correct.

\boxed{M-L=9.71\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #154 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Duration and Convexity question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: comparing two duration estimates for a housing note

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution