Verified solution · Exam FM

SOA Exam FM Sample Question #152 Solution

This Exam FM sample reference tests Duration and Convexity. Macaulay duration 11 at yield 10% corresponds to modified duration 10; a 0.25-point yield increase therefore changes price by approximately −10(0.0025) = −2.50%, choice C.

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 the supplied Macaulay duration to modified duration at the original yield.

D_{mod}=\frac{11}{1.10}=10

Model

The first-order modified-duration approximation multiplies the yield change in decimal form by negative modified duration.

\frac{\Delta P}{P}\approx-D_{mod}\Delta i

Compute

A 25-basis-point increase is 0.0025, producing a proportional price change of negative 0.025.

\frac{\Delta P}{P}\approx-10(0.0025)=-0.025

Answer

The approximate decline is 2.50%, corresponding to choice C.

\boxed{-2.50\%\quad\text{(C)}}

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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 modified-duration linear price approximation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the modified-duration linear price approximation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the modified-duration linear price approximation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the modified-duration linear price approximation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: infer modified duration from an observed price move

A food-bank bond is priced at 5,000. After a 20-basis-point increase in yield, its first-order estimated price change is a decrease of 75. Determine the modified duration used in the estimate.

A
5.0
B
6.0
C
7.5
D
8.5
E
10.0

Variant answer in brief

A 75 decline is 1.5% of price; dividing by the 0.002 yield increase gives modified duration 7.5, choice C.

Setup

Convert the dollar decline to a proportional price change and 20 basis points to 0.002.

\frac{\Delta P}{P}=\frac{-75}{5000}=-0.015

Model

The first-order relation equates the magnitude of that proportional decline to duration times yield change.

\frac{\Delta P}{P}\approx-D_{\mathrm{mod}}\Delta i

Compute

Dividing 0.015 by 0.002 gives 7.5.

D_{\mathrm{mod}}=\frac{0.015}{0.002}=7.5

Answer

The inferred modified duration is 7.5, corresponding to choice C.

\boxed{D_{\mathrm{mod}}=7.5\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #152 — 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: infer modified duration from an observed price move

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution