Verified solution · Exam FM

SOA Exam FM Sample Question #354 Solution

This Exam FM sample reference tests Portfolio Duration under a Common Yield. Bond A is at par, so the common yield is 6%. Its duration is 7.8017 years; the zero prices are 747.26 and 558.39. Weighting all three durations by market value gives 7.4261 years, 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 Portfolio Duration under a Common Yield question

Setup

Because the coupon bond sells at par, its annual effective yield equals its 6% coupon rate.

i=0.06

Model

Compute Bond A's price-weighted timing at this yield.

D_A=\frac{\sum_{t=1}^{9}t(60)v^t+10(1{,}060)v^{10}}{1{,}000}=7.8016923

Compute

Price the two zeroes and use their maturities as durations.

P_B=1{,}000v^5=747.2582

P_C=1{,}000v^{10}=558.3948

Answer

Market-value weighting gives 7.4261 years, choice B.

D_P=\frac{1{,}000(7.8016923)+747.2582(5)+558.3948(10)}{1{,}000+747.2582+558.3948}=7.426066

\boxed{D_P\approx7.43\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.

AChoice A gives equal one-third weights to the three bond durations rather than market-value weights.
CChoice C omits the five-year zero from the portfolio value and duration numerator.
DChoice D treats both zero-coupon bonds as if they were priced at face.
EChoice E uses face amounts as weights and replaces the coupon bond duration with maturity ten.

Original practice · fully worked

Original variant: zero position required for a target duration

A coupon bond has market value 1,000 and Macaulay duration 7.8 years at a common 6% yield. It is combined with a five-year zero-coupon bond to obtain portfolio duration 6.4 years. Determine the zero's maturity value.

A
1,191.02
B
1,250.00
C
1,300.00
D
1,338.23
E
1,400.00

Variant answer in brief

The duration equation requires the zero to have present value 1000. Accumulating that value five years at 6% gives maturity value 1338.23, choice D.

Setup

Let Z be the zero's current market value.

\frac{1{,}000(7.8)+5Z}{1{,}000+Z}=6.4

Model

Solve the market-value weighted duration equation.

7{,}800+5Z=6{,}400+6.4Z

Z=1{,}000

Compute

Convert the zero's present value to its year-5 maturity amount.

F=1{,}000(1.06)^5=1{,}338.2256

Answer

The maturity value is 1338.23, choice D.

\boxed{F=1{,}338.23\quad\text{(D)}}

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ActuaryProof. “SOA Exam FM Sample Question #354 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Portfolio Duration under a Common Yield question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: zero position required for a target duration

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution