Worked solution · Exam FM

SOA Exam FM Sample Question #346 Solution

This Exam FM sample reference tests Cost of an Exactly Matched Bond Portfolio. Matching the one-year liability requires 1500/1030 units of the coupon bond, costing 1481.72 and producing 43.69 at six months. A six-month zero supplies the remaining early liability for 1922.66, so total cost is 3404.39 and choice B.

Independent analysis by ActuaryProof · reviewed October 6, 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 Cost of an Exactly Matched Bond Portfolio question

Setup

Price a 1000-face one-year coupon bond at the 2.1% half-year yield.

P_B=\frac{30}{1.021}+\frac{1{,}030}{1.021^2}=1{,}017.4485

Model

Choose its face scale to match the year-1 liability exactly.

u=\frac{1{,}500}{1{,}030}

uP_B=1{,}481.7211

30u=43.6893

Compute

A six-month zero must supply the remainder of the earlier liability.

P_Z=\frac{2{,}000-43.6893}{1.0175}=1{,}922.6641

Answer

The dedicated portfolio costs 3404.39, choice B.

\boxed{1{,}481.7211+1{,}922.6641=3{,}404.39\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 prices the coupon bond at its 6% coupon rate instead of its 4.2% nominal yield.
CChoice C neglects the coupon bond's six-month coupon when sizing the zero-coupon position.
DChoice D buys 1500 of coupon-bond face instead of scaling face to a 1500 maturity cash flow.
EChoice E adds the two liability amounts and discounts both for only six months.

Original practice · fully worked

Original variant: dedicate a two-date liability

A liability pays 1,000 after six months and 2,000 after one year. Available assets are six-month zeroes yielding 3% nominal convertible semiannually and one-year par bonds with 4% nominal coupons and 5% nominal yield, both convertible semiannually. Find the cost of an exactly matched portfolio.

A
2,801.33
B
2,844.19
C
2,888.47
D
2,927.60
E
2,965.18

Answer and calculation

The one-year bonds cost 1941.89 and contribute 39.22 at six months. Discounting the remaining early liability costs 946.59, for total cost 2888.47 and choice C.

Setup

Price a 1000-face one-year bond using 2.5% per half-year.

P_B=\frac{20}{1.025}+\frac{1{,}020}{1.025^2}=990.3629

Model

Scale its final payment to the 2000 year-1 liability.

u=\frac{2{,}000}{1{,}020}

uP_B=1{,}941.8880

20u=39.2157

Compute

Supply the six-month residual with zeroes discounted at 1.5%.

P_Z=\frac{1{,}000-39.2157}{1.015}=946.5855

Answer

The exact-match cost is 2888.47, choice C.

\boxed{P_Bu+P_Z=2{,}888.47\quad\text{(C)}}

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How to solve this Cost of an Exactly Matched Bond Portfolio question

Setup

Model

Compute

Answer

Financial Mathematics Duration & Immunization Workbook

Why the other letters tempt

Original variant: dedicate a two-date liability

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM General Cash Flows, Portfolios, and Asset Liability Management