Worked solution · Exam FM

SOA Exam FM Sample Question #260 Solution

This Exam FM sample reference tests Duration and Convexity. The three zero-coupon positions have market values 14423.10, 19322.80, 26352.30. Their market-value-weighted maturity is 2.1985 years, so the portfolio duration is 2.20 and choice D.

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 Duration and Convexity question

Setup

For each zero-coupon position, market value is bond count times current price and duration equals maturity.

V_k=N_kP_k

Model

Portfolio Macaulay duration is the market-value-weighted average of the three maturities.

D=\frac{15(961.54)(1)+20(966.14)(2)+30(878.41)(3)}{15(961.54)+20(966.14)+30(878.41)}

Compute

The portfolio market value is 60098.20 and the weighted numerator is 132125.60, giving duration 2.198495.

D=2.19849513

Answer

The portfolio duration is approximately 2.20 years, selecting choice D.

\boxed{D\approx2.20\quad\text{(D)}}

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Financial Mathematics Duration & Immunization Workbook

30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.

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Original practice · fully worked

Original variant: long-zero quantity required for a target portfolio duration

A portfolio holds ten one-year zero-coupon bonds priced at 950 each. It may add four-year zero-coupon bonds priced at 800 each. How many four-year bonds are required for the combined portfolio to have Macaulay duration exactly 3.0 years?

A
21.38
B
22.56
C
23.75
D
24.94
E
26.13

Answer and calculation

The existing short position has value 9,500. Solving the market-value-weighted duration equation for the four-year position gives 23.75 bonds, choice C.

Setup

The one-year position has market value 10 times 950.

V_1=9500

Model

Let n be the number of four-year bonds and impose the target weighted maturity.

3=\frac{1(9500)+4(800n)}{9500+800n}

Compute

Solving the linear equation gives n = 23.7500.

n=23.75000000

Answer

The portfolio needs 23.75 four-year bonds, selecting choice C.

\boxed{n=23.75\quad\text{(C)}}

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How to solve this Duration and Convexity question

Setup

Model

Compute

Answer

Financial Mathematics Duration & Immunization Workbook

Original variant: long-zero quantity required for a target portfolio duration

Answer and calculation

Setup

Model

Compute

Answer

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