Verified solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. A year-2 single liability lies midway between the year-1 and year-3 zeros, so duration matching requires equal present-value weights. Half the discounted liability accumulated one year gives face 9478.67 for the one-year zero, choice A.
Independent solution
Setup
Discount the year-2 liability to obtain the total required asset present value.
Model
Because the asset maturities are symmetric around year 2, equal present-value weights match duration.
Compute
Accumulate the one-year present-value weight to face amount 9478.672986.
Answer
The one-year zero face is approximately 9,479, selecting choice A.
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Original practice · fully worked
At a 4% flat annual yield, one-year and five-year zero-coupon bonds are combined to match the duration of a single liability due at year 3. Calculate the five-year bond face amount divided by the one-year bond face amount.
Year 3 is the midpoint of years 1 and 5, so the two zero positions need equal present values. Converting equal present values to face amounts gives ratio 1.04 to the fourth, or 1.1699, choice D.
Setup
Duration 3 is midway between the two zero maturities, requiring equal present-value weights.
Model
Write each present value from its face amount at the common yield.
Compute
Rearranging gives face ratio 1.16985856.
Answer
The long-to-short face ratio is 1.1699, selecting choice D.
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ActuaryProof. “SOA Exam FM Sample Question #307 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
