Verified solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. At 5%, convexities are 800 for the level perpetuity, about 2,313 for the 50-year zero, and 5,000 for the 3%-growing perpetuity; hence y < x < z, choice B.
Independent solution
Setup
Use price convexity defined as the second yield derivative divided by price.
Model
A level perpetuity has convexity two divided by yield squared, while a long zero uses its maturity factors.
Compute
Replacing yield by yield minus growth gives the growing perpetuity's larger convexity.
Answer
The order from lowest to highest is y, x, z, corresponding to choice B.
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Original practice · fully worked
A perpetuity pays its first amount in one year and grows 2% annually. At a 7% annual effective yield, calculate its price convexity.
For a growing perpetuity, convexity is two divided by yield minus growth squared, giving 800, choice C.
Setup
Write the growing perpetuity price using the spread between yield and growth.
Model
Differentiate twice and divide by price so the payment scale cancels.
Compute
The relevant spread is 5%, producing convexity 800.
Answer
The price convexity is 800, corresponding to choice C.
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Drill the method: Exam FM Duration and Convexity problems
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ActuaryProof. “SOA Exam FM Sample Question #390 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
