Verified solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The portfolio Macaulay duration is the price-weighted value 10.829; solving 105,000 = 100,000(1.0432/(1+i))¹⁰·⁸²⁹ gives i = 3.85%, choice C.
Independent solution
Setup
Combine the two bond durations using their current prices as portfolio weights.
Model
The estimated portfolio value at the new yield follows the Macaulay yield-factor relation with that weighted duration.
Compute
Rearranging the value ratio and taking the duration root gives a new accumulation factor of about 1.0385.
Answer
The implied annual yield is 3.85%, which is choice C.
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Original practice · fully worked
An arts portfolio contains a 40,000 bond of Macaulay duration 5 and a 60,000 bond of duration 9, both valued at 4% yield. Using the Macaulay approximation, a new portfolio value of 105,000 implies what annual yield?
Portfolio duration is 7.4; inverting the 1.05 value ratio gives yield 3.32%, choice C.
Setup
Market-value weights 40% and 60% produce the portfolio duration.
Model
A five-percent estimated value increase implies a yield below the original 4%, and the yield-factor ratio can be inverted.
Compute
Taking the 7.4th root gives an implied yield of 0.0331656.
Answer
The estimated annual yield is 3.32%, 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 #155 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
