Implied Macaulay Duration: SOA Exam FM Sample 145 Solution

Direct answer

What “implied Macaulay duration” means here

An implied Macaulay duration is the Macaulay duration recovered from a known modified duration and annual effective yield. It is not a separate duration measure. For the convention used in this Exam FM problem, multiply modified duration by one plus the yield.

For example, a modified duration of 6.00 at a 6% annual effective yield implies a Macaulay duration of 6.36. In SOA sample question 145, the positive common yield first identifies which Macaulay and modified durations belong together; the same multiplier then gives the other bond’s duration as bc/a.

This relationship sits inside the duration and convexity work required by the August 2026 SOA Exam FM syllabus. Continue with the duration and convexity formula guide and problem set, or use the official source linked above to read the question wording.

1. BThe ratio ac/b pairs c with the larger modified duration, contradicting c < b at positive yield.
2. CThe product ab/c does not apply the common factor c/a to the second modified duration.
3. DAdding and subtracting durations is inconsistent with the multiplicative conversion by one plus yield.
4. EThis additive expression likewise ignores the common yield scale.

Drill the method: Exam FM Duration and Convexity problems