Worked solution · Exam FM
This Exam FM sample reference tests Perpetuity Duration Conversion. The immediate-perpetuity Macaulay duration 32.25 implies i = 3.2%. A due perpetuity then has Macaulay duration 31.25 and modified duration 30.2810, choice A.
Independent solution
Setup
Payment scale does not affect duration. Use the level perpetuity-immediate duration to recover the yield.
Model
Solve for i, then write the due-perpetuity Macaulay duration.
Compute
Convert the due duration to modified duration.
Answer
The modified duration is 30.28, choice A.
Test the method on unseen problems
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.
Error diagnosis
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Original practice · fully worked
A level annual perpetuity-due has modified duration 15 years. Determine the annual effective yield.
For a perpetuity-due, modified duration is 1 divided by i times 1 plus i. Solving the resulting quadratic gives i = 6.2731%, choice C.
Setup
Use the modified-duration formula obtained from the due-perpetuity price.
Model
Rearrange to a quadratic in i.
Compute
Select the positive root because an effective yield must exceed zero here.
Answer
The annual effective yield is 6.27%, choice C.
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