Worked solution · Exam FM
This Exam FM sample reference tests Perpetuity Duration Sensitivity. At 7% the perpetuity-due is worth 152857.14 and has modified duration 13.35113. A 2% yield decline raises the first-order estimate by 40816.33, choice A.
Independent solution
Setup
The stream begins immediately, so price it as a perpetuity-due at 7%.
Model
Use the modified duration of a level perpetuity-due.
Compute
Apply the yield change from 7% to 5% in the first-order price formula.
Answer
The estimated increase is 40816, choice A.
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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.
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Original practice · fully worked
A level perpetuity-immediate pays 500 annually and is valued at 6% effective. The yield immediately falls to 5%. Using first-order modified duration, estimate the dollar increase in value.
The initial price is 8333.33 and modified duration is 16.6667. A one-percentage-point decline produces an estimated gain of 1388.89, choice D.
Setup
Price the immediate perpetuity and compute its modified duration.
Model
The yield change is negative 0.01.
Compute
Apply the first-order relative price change and convert it to dollars.
Answer
The estimated gain is 1388.89, choice D.
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