Worked solution · Exam FM
This Exam FM sample reference tests Bond Modified Duration. Present-value weighting gives Macaulay duration 6.89216 years. Dividing by 1.10 gives modified duration 6.26560, which rounds to choice A.
Independent solution
Setup
Scale face amount to 1000 without changing duration. Annual cash flows are 90 for years 1 through 9 and 1090 at year 10.
Model
Compute price and the time-weighted present-value numerator.
Compute
The price is 938.5543 and Macaulay duration is 6.892158. Convert to modified duration.
Answer
The modified duration is 6.27 years, choice A.
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30 original bonds 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 seven-year corporate bond has Macaulay duration 7.2 years at an annual effective yield of 8%. Estimate the percentage price change, using modified duration, if the yield rises by 20 basis points.
Modified duration is 7.2 divided by 1.08. Multiplying its negative by the 0.002 yield increase gives an estimated price change of negative 1.333%, choice C.
Setup
Convert the given Macaulay duration to modified duration at the current yield.
Model
The first-order relative price change is negative modified duration times the yield change.
Compute
Insert a positive 20-basis-point change.
Answer
The estimated decline is 1.33%, choice C.
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