Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. Modified duration 8 at yield 6.4% implies Macaulay duration 8.512; the Macaulay and modified estimates are 107,676 and 107,533, differing by 143, choice E.
Independent solution
Setup
Convert modified duration to Macaulay duration before using the yield-factor estimate.
Model
Evaluate the Macaulay ratio estimate and the linear modified-duration estimate at the same 0.6-point yield increase.
Compute
The two estimated prices are 107,676 and 107,533.
Answer
Their difference is 143, corresponding to choice E.
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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.
Original practice · fully worked
A housing note is worth 10,000 at 5% yield and has modified duration 4. Yield rises to 6%. Let M be the Macaulay-ratio estimate and L the modified-duration linear estimate. Calculate M − L.
Macaulay duration 4.2 gives M = 9,609.71 while L = 9,600; the difference is 9.71, choice C.
Setup
The ratio approximation requires Macaulay duration, obtained by multiplying the given modified duration by 1.05.
Model
Evaluate both estimates at the same one-point increase before comparing them.
Compute
The ratio method gives 9,609.7131 and the linear method gives 9,600.
Answer
Their difference is 9.71, so choice C is correct.
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Drill the method: Exam FM Duration and Convexity problems
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