Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. The liabilities have present value 1153.84 and duration 2.4278. Matching those with year-1 and year-3 asset payments gives X = 346.61 and Y = 953.57, so Y/X = 2.75 and choice B.
Independent solution
Setup
Compute the liability present value and time-weighted present value at 5%.
Model
Match both quantities with the asset payments at years 1 and 3.
Compute
Solving gives X = 346.6148, Y = 953.5714, and ratio 2.751098.
Answer
The required payment ratio is approximately 2.75, selecting choice B.
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.
Original practice · fully worked
At a 5% annual yield, assets pay 600 at year 1 and 800 at year 4. Liabilities pay 500 at year 2 and 900 at year 3. Calculate asset Macaulay duration minus liability Macaulay duration.
The asset and liability durations are 2.6058 and 2.6316 years. Their difference is -0.0258 years, choice A.
Setup
Discount each asset and liability payment at 5% and retain its payment time.
Model
The duration mismatch is asset duration minus liability duration.
Compute
The two durations are 2.605808 and 2.631579, giving mismatch -0.025771 years.
Answer
The duration mismatch is -0.0258 years, selecting choice A.
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