Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. At 7%, the liability present value is 777020.93 and the five-year zero is worth 172670.99, leaving long-zero present value 604349.94 and face 1558336.95. Repricing both assets and the liability at 4% gives surplus 5910.23, choice A.
Independent solution
Setup
At the immunization yield, match liability present value with the two zero-coupon asset values.
Model
Accumulate the long-zero present value to its year-14 face amount.
Compute
The long face is 1558336.95. Repricing at 4% produces asset-minus-liability value 5910.228024.
Answer
The present-value surplus is approximately 5,910, selecting 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.
Original practice · fully worked
A 100,000 liability due at year 6 is immunized at 5% using three-year and nine-year zero-coupon bonds with equal present-value weights. Immediately afterward the flat annual yield becomes 3%. Calculate asset present value minus liability present value.
The initial equal weights determine zero faces 43,191.88 and 57,881.25. Repricing both at 3% and subtracting the year-6 liability value gives surplus 139.42, choice C.
Setup
At 5%, split the liability present value equally because years 3 and 9 are symmetric around duration 6.
Model
Accumulate each present-value weight to its own maturity face amount.
Compute
Repricing at 3% gives surplus 139.421487.
Answer
The yield shift creates surplus 139.42, selecting choice C.
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