Worked solution · Exam FM
This Exam FM sample reference tests Cash-Flow and Risk Matching. Only set I matches the liability's present value and duration while placing assets on both sides of year 3; set II misses duration and set III misses present value, so choice A.
Independent solution
Setup
Full immunization of one liability requires equal present value, equal duration, and asset payments before and after the liability date.
Model
Set I has the correct current value and a weighted payment time of three years.
Compute
Set II matches value but not duration, while set III already fails the value test.
Answer
Only set I satisfies all conditions, corresponding to 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.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A liability of 6,000 is due in year 3 and is valued at 5% effective. A fund uses one-year and five-year zero-coupon securities to match present value and Macaulay duration. How much current value is placed in the one-year zero?
A year-3 target lies midway between maturities 1 and 5, so half the liability present value, 2,591.51, goes into each zero; choice C.
Setup
Discount the liability to obtain the total current asset value required.
Model
Match both value and the first time moment using the two zero maturities.
Compute
Because year three is the midpoint of years one and five, the current values split equally.
Answer
The one-year zero receives 2,591.51, corresponding to choice C.
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These references share syllabus concepts or sit nearby in the official sequence. All 117 Exam FM general cash flows, portfolios, and asset liability management practice problems.
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