Worked solution · Exam FM
This Exam FM sample reference tests Cash-Flow and Risk Matching. Backward cash-flow matching fixes the year-three zero at 1,000, the year-two bond face at 980.39, and the year-one bond face at 970.68; choice A.
Independent solution
Setup
Exact cash-flow matching is triangular, so begin with the latest liability.
Model
Only the year-three zero can meet the final payment; then the year-two bond's coupon plus redemption meets year two.
Compute
At year one, the year-two coupon reduces what the year-one bond must supply.
Answer
The required face values are 970.68, 980.39, and 1,000, which is choice A.
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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 ladder holds a one-year 2% coupon bond with face 452.85, a two-year 5% coupon bond with face 761.90, and a three-year zero with face 1,000. Coupons are annual. If years two and three are exactly matched, what year-one liability does the ladder support?
Year one receives 1.02(452.85) plus 5% of 761.90, totaling 500.00, choice C.
Setup
At year one, the first bond pays coupon plus redemption while the second bond pays its first coupon.
Model
The three-year zero contributes nothing before year three.
Compute
Adding the two available year-one cash flows gives 500.002, with the difference caused by quoted face-value rounding.
Answer
The ladder supports a year-one liability of 500.00, corresponding to choice C.
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