Worked solution · Exam FM
This Exam FM sample reference tests Exact Cash-Flow Matching with Coupon Bonds. The year-4 liability fixes Bond C face at 7300, and the year-3 liability then fixes Bond B face at 14200. Their year-2 coupons total 1221, giving choice A.
Independent solution
Setup
Let a, b, and c be the face amounts invested in the one-, three-, and four-year bonds.
Model
The last liability gives c, and the year-3 liability then determines b.
Compute
Only coupons from Bonds B and C are available at year 2.
Answer
Substitution gives 1221, 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
Liabilities of 3,000, 5,000, and 8,000 fall due at years 1, 2, and 3. They are exactly matched with annual coupon bonds maturing at years 1, 2, and 3, carrying coupon rates 2%, 4%, and 6% respectively. Each bond redeems at par. Find the face amount of the two-year bond.
The three-year bond face is 7547.17 from the last liability. Removing its year-2 coupon leaves a two-year bond face of 4372.28, choice C.
Setup
Back-solve the three-year face C from its maturity cash flow.
Model
At year 2, the two-year maturity and the three-year coupon must total 5000.
Compute
Solve for the requested face amount.
Answer
The two-year bond face is 4372.28, choice C.
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