Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. Exact cash-flow matching requires investing 925.93 for the year-1 liability and 751.31 for the year-3 liability. Their difference is 174.61, so choice E is correct.
Independent solution
Setup
With zero-coupon bonds, each liability date is matched independently by the bond maturing on that date.
Model
Only the one- and three-year investments are needed for the requested difference.
Compute
Subtracting the two required present investments gives 174.61.
Answer
The one-year bond investment exceeds the three-year investment by about 175, selecting choice E.
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 scholarship plan must pay 800 at the end of year 1 and 1,200 at the end of year 3. One- and three-year zero-coupon securities yield 4% and 6% annually. Calculate the total amount that must be invested today to match both payments exactly.
The two matching investments are 769.23 and 1,007.54. Their total present cost is 1,776.77, choice C.
Setup
Assign each liability to the zero-coupon security with the same maturity.
Model
Because the cash flows are exactly matched, the required budget is the sum of the two present investments.
Compute
The year-1 security costs 769.23 and the year-3 security costs 1007.54, totaling 1776.77.
Answer
The matching budget is 1776.77, which is choice C.
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