Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. Matching duration 3 with one- and four-year zeros requires the four-year present value to be twice the one-year present value. The face amounts then imply the annual accumulation factor cubed is 1.25. Matching present values and accumulating to year 3 gives liability 69623.83, choice C.
Independent solution
Setup
A single year-3 liability has duration 3, so impose that duration on the two zero-coupon assets.
Model
Insert the face amounts to recover the flat annual accumulation factor.
Compute
The annual yield is 7.721735%. Asset present value is 55699.07, which accumulates to liability 69623.83 at year 3.
Answer
The liability amount is approximately 69,624, selecting choice C.
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 one-year zero-coupon bond has face 20,000 and a five-year zero has face 60,000. Under a flat annual yield, the two-bond portfolio must have Macaulay duration 3 years. Calculate the annual effective yield.
Duration 3 requires equal present values in the one- and five-year positions. Equating their discounted faces gives the fourth power of 1 + i equal to 3, so yield 31.61%, choice E.
Setup
A duration midway between years 1 and 5 requires equal market-value weights.
Model
Equate the discounted face amounts under the flat yield.
Compute
Thus the fourth power of 1 + i is 3, giving yield 31.607401%.
Answer
The annual effective yield is 31.61%, selecting choice E.
Keep practicing
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.
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
