Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. A year-2 single liability lies midway between the year-1 and year-3 zeros, so duration matching requires equal present-value weights. Half the discounted liability accumulated one year gives face 9478.67 for the one-year zero, choice A.
Independent solution
Setup
Discount the year-2 liability to obtain the total required asset present value.
Model
Because the asset maturities are symmetric around year 2, equal present-value weights match duration.
Compute
Accumulate the one-year present-value weight to face amount 9478.672986.
Answer
The one-year zero face is approximately 9,479, selecting 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.
Original practice · fully worked
At a 4% flat annual yield, one-year and five-year zero-coupon bonds are combined to match the duration of a single liability due at year 3. Calculate the five-year bond face amount divided by the one-year bond face amount.
Year 3 is the midpoint of years 1 and 5, so the two zero positions need equal present values. Converting equal present values to face amounts gives ratio 1.04 to the fourth, or 1.1699, choice D.
Setup
Duration 3 is midway between the two zero maturities, requiring equal present-value weights.
Model
Write each present value from its face amount at the common yield.
Compute
Rearranging gives face ratio 1.16985856.
Answer
The long-to-short face ratio is 1.1699, selecting choice D.
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.
