This Exam FM sample reference tests Immunization and Asset-Liability Management. The liability present value is 548387.92 with duration 2. Solving the asset present-value and duration equations assigns 365591.95 of present value to the one-year bond, so its maturity value is 382409, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (218,800) does not satisfy the simultaneous present-value and two-year duration matching equations; no distinct standard one-step error is identifiable.
BChoice B (325,400) does not satisfy the simultaneous present-value and two-year duration matching equations; no distinct standard one-step error is identifiable.
CChoice C (365,600) does not satisfy the simultaneous present-value and two-year duration matching equations; no distinct standard one-step error is identifiable.
EChoice E (402,800) does not satisfy the simultaneous present-value and two-year duration matching equations; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: single-liability date implied by a two-zero asset portfolio
An asset portfolio pays 300 at year 1 and 500 at year 5. At a 4% annual effective yield, it will immunize one single-payment liability by matching present value and Macaulay duration. Determine the liability's payment time.
A 3.18 years
B 3.35 years
C 3.52 years
D 3.69 years
E 3.85 years
Variant answer in brief
The discounted asset cash flows are 288.46 and 410.96. Their present-value-weighted payment time is 3.35 years, which must be the single liability's date; choice B.
Setup
Setup
Discount the two asset payments at 4%.
PV1=300(1.04)−1
PV5=500(1.04)−5
Model
Model
A single liability has duration equal to its payment time, so match that time to the asset portfolio's duration.
T=DA=PV1+PV5PV1+5PV5
Compute
Compute
The weighted time is 3.350293 years.
T=3.35029345
Answer
Answer
The liability must be due in 3.35 years, selecting choice B.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
