This Exam FM sample reference tests Immunization and Asset-Liability Management. Present-value and duration matching require x + y = 2,000 and x + 4y = 6,000, giving one-year investment x = 666.67. Asset convexity 11 exceeds liability convexity 9, so the plan is valid and choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (400) does not satisfy present value, three-year duration, and favorable convexity of the two-zero portfolio; no distinct standard one-step error is identifiable.
CChoice C (858) does not satisfy present value, three-year duration, and favorable convexity of the two-zero portfolio; no distinct standard one-step error is identifiable.
DChoice D (1,000) does not satisfy present value, three-year duration, and favorable convexity of the two-zero portfolio; no distinct standard one-step error is identifiable.
EChoice E does not satisfy present value, three-year duration, and favorable convexity of the two-zero portfolio; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: convexity margin of a duration-matched two-zero portfolio
A single liability due in three years has present value 2,000. A duration-matched asset portfolio invests 666.67 in a one-year zero and 1,333.33 in a four-year zero. Using squared payment times as the convexity measure, calculate asset convexity minus liability convexity.
A 1.80
B 1.90
C 2.00
D 2.10
E 2.20
Variant answer in brief
The asset squared-time average is 11, while the single year-3 liability has measure 9. The convexity margin is 2, choice C.
Setup
Setup
Compute the asset present-value-weighted squared payment time.
CA=2000666.67(12)+1333.33(42)=11
Model
Model
A single liability at year 3 has squared-time measure 9.
CL=32=9
Compute
Compute
Subtract the liability measure from the asset measure.
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