This Exam FM sample reference tests Cash-Flow and Risk Matching. The asset present values already total 60,000, matching the liability; equating modified durations gives 0.25(1.80) + 0.75D = 3/1.10, so D = 3.04, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the current-value-weighted modified-duration equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the current-value-weighted modified-duration equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the current-value-weighted modified-duration equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the current-value-weighted modified-duration equation; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: duration of the second bond in a wetlands reserve
A wetlands reserve owes 50,000 in four years and values cash flows at 8%. It holds 10,000 today in a bond of modified duration 2.0 and invests the rest of the liability present value in a second bond. What modified duration must the second bond have?
A 3.50
B 4.00
C 4.34
D 4.75
E 5.00
Variant answer in brief
Matching the four-year liability's modified duration with market-value weights gives 4.34 for the second bond, choice C.
Setup
Setup
Compute the liability's current value and convert its four-year Macaulay duration to modified duration.
PVL=50000(1.08)−4=36751.49,DL=4/1.08=3.70370
Model
Model
The second bond's market value is the liability value less the 10,000 already invested.
36751.49DL=10000(2)+(26751.49)D2
Compute
Compute
Equating the asset and liability duration numerators gives 4.34057 for the unknown measure.
D2=4.34057
Answer
Answer
The required modified duration is 4.34 years, which is choice C.
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.
