This Exam FM sample reference tests Cash-Flow and Risk Matching. The liability duration is 1.9365 years; solving the one- and three-year zero allocation gives 531.75 in the one-year bond and 468.25 in the three-year bond, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the present-value-weighted maturity equation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the present-value-weighted maturity equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the present-value-weighted maturity equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the present-value-weighted maturity equation; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: duration allocation for regional water reserve
A regional water reserve has present value 5,000 and Macaulay duration 6.40. Available zero-coupon securities mature in years 3 and 8. Determine the amount invested today in each maturity so that present value and duration both match.
A 3400 in year-3 zeros and 1600 in year-8 zeros
B 2500 in each maturity
C 1600 in year-3 zeros and 3400 in year-8 zeros
D 1280 in year-3 zeros and 3720 in year-8 zeros
E 1920 in year-3 zeros and 3080 in year-8 zeros
Variant answer in brief
The two allocation equations give 1600 in year-3 zeros and 3400 in year-8 zeros, choice C.
Setup
Setup
Let x and y be current market values placed in the shorter and longer zero-coupon securities.
x+y=5000
Model
Model
Matching present value fixes their sum, while matching Macaulay duration fixes the time-weighted sum.
3x+8y=6.40(5000)
Compute
Compute
Solving the two linear equations yields the displayed allocation; both amounts are nonnegative.
x=1600.00,y=3400.00
Answer
Answer
The resulting weighted maturity equals the liability duration, so choice C is the required match.
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