This Exam FM sample reference tests Cash-Flow and Risk Matching. The liability present value is 1,000 and its Macaulay duration is 1.93653; matching that duration with one- and three-year zeros gives a one-year allocation of 531.74, choice E.
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 zero-coupon duration equation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the present-value-weighted zero-coupon duration equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the present-value-weighted zero-coupon duration equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the present-value-weighted zero-coupon duration equation; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: recover the duration supported by a zero portfolio
A reserve invests 382.23 today in a one-year zero-coupon security and 301.23 in a six-year zero-coupon security. What Macaulay duration can this portfolio match for a liability of the same present value?
A 2.204
B 2.704
C 3.204
D 3.704
E 4.204
Variant answer in brief
The present-value-weighted maturity is 3.204 years, so the portfolio matches liability duration 3.204, choice C.
Setup
Setup
The quoted investments are already present values, so use them directly as duration weights.
P=382.23+301.23=683.46
Model
Model
Each zero-coupon security contributes its maturity times its current portfolio value.
DM=683.461(382.23)+6(301.23)
Compute
Compute
The weighted maturity is 3.20375 years.
DM=3.20375
Answer
Answer
A liability with the same value and duration 3.204 is matched to first order, choice C.
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