This Exam FM sample reference tests Cash-Flow and Risk Matching. Matching value and duration at the liability date gives the later asset time y = 8.9607 and amount X = 701,459, which rounds to choice D.
How to solve this Cash-Flow and Risk Matching question
Setup
Setup
Use the liability date as the comparison time; the earlier asset is accumulated two years and the later asset is discounted back from its unknown date.
300000(1.04)2+X(1.04)8−y=1000000
Model
Model
Full immunization with two assets straddling the liability date requires both value and first-order sensitivity to match.
600000(1.04)+(8−y)X(1.04)7−y=0
Compute
Compute
Eliminating the discounted value of the second asset gives its payment year, after which its nominal amount follows from the value equation.
y=8.9607,X=701459
Answer
Answer
The required later payment is approximately 701,500, so choice D is the listed result.
X≈701500(D)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the two full-immunization equations centered at year eight; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the two full-immunization equations centered at year eight; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the two full-immunization equations centered at year eight; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the two full-immunization equations centered at year eight; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: verifying a two-sided habitat-restoration reserve
A habitat trust owes a single amount whose present value is 1,000 and duration is 10 years. It holds a seven-year zero worth 400 today and a twelve-year zero worth 600 today. Do these assets meet the two-sided full-immunization conditions?
A No; asset value is 1,200.
B No; asset duration is 9.
C No; both assets mature before the liability.
D Yes; value and duration match, and maturities straddle year 10.
E Yes, but only because convexities are equal.
Variant answer in brief
The asset value is 1,000 and its duration is 10; the two maturities straddle the liability, so choice D.
Setup
Setup
Current market values are the weights in the duration calculation for zero-coupon assets.
PVA=400+600=1000
Model
Model
Check equality of present value, equality of duration, and placement of one maturity on each side of the liability date.
DA=10007(400)+12(600)=10
Compute
Compute
The weighted maturity is exactly ten years, and the two asset maturities lie at seven and twelve years.
7<10<12
Answer
Answer
All stated two-sided conditions are met, giving choice D.
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.
