This Exam FM sample reference tests Cash-Flow and Risk Matching. A 5-year/20-year allocation of 3,077.18 and 6,619.82 matches value and duration and has convexity 281.00 above 242.47; the alternative pair has inadequate convexity, so choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BReversing the 5- and 20-year amounts drives duration far below 15.24.
CThis 15/20 allocation reverses the weights and does not match the stated duration.
DThese 15/20 amounts fail both the value-duration solution and the required convexity comparison.
EAlthough this pair matches value and duration, its convexity is 233.40, below the liability convexity 242.47.
Original practice · fully worked
Original variant: choosing maturities for a coastal barrier reserve
A coastal barrier liability has present value 12,000, duration 8 years, and convexity 65. A manager may pair zero-coupon holdings at maturities (2,10), (4,10), or (8 only). Which value allocation both matches duration and has convexity above 65?
A 4,000 at year 2 and 8,000 at year 10
B 4,000 at year 4 and 8,000 at year 10
C 6,000 at year 4 and 6,000 at year 10
D 12,000 at year 8
E 8,000 at year 4 and 4,000 at year 10
Variant answer in brief
The 4/10 allocation 4,000 and 8,000 has duration eight and convexity 72, so choice B.
Setup
Setup
Test the offered allocations with current values as weights rather than comparing maturities alone.
4x+10(12000−x)=8(12000)
Model
Model
The 4/10 pair gives a direct linear duration equation for the amount in the shorter zero.
x=4000,12000−x=8000
Compute
Compute
Solving produces 4,000 and 8,000; their weighted squared maturity is 72.
CA=1200042(4000)+102(8000)=72>65
Answer
Answer
That allocation matches value and duration and supplies excess convexity, so choice B is correct.
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