This Exam FM sample reference tests Cash-Flow and Risk Matching. Present-value and first-derivative matching give Y = 1413.82 and X = 75.36; the surplus second derivative is negative, so Redington's convexity condition fails and choice A is correct.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B is inconsistent with the surplus value, duration, and convexity conditions at 10%; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the surplus value, duration, and convexity conditions at 10%; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the surplus value, duration, and convexity conditions at 10%; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the surplus value, duration, and convexity conditions at 10%; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: convexity test for a conservation fund
A conservation fund's liabilities have present value 10,000, Macaulay duration 6, and Macaulay convexity 40. It allocates current values 5,000 to a two-year zero and 5,000 to a ten-year zero. Determine whether the Redington conditions hold.
A They fail because present value differs.
B They fail because duration differs.
C They hold: value and duration match, and asset convexity is larger.
D They fail because asset convexity is larger.
E The information is insufficient.
Variant answer in brief
Asset value is 10,000, duration is 6, and convexity is 52, which exceeds 40; choice C.
Setup
Setup
For zero-coupon positions, duration equals maturity and Macaulay convexity equals squared maturity.
PVA=5000+5000=10000
Model
Model
Current values supply the weights for both risk measures.
DA=100002(5000)+10(5000)=6
Compute
Compute
The two equal investments average to duration six and convexity 52 while preserving the required present value.
CA=1000022(5000)+102(5000)=52>40
Answer
Answer
Since value and duration match and asset convexity is higher, choice C is correct.
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