This Exam FM sample reference tests Cash-Flow and Risk Matching. The liabilities have present value 1,000, duration 3.5, and convexity 14.5; only portfolio A matches value and duration while having convexity 18.5 greater than the liabilities, so choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BPortfolio B has value 1,000 but duration 3.14, so it fails before convexity is considered.
CThe amounts in portfolio C total more than the liability present value and cannot satisfy the value condition.
DPortfolio D also has total value above 1,000, so it is not a present-value match.
EThe single 3.5-year zero matches value and duration but has convexity 12.25, below the liability convexity 14.5.
Original practice · fully worked
Original variant: selecting a Redington hedge for a civic archive
A civic archive's liability has present value 2,000, duration 4 years, and convexity 18. Three zero-coupon portfolios all cost 2,000: R invests equally in years 2 and 6; S invests equally in years 3 and 5; T invests only in year 4. Which is Redington immunized?
A R only
B S only
C T only
D R and S
E All three
Variant answer in brief
All three match duration four, but only R has convexity 20 exceeding 18; choice A.
Setup
Setup
Equal investments at symmetric maturities have duration at the midpoint, so each candidate matches four years.
DR=DS=DT=4
Model
Model
The distinguishing Redington test is whether asset convexity exceeds the liability convexity of 18.
CR=(22+62)/2=20
Compute
Compute
R has value-weighted squared maturity 20; S and T have 17 and 16, respectively.
CS=17,CT=16
Answer
Answer
Only R supplies the required excess convexity, so choice A is correct.
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