This Exam FM sample reference tests Redington Immunization Conditions. Redington immunization protects surplus locally against small parallel yield shifts when present value and duration match and asset convexity exceeds liability convexity. Therefore E is true.
How to solve this Redington Immunization Conditions question
Setup
Setup
State the local immunization objective in terms of surplus, the value of assets minus liabilities.
S(i)=A(i)−L(i)
Model
Model
At the immunization yield, Redington conditions set surplus to zero or positive, match first derivatives through duration, and require favorable second-order curvature.
A(i0)=L(i0)
DA(i0)=DL(i0)
CA(i0)>CL(i0)
Compute
Compute
These conditions make the matched point a local minimum of surplus as a function of a parallel interest-rate shift.
S′(i0)=0,S′′(i0)>0
Answer
Answer
That is precisely the small-parallel-change protection described in choice E.
choice E
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AChoice A removes duration matching, even though equality of first-order interest sensitivity is a core Redington condition.
BChoice B reverses the practical comparison: cash-flow matching needs no interest-rate rebalancing, while immunization generally does.
CChoice C reverses the convexity inequality; asset convexity must exceed liability convexity for local surplus protection.
DChoice D assigns zero duration to the entire portfolio and negative convexity, neither of which states the Redington conditions.
Original practice · fully worked
Original variant: diagnose a failed immunization
At a chosen yield, an asset portfolio and its liability have equal present value and equal Macaulay duration. The asset convexity is 84 while the liability convexity is 91. Which conclusion is correct under the Redington criterion?
A The portfolio is immunized because present values match.
B The portfolio is immunized because durations match.
C The portfolio fails because asset convexity is too low.
D The portfolio fails because liability duration must be zero.
E No conclusion is possible without coupon rates.
Variant answer in brief
Present-value and duration equalities remove the zero- and first-order gaps, but the asset convexity must exceed liability convexity. Since 84 is below 91, the portfolio fails, choice C.
Setup
Setup
The first two Redington requirements are already supplied.
A=L,DA=DL
Model
Model
Inspect the remaining curvature requirement for local surplus protection.
CA>CL
Compute
Compute
The stated figures have the opposite ordering.
84<91
Answer
Answer
The asset portfolio is not Redington immunized, so choice C is correct.
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