This Exam FM sample reference tests Cash-Flow and Risk Matching. Redington immunization requires asset and liability duration equality but asset convexity strictly greater than liability convexity; therefore the equality statement in choice E is false.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AA single immunization yield represents a locally flat term structure in the standard Redington framework.
BThe method's single-rate shock is a parallel-shift approximation, so this statement is consistent with it.
CDuration-convexity immunization is local and is intended for small rate changes.
DEqual modified durations are the first-order sensitivity-matching condition.
Original practice · fully worked
Original variant: identify a shock outside Redington scope
An asset and liability portfolio satisfy Redington value, duration, and convexity conditions at a common yield. Which market movement is least directly covered by that local immunization?
A A small parallel upward shift
B A small parallel downward shift
C An infinitesimal common-yield change
D A small change evaluated with the local Taylor expansion
E A yield-curve twist with short rates down and long rates up
Variant answer in brief
Redington matching is built around a single common-yield shift, so a nonparallel curve twist lies outside its direct protection, choice E.
Setup
Setup
Redington conditions summarize rate exposure with one yield variable.
Δit=Δifor a parallel shift
Model
Model
Small parallel changes can therefore be approximated through matched duration and favorable convexity.
ΔP/P≈−DmodΔi+21C(Δi)2
Compute
Compute
A twist assigns different yield shocks to different maturities and cannot be represented by that single variable.
curve twist: Δitvaries by maturity
Answer
Answer
The nonparallel yield-curve twist is least directly covered, corresponding to choice E.
the yield-curve twist is outside the direct model(E)
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