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
Answer and calculation
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: Δit varies 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) 