This Exam FM sample reference tests Cash-Flow and Risk Matching. Cash-flow matching restricts the manager to instruments that reproduce each dated liability, whereas Redington immunization permits a wider set that matches summary risk measures; therefore statement B is true.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
ARedington requires asset convexity greater than liability convexity, not the reverse.
CThe technique's local assumptions concern rate shifts and risk measures, not a required upward-sloping yield curve.
DFull immunization does not guarantee dominance under every possible nonparallel curve shift.
EExact cash-flow matching generally requires the least rebalancing because each liability is funded directly.
Original practice · fully worked
Original variant: comparing reserve-management constraints
A reserve manager can either reproduce every liability payment date or match only present value, duration, and excess convexity. Which statement correctly compares the two approaches?
A The summary-measure approach is always exact.
B Date matching permits more asset combinations.
C Date matching is more restrictive but removes reinvestment risk between liability dates.
D Both methods require identical asset cash flows.
E Neither method responds to interest-rate changes.
Variant answer in brief
Date-by-date matching narrows the asset set but directly funds liabilities, so choice C.
Setup
Setup
One approach constrains the entire cash-flow vector; the other constrains only selected value and sensitivity moments.
CFA,t=CFL,t∀t
Model
Model
Matching every date necessarily admits fewer portfolios than matching three summary quantities.
versusPVA=PVL,DA=DL,CA>CL
Compute
Compute
Its benefit is that each liability payment is already supplied by an asset payment, avoiding reliance on intermediate reinvestment.
Fexact⊂Fsummary
Answer
Answer
Choice C states both the restriction and its practical consequence.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
