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.
Answer and calculation
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.
choice C 