Original practice · fully worked
Original variant: choosing maturities for a coastal barrier reserve
A coastal barrier liability has present value 12,000, duration 8 years, and convexity 65. A manager may pair zero-coupon holdings at maturities (2,10), (4,10), or (8 only). Which value allocation both matches duration and has convexity above 65?
- A
4,000 at year 2 and 8,000 at year 10 - B
4,000 at year 4 and 8,000 at year 10 - C
6,000 at year 4 and 6,000 at year 10 - D
12,000 at year 8 - E
8,000 at year 4 and 4,000 at year 10
Answer and calculation
The 4/10 allocation 4,000 and 8,000 has duration eight and convexity 72, so choice B.
Setup
Setup
Test the offered allocations with current values as weights rather than comparing maturities alone.
4x+10(12000−x)=8(12000) Model
Model
The 4/10 pair gives a direct linear duration equation for the amount in the shorter zero.
x=4000,12000−x=8000 Compute
Compute
Solving produces 4,000 and 8,000; their weighted squared maturity is 72.
CA=1200042(4000)+102(8000)=72>65 Answer
Answer
That allocation matches value and duration and supplies excess convexity, so choice B is correct.
(4000, 8000)(B) 