Independent solution

How to solve this Immunization and Asset-Liability Management question

Setup

Setup

Let x and y be current amounts invested in the one- and four-year zeros; match the 2,000 liability present value.

x+y=2000x+y=2000

Model

Model

The single year-3 liability has duration 3, so match the asset duration numerator.

x+4y=3(2000)x+4y=3(2000)

Compute

Compute

Solving gives x = 666.666667 and y = 1333.333333. The asset second-moment measure is 11.00, above the liability value 9.00.

CA=x+16y2000=11.00000000C_A=\frac{x+16y}{2000}=11.00000000
CL=9C_L=9

Answer

Answer

The one-year investment is approximately 667 and satisfies Redington's convexity condition, selecting choice B.

x≈667(B)\boxed{x\approx667\quad\text{(B)}}