Independent solution

How to solve this Exact Cash-Flow Matching question

Setup

Setup

Match the liabilities backward from the final date because only the second security pays at that date. Let x and y be the holdings of the two available securities.

1025y=1000⟹y=0.975611025y=1000\Longrightarrow y=0.97561

Model

Model

The final-date equation gives y = 1,000/1,025 = 0.97561. Insert that holding into the earlier cash-flow equation to solve for x.

1040x+25y=10001040x+25y=1000

Compute

Compute

The earlier match gives x = 0.93809. The required holding pair is (0.93809, 0.97561).

x=0.93809x=0.93809

Answer

Answer

The calculation gives the statement identified by the conditions above for exact cash-flow matching, matching published choice D.

(0.93809, 0.97561)(D)\boxed{(0.93809,\ 0.97561)\quad\text{(D)}}