Assume a constant annual interest rate of 5%. A bank has an asset base that delivers cash flows for the next 5 years as shown in the table below. It wishes to structure its liabilities so as to match the value and duration of its assets. Two bonds (A and B) are available to the bank as liabilities and their respective cash flows are shown below.

 

 

a. Derive the quantities of the two bonds that the bank should use to meet its objectives.
b. Check that the value and duration of the bond portfolio match those of the asset cash flow stream.

Time Assets Bond A Bond B 1 2 3 4 5 400 200 300 88 450 600 8 8 0 0 480 8 100 108