Modified duration gap of 3 year and market value of assets of 3 million. Manager expects interest rates to go up from 9% to 10%.

Question:

Show how can the manager immunize the bank assets from interest rate change by using following 2 Swaps:

Swap 1: pay T-bill +1% in exchange for 7% fixed rate.

Swap 2: pay fixed rate of 7% in exchange for a floating rate of T-bill +1%.

Assume modified duration on 7% fixed rate security is 7.5 and the modified duration on T-bill is 1.