Consider a bank with the following balance sheet:

a) Find the duration gap.

b) Suppose the portfolio manager wants to reduce the duration gap to 0.50. For that purpose he wants to swap $x of the 4yr loan @ Libor with a 6yr loan at 7% fixed rate. The duration of the 6yr loan at 7% is 5 yrs. What is the size $x of the swap that makes duration gap equal to 0.50?

Assets Value Duration of the Asset 6yr loan 25% $20,000 3 5yr loan 26% $20,000 4 Liabilities Value Duration of Liability 4yr loan QLibor $15,000 1 6yr loan 25% $15,000 5