P1 (35 points) Consider a bank with the following balance sheet: Assets Value Duration of the Asset 8yr loan 98% $6,000 6 6yr loan @5% $14,000 5 Liabilities Value Duration of Liability 5yr loan Libor $12,000 1.5 4yr loan 25% $18,000 3.5 a) (10 points) Find the duration gap. Suppose there are two swaps available to the manager Swap #1: Swap $x of the 5yr loan Q Libor with a 5yr loan at 5% fixed rate. The duration of the 5yr loan at 5% is 4 years. Swap #2: Swap $x of the 4yr loan @ 5% with a 4yr loan @Libor. The duration of the 4yr loan @Libor is 1 year b) (15 points) Suppose the portfolio manager wants to make the duration gap +2. Which swap should be used? Find the swap size 2. c) (10 points) Suppose the portfolio manager wants to make the duration gap 0. Which swap should be used? Find the swap size x