Question 3 (17 marks)

(a) Bank ABC has a bond with a maturity of 4 years. The coupon rate of the bond is 8%, the yield to maturity is 9%, and total face value is 1 million dollars. Interest payment is paid semiannually. Compute the duration of the bond.

(5 marks)

(b) Predict the change in the bond price if interest rates rise by 25 basis points based on the duration of the bond that you have calculated in part (a).

(4 marks)

(c) Compute the leverage adjusted duration gap if the ratio of total equity to total asset is 0.2, and the duration of all its liabilities is 2. (Assume that the bank holds the bond in part (a) as its only one asset)

(4 marks)

(d) It is expected that the market interest rate will increase in the future. Assume that the ratio of total equity to total asset, and the duration of all the liabilities remain unchanged. The bank aims to rebalance its assets to completely immunize interest rate risk. Compute a new value of duration of all assets. How does the bank restructure its assets to achieve the new value of duration of all assets?