Question 1 - Macaulay Duration of Bond Portfolio + Modified Duration [8 marks] (a) An investor decides to construct a bond portfolio made up of $10,000 in the 4-year 5% coupon bond and $30,000 in a 3-year zero coupon bond. Assume the par value of bond is $1000 and the market interest rate =4%. What is the Macaulay duration of this bond portfolio? (4 marks) (b) Estimate, using modified duration, the change in the price of the 4-year 5% coupon bond if the market interest rate decreases from 4% to 3%. (4 marks) Question 2- Income Gap + Overall Duration Gap [17 marks] (a) Consider the following balance sheet of Banco Credit: Assumptions - Fixed rate mortgages repaid in the coming year =25% - Savings deposits that become rate sensitive in the coming year =20% - All commercial loans are rate sensitive - All money market deposits are rate sensitive Using income gap analysis, calculate the change in net interest income over the coming year if interest rates increase by 1% from 4% to 5% (4 marks) (b) What is the duration gap for Banco Credit? (4 marks) (c) What is the estimated change in the value of equity (in $s ) for Banco Credit if interest rate increase by 1% from 4% to 5% ? (4 marks) (d) Explain why a bank with a positive duration gap is estimated to see a fall in the value of it equity when interest rates increase. (5 marks) Question 1 - Macaulay Duration of Bond Portfolio + Modified Duration [8 marks] (a) An investor decides to construct a bond portfolio made up of $10,000 in the 4-year 5% coupon bond and $30,000 in a 3-year zero coupon bond. Assume the par value of bond is $1000 and the market interest rate =4%. What is the Macaulay duration of this bond portfolio? (4 marks) (b) Estimate, using modified duration, the change in the price of the 4-year 5% coupon bond if the market interest rate decreases from 4% to 3%. (4 marks) Question 2- Income Gap + Overall Duration Gap [17 marks] (a) Consider the following balance sheet of Banco Credit: Assumptions - Fixed rate mortgages repaid in the coming year =25% - Savings deposits that become rate sensitive in the coming year =20% - All commercial loans are rate sensitive - All money market deposits are rate sensitive Using income gap analysis, calculate the change in net interest income over the coming year if interest rates increase by 1% from 4% to 5% (4 marks) (b) What is the duration gap for Banco Credit? (4 marks) (c) What is the estimated change in the value of equity (in $s ) for Banco Credit if interest rate increase by 1% from 4% to 5% ? (4 marks) (d) Explain why a bank with a positive duration gap is estimated to see a fall in the value of it equity when interest rates increase