PBF-CA3 [Due date: 18 Dec 2021, 5pm] [Topic 6- Interest Rate Risk Management] 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 $1000 and the market interest rate = 4%. What is the Macaulay duration of this bond portfolio? (4 marks) (b) Estimate, using modified duration, the change in the price of the 4-year 5% coupon bond if the market interest rate decreases from 4% to 3%. (4 marks) Question 2- Income Gap + Overall Duration Gap [17 marks] (a) Consider the following balance sheet of Banco Credit: Assets ($) Duration (years) Variable rate mortgages 250 9.2 Fixed rate mortgages 170 5.2 Commercial loans 790 4.5 Physical capital 300 Total 1510 Liabilities (S) Duration (years) Money market deposits 450 0.8 Savings deposits 300 2.7 Variable rate CDs 100 1 . 1 Equity 660 Total 1510 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 rates 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 its equity when interest rates increase