Question 5 (6 marks) Table 2 illustrates a hypothetical balance sheet of an imaginary bank. Asset Cash Loan T-bills Total Table 2. Hypothetical balance sheet of an imaginary bank Value ($ mil) 1,000 10,000 4,000 15,000 Interest rate (%) 0 6 5 Amount to Exchange = Suggested formula: DEquity = DAsset-Liabilities Modified Liability duration and equity Deposits Bonds CDs Total Equity Total 0 4.47 1 3.25 Ass Ass-Liab DAsset Value ($ mil) Liab Ass-Liab 9,000 3,000 2,200 14,200 800 15,000 (a) Calculate the duration of the bank's equity. [1 mark] (b) To immunize the bank's balance sheet from interest risk, the risk manager decides to increase the liability duration by reducing the dependence on deposits and holding more bonds. Show how the risk manager can achieve an immunization from interest risk. [5 marks] DLiabilities Interest rate (%) Change in Portfolio Duration x Portfolio Value Change in Asset Duration 3 4.5 4 Modified duration 0 3.74 1.96 1.094