Question 3. Bond (35 marks in total) Consider a bank with the following balance sheet (M means million): Assets Value $550M Duration of the Asset | Convexity of the Asset 4.562 12.026 Syr bond bought at a yield of 3.4% (lending money) $800M 9.453 53.565 12yr bond bought at a yield of 4% (lending money) Value $300M Duration of the Liability Convexity of the Liability 1.941 2.384 Liabilities 2yr bond sold at a yield of 2.4% (borrowing money) 4yr bond sold at a yield of 2.8% (borrowing money) $500M 3.759 8.206 b) Calculate the duration and convexity of the both asset and liability sides; (8 marks) c) If the interest rates go up by 1%, using the duration and convexity rule to determine the net worth of the bank and the equity to asset ratio; (10 marks) d) In c)'s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation, the bank decides to raise cash (zero duration and zero convexity) from the equity holders. How much cash does the bank need to raise? (10 marks)