Consider a bank with the following balance sheet (M means million): Assets 5yr bond bought at a yield of 3.4% (lending money) Value | Duration of the Asset $550M 4.562 Convexity of the Asset 12.026 $800M 9.453 53.565 12 yr bond bought at a yield of 4% (lending money) Duration of the Liability | Value $300M Convexity of the Liability 2.384 1.941 Liabilities 2 yr 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 a) Calculate the equity (total asset-total liability) to asset ratio of the bank (Hint: equity to asset ratio = total equity/total asset) (2 marks) 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) e) Do you agree with the following statement? Explain why. (5 marks) "The information about a bond's duration and convexity adjustment is sufficient to quantify interest rate risk exposure