Consider a bank with the following balance sheet (M means million):
Assets
5yr bond bought at a yield of 3.4% (lending money)
Value $550M
Duration of the Asset 4.562
Convexity of the Asset 12.026
12yr bond bought at a yield of 4% (lending money)
Value $800M
Duration of the Asset 9.453
Convexity of the Asset 53.565
Liabilities
2yr bond sold at a yield of 2.4% (borrowing money)
Value $300M
Duration of the Liability 1.941
Convexity of the Liability 2.384
4yr bond sold at a yield of 2.8% (borrowing money)
Value $500M
Duration of the Liability 3.759
Convexity of the Liability 8.206
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;
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?