A bank has the following assets and liabilities:
i) Total Assets: $200 million of 3-year loans which pays 10% annual coupon, and 10% bond yield.
ii) Total Liabilities: $150 million of 8-year debt issued to the public (duration = 6.6 years).
In order to fully immunize the bank’s equity ratio from interest rate risk, the risk manager of the bank has decided to restructure the total assets. More specifically, she is hoping that the immunization could be achieved by selling some of the existing 3-year loans and using the proceeds from the sale to purchase a consol bond with yield of 12%. To make this immunization strategy successful, how much (in dollar amount) of the existing 3-year loans does the risk manager need to sell?