Your client is a regional savings and loan institution. You have been hired to assess the client’s exposure to interest rate risk and advise on possible ways to reduce it. You have the following information on the S&L’s balance sheet: The total assets are mortgages and are worth $3,096.87M. The assets have a duration of 9.23 years. The liabilities are 5-year Certificates of Deposit (CDs) with a coupon rate of 8%, which we assume is paid annually (CDs are coupon bonds, so all coupon bond formulas apply to them). The total face value of the CDs that have been issued by your client is $2.5 billion. The yield curve is flat at 8%.
a) Compute the duration of the liabilities.
b) Compute the duration of the (net) market value of the bank.
c) Your recommendation to the client is to sell some of the mortgage portfolio and buy 1-year CDs (which pay an annual coupon rate of 8%) with the proceeds. How many dollars worth of the assets does your client have to sell to reduce the duration of the (net) market value of the bank to 0 (i.e., to achieve immunization)?