Assume that a goal of the regulatory agencies of financial institutions is to immunize the ratio of equity to total assets, that is, . Explain how this goal changes the desired duration gap for the institution. Why does this differ from the duration gap necessary to immunize the total equity? How would your answers to part (h) in problem 24 and part (g) in problem 26 change if immunizing equity to total assets was the goal?

Problem 24

The balance sheet for Gotbucks Bank Inc. (GBI) is presented below ($ millions).

a. What is the duration of the fixed-rate loan portfolio of Gotbucks Bank?

b. If the duration of the floating-rate loans and fed funds is 0.36 year, what is the duration of GBIâ€™s assets?

c. What is the duration of the core deposits if they are priced at par?

d. If the duration of the Euro CDs and fed funds liabilities is 0.401 year, what is the duration of GBIâ€™s liabilities?

e. What is GBIâ€™s duration gap? What is its interest rate risk exposure?

f. What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 percent (100 basis points)? Note that the relative change in interest rates is

g. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of Â percent (Â basis points)?

h. What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP to equal zero?

Problem 26

The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution:

Treasury bonds are five-year maturities paying 6 percent semiannually and selling at par

a. What is the duration of the T-bond portfolio?

b. What is the average duration of all the assets?

c. What is the average duration of all the liabilities?

d. What is the leverage adjusted duration gap? What is the interest rate risk exposure?

e. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 0.5 percent Â

f. If the yield curve shifts downward 0.25 percentÂ , what is the forecasted impact on the market value of equity?

g. What variables are available to the financial institution to immunize the balance sheet? How much would each variable need to change to get DGAP to equal 0?