Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900,000, two-year, 7.25 percent semiannual coupon capital note selling at par.
a. What is the leverage adjusted duration gap of Financial Institution XY?
b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note:The relative change in interest rates is ?R/ (1 + R/2) = -0.0020.
c. Using the information in parts (a) and (b), what can be said about the desired duration gap for a financial institution if interest rates are expected to increase or decrease.
d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points.
e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates?