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 DR/(1+R/2) = -0.0020.
　　c. Using the information calculated 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?
　　Answer:
　　a.The duration of the capital note is 1.8975 years.
　　Two-year Capital Note (values in thousands of $s)
　　Par value = $900 Coupon rate = 7.25% Semiannual payments
　　R = 7.25% Maturity = 2 years
　　Duration = $1,707.73/$900.00 = 1.8975
　　Leverage adjusted duration gap= 8.23225years
　　b.The change in net worth using leverage adjusted duration gap is given by:
　　Change in the market value of equity =-[8.23225](1,000,000)(.002)= $16,464
　　c.If the FI wishes to be immune from the effects of interest rate risk (either positive or negative changes in interest rates), a desirable leverage-adjusted duration gap (DGAP) is zero. If the FI is confident that interest rates will fall, a positive DGAP will provide the greatest benefit. If the FI is confident that rates will increase, then negative DGAP would be beneficial.
　　d.Change in the market value of equity=-[8.23225](1,000,000)(.003)= -$24,697
　　e.Immunizing the equity from changes in interest rates requires that the DGAP be 0. Thus, (DA-DLk) = 0 ? DA = DLk, or DA = 1.8975x0.9 = 1.70775 years.

 
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