Question

Consider the following.

a. Calculate the leverage-adjusted duration gap of an FI that has assets of $2.4 million invested in 25-year, 9 percent semiannual coupon Treasury bonds selling at par and whose duration has been estimated at 10.08 years. It has liabilities of $1,040,000 financed through a two-year, 6.50 percent semiannual coupon note selling at par.

b. What is the impact on equity values if all interest rates fall 20 basis points—that is, ΔR/(1 + R/2) = –0.0020?

Answer 1

(a) Assets: Par Value = Market Value = $ 2.4 million and Modified Duration = Da = 10.08 years

Liabilities: Par Value = Market Value = $ 1040000 or $ 1.04 million, Liability Tenure = 2 years or 4 half-years, Annual Coupon Rate = 6.5 % payable semi-annually, As the liability sells at par the coupon rate equals the yield

Therefore, Yield = 6.5 %

Modified Duration = 1.91 years

Liability to Asset Ratio = K = L/A = 1040000 / 2400000 = 0.433

Leverage Adjusted Duration Gap = Da - Dl x (K) = 10.08 - 1.91 x (0.4333) = 9.25 years

(b) Change in Basis Points = 20 basis points

Impact on Equity Value = - 9.25 x 2400000 x - 0.002 = $ 19247.08