Question

3. Consider the following: A) Calculate the leverage-adjusted duration gap of an Fl that has assets of $1 million invested in 30-year, 10% semiannual coupon Treasury bonds selling at par and whose duration has been estimated at 9.94 years. It has liabilities of $900,000 financed through a two-year, 7.25 % semiannual coupon note selling at par. [9 pts) B)What is the impact on equity value if all interest rates falt 20 basis points? [6 pts)

Answer 1

A B C D E F G H I J | Period Payment PV factor Present value Weight | Duration 36.25 0.965018/ 34.98 10.034982 | 0.034982 36.25 0.93126 33.76 0.033758 0.067516 36.25 0.898683 32.58 0.032577 0.097732 1036.25 0.867245 898.68 0.898683 3.594731 1000.00 Total 3.794961 3 4 Duration = 3.794961 / 2 = 1.89748 Leverage adjusted duration gap = Asset duration - Liability duration * (Liability / liability + equity)) = 9.94 - 1.89748 * ($900,000 / $1,000,000) = 9.94 - 1.707732 = 8.23 years Leverage adjusted duration gap = 8.23 years b) Change in equity = Duration gap * total assets * change in rate = -8.23 * 1000000 * (-0.002) = $16,464.54

EXCEL FORMULA:

B C D E F G -Nm 7 Period Payment PV factor =1000*7.25%/2 =1/(1+3.625%)^B4 =1000*7.25%/2 =1/(1+3.625%)^B5 =1000*7.25%/2 =1/(1+3.625%)^B6 =1000+(1000*7.25%/=1/(1+3.625%)^B7 N Present value =C4*D4 =C5*D5 =C6*D6 =C7*D7 =E4+E5+E6+E7 Weight =E4/1000 =E5/1000 =E6/1000 =E7/1000 Total Duration =B4* F4 =B5*F5 =B6*F6 =B7*F7 =SUM(G4:47) 00