Question

Hedge Row Bank has the following balance sheet (in millions): Assets $135 $150 Liabilities Equity $150 Total 15 Total Sise The duration of the assets is 6 years and the duration of the liabilities is 4 years. The bank is expecting interest rates to fall from 10 percent to 9 percent over the next year. a. What is the duration gap for Hedge Row Bank? (Round your answer to 1 decimal place. (e.g.. 32.1)) b. What is the expected change in net worth for Hedge Row Bank if the forecast is accurate? (Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161)) c. What will be the effect on net worth if interest rates increase 100 basis points? (Negative amount should be indicated by a minus sign. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161)) d. If the existing interest rate on the liabilities is 6 percent and that on the assets is 10 percent, what will be the effect on net worth of a 1 percent increase in interest rates? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places. (e.g., 32.1616)) 30 years a Duration gap b Expected change in net worth c. Expected change in net worth d Expected change in net worth milion million million

Answer 1

Answer A) Duration GAP = Duration _Asset – k x Duration _Liabilities = 6 – 0.9x4 = 6 – 3.6 = 2.4 years

Answer B) Expected change in net worth for Hedge Row Bank = Duration GAP[ΔR/(1 + R)]A

= -2.4(-0.01/1.10)$150 = $3.272.

Answer C) Effect on net worth if interest rates increase 100 basis points

Expected ΔE = -DGAP[ΔR/(1 + R)]A = -2.4(0.01/1.10)$150 = -$3.272

Answer D) Solving for the impact on the change in equity under this assumption involves finding the impact of the change in interest rates on each side of the balance sheet, and then determining the difference in these values. The analysis is based on the original equation:

Expected ΔE = ΔA - ΔL

ΔA = -D_A[ΔR_A/(1 + R_A)]A = -6[0.01/1.10]$150 = -$8.1818

and   ΔL = -D_L[ΔR_L/(1 + R_L)]L = -4[0.01/1.06]$135 = -$5.0943

Therefore, ΔE = ΔA - ΔL = -$8.1818 – (-$5.0943) = - $3.0875.