Question

The balance sheet of FIN 4100-601 Bank is listed below. Market yields are in parentheses, and amounts are in millions Liabilities and Equity Assets Cash Fed funds (2.05%) 3-month T-bills (3.25%) 8-year T-bonds (6.50%) 5-year munis (7.20%) 7-month C&I loans (4.8%) 2-year C&I loans (4.15%) Fixed-rate mortgages (5.10%) Duration Duration $30 150 200 250 50 200 275 Demand deposits $150 0.02 Savings accounts (0.5%) 0.22 MMDAs (3590) 7.55 (no minimum balance requirement) 4.25 3-month CDs (3.200) 0.55 5-year CDs (5%) 1.65 Fed funds (2%) 1.25 260 175 350 225 4.85 0.02 6- month commercial paper (4.05%) (maturing in 5 months) Fixed-rate mortgages (5.30%) (maturing in 5 years) 0.48 300 Subordinated debt 275 4.45 7-year fixed rate (6.25%) 6.65 100 $1,610 ixed-rate mortgages (5.40%) Total liabilities 355 20 (maturing i 20 years) 18.25 Premises and equipment Total assets Equity Total liabilities and equity $645 255 (1) What is the duraton gap? (2) What is the change in equity value forecasted from the duration values for a predicted increase in interest rates of 0.5 percent?

Answer 1

ANSWER:

ΔMVfedfunds= 0.0205 x 0.005/1.0205 x 150m = $15066.1

ΔMVT-bills= 0.22 x0.005/1.0325 x 200m = $213075

ΔMVT-bonds= 7.55 x 0.005/1.0650 x 250m = $6661502

ΔMVmunis= 4.25 x 0.005/1.0720 x 50m = $991138

ΔMVC&Iloans= 0.55 x0.005/1.0480 x 200m = $524809

ΔMVC&Iloans= 1.65 x 0.005/1.0415 x 275m = $2178348

ΔMVfixed-ratemortgages= 0.48 x0.005/1.0510 x 450m = $1027592

ΔMVfixed-ratemortgages= 4.45 x0.005/1.0530 x 275m = $5810779

ΔMVfixed-ratemortgages= 18.25 x0.005/1.0540 x 355m= $30734108

=>ΔMVA = $48156517

ΔMVsavings=1.25 x0.005/1.0050 x 50m = $310,945

ΔMVCDs= 0.20 x 0.005/1.0320 x 175m = $169,574

ΔMVCDs= 4.85 x 0.005/1.0500 x 350m = $8,083,333

ΔMVfedfunds= 0.02 x 0.005/1.0200 x 225m = $22,059

ΔMVcommericalpaper= 0.55 x 0.005/1.0405 x 300m = $792,888

ΔMVsubordinatedebt= 6.65 x 0.005/1.0625 x 100m = $3,129,412

=>ΔMVL = $12508211.

equity value forecasted from the duration values for increase of 0.5 percent in interest rates on assets and liabilities

ΔMVE = ΔMVA – ΔMVL = $48156517 – ($2508211) = $35648306