Question

Assume a bank with the following balance sheet at the end of the financial year.

Assets Amount Avg Duration (in years) Liabilities Amount Avg Duration (in years)

Reserves $100 0 Deposits $2000 1.5

T-notes $350 3 L T Debt $1000 15

Loans $1725 6 Equity $500 0

Mortgages $1325 12

Calculate the duration of assets and liabilities and the duration gap.

Answer 1

Total assets = A = Reserves + T notes + Loans + Mortgages = 100 + 350 +1725 + 1325 = 3500

Total liabilities(excluding equity) = L = Deposits + LT debt = 2000 + 1000 = 3000

Duration of Assets = D_A = Weighted average duration of Assets

where Weight of an asset = Amount of an asset / Total assets

D_A = Weight of reserve x duration of reserve + Weight of T notes x Duration of T notes + Weight of Loans x Duration of Loans + Weight of Mortgages x Duration of Mortgages = (100/3500)(0) + (350/3500)(3) + (1725/3500)(6) + (1325/3500)(12) = 0 + 0.30 + 2.96 + 4.54 = 7.80

Hence Duration of Assets = 7.80 years

Duration of Liabilities = D_L = Weighted average duration of Liabilities

where Weight of a Liability = Amount of a Liability / Total Liabilities(excluding Equity)

D_L = Weight of Deposits x duration of deposist + Weight of LT Debt x Duration of LT debt = (2000/3000)(1.5) + (1000/3000)(15) = 1.00 + 5.00 = 6.00

Hence Duration of Liabilities = 6.00 years

Duration Gap = D_A - [(L/A)(D_L) = 7.80 - [(3000/3500)(6.00) = 7.80 - 5.14 = 2.66 years

Hence Duration Gap = 2.66 years