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

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.

Solutions

Expert Solution

Total Asset value = Value of Reserves + Value of T notes + Value of Loans + Value of Mortgages
=100+350+1725+1325
=3500
Weight of Reserves = Value of Reserves/Total Asset Value
= 100/3500
=0.0286
Weight of T notes = Value of T notes/Total Asset Value
= 350/3500
=0.1
Weight of Loans = Value of Loans/Total Asset Value
= 1725/3500
=0.4929
Weight of Mortgages = Value of Mortgages/Total Asset Value
= 1325/3500
=0.3786
Duration of Asset = Weight of Reserves*Duration of Reserves+Weight of T notes*Duration of T notes+Weight of Loans*Duration of Loans+Weight of Mortgages*Duration of Mortgages
Duration of Asset = 0*0.0286+3*0.1+6*0.4929+12*0.3786
Duration of Asset = 7.8
Total Liabilities value = Value of Deposits + Value of Lt debt + Value of Equity
=2000+1000+500
=3500
Weight of Deposits = Value of Deposits/Total Liabilities Value
= 2000/3500
=0.5714
Weight of Lt debt = Value of Lt debt/Total Liabilities Value
= 1000/3500
=0.2857
Weight of Equity = Value of Equity/Total Liabilities Value
= 500/3500
=0.1429
Duration of Liabilities = Weight of Deposits*Duration of Deposits+Weight of Lt debt*Duration of Lt debt+Weight of Equity*Duration of Equity
Duration of Liabilities = 1.5*0.5714+15*0.2857+0*0.1429
Duration of Liabilities = 5.1429

Duration gap = duration of assets-duration of liabilities = 7.8-5.1429=2.6571

jeff jeffy answered 6 months ago
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