A bank has $100 million of investment grade bonds with a duration of 9.0 years. This...

A bank has $100 million of investment grade bonds with a duration of 9.0 years. This bank also has $500 million of commercial loans with a duration of 5.0 years. This bank has $300 million of consumer loans with a duration of 2.0 years. This bank has deposits of $600 million with a duration of 1.0 year and non-deposit borrowings of $100 million with an average duration of.25 years. What is this bank's duration gap? These are all of the assets and liabilities this bank has

Solutions

Expert Solution

To calculate the duration gap of bank we will first calculate Weighted average duration of assets of bank

Total assets of bank = Value of investment grade bonds + Value of commercial loans + Value of consumer loans = 100 + 500 + 300 = 900 million

Weight of investment grade bond = value of investment grade bond / Total assets = 100/900

Weight of commercial loan = Value of commercial loan / total assets = 500 / 900

Weight of consumer loan = value of consumer loan / total assets = 300/900

Weighted average duration of assets = D_A = Weight of investment grade bonds x duration of investment grade bonds + Weight of commercial loan x duration of commercial loan + Weight of consumer loan x duration of consumer loan

= (100/900)(9) + (500/900)(5) + (300/900)(2) = 1 + 2.7777 + 0.6666 = 4.4443

Now we will calculate weighted average duration of liabilities

Total liabilities of bank = Value of deposits + Value on non deposit borrowings = 600 + 100 = 700 million

Weight of deposits = Value of deposits / Total liabilities = 600/700

Weight of non deposit borrowings = 100/700

Weighted average duration of liabilities = D_L = Weight of deposits x duration of deposits + Weight of non deposit borrowings x duration of non deposit borrowings = (600/700)(1) + (100/700)(0.25) = 0.8571 + 0.0357 = 0.8928

Duration gap = D_A - (D_L)(Total liabilities / Total assets) = 4.4443 - (0.8928)(700/900) = 4.4443 - 0.6944 = 3.7499 years

Hence duration gap of bank = 3.7499 years = 3.75 years (rounded to two decimal places)

jeff jeffy answered 7 months ago

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