Question

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

Answer 1

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)