Question 2 A bank has $100 million of investment grade bonds with a duration of 8.0...

Question 2 A bank has $100 million of investment grade bonds with a duration of 8.0 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 years and nondeposit 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. A. This bank has a duration gap of 3.44 years B. This bank has a duration gap of 3.75 years C. This bank has a duration gap of 5.15 years D. This bank has a duration gap of 3.64 years E. This bank has a duration gap of 13.75 years

Solutions

Expert Solution

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

Weighted Average Asset Duration = DA = Weight of investment grade bonds x duration of investment grade bonds + Weight of commercial loans x duration of commercial loans + Weight of consumer loan x duration of consumer loan

Weighted Average Asset Duration = DA = (Investment grade bonds / Total Assets) x duration of investment grade bonds + (Commercial loans / Total Assets) x duration of commercial loans + (Consumer loan / Total Assets) x duration of consumer loan = (100/900)(8) + (500/900)(5) + (300/900)(2) = 0.8888 + 2.7777 + 0.6666 = 4.3331 years

Total Liabilities = Value of deposits + Value of non deposit borrowing = 600 + 100 = 700 million

Weighted Average liability duration = DL = Weight of deposits x Duration of deposits + Weight of non deposit borrowing x Duration of non deposit borrowing = (Deposits / Total liabilities) x Duration of deposits + (Non deposit borrowing / Total liabilities) x Duration of non deposit borrowing = (600/700)(1) + (100/700)(0.25) = 0.8571 + 0.0357 = 0.8928

Duration Gap = DA - [(Total Liabilities / Total Assets)(DL)] = 4.3331 - [(700/900)(0.8928)] = 4.3331 - 0.6944 = 3.6387 = 3.64 years

Hence Duration Gap of Bank = 3.64 years

Answer D. This bank has a duration gap of 3.64 years

jeff jeffy answered 2 hours ago

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