ABLE Bank has the following market value balance sheet (in millions, all interests at annual rates and paid annually).Assets $ Liabilities and Equity $2-year corporate bonds, annual fixed rate at 5% 375 3-year zero coupon bonds, annual fixed rate at 3% 5002-year zero coupon bond, annual coupon rate at 4% 300 Equity 175Note to the balance sheet : All securities are selling at par equal to book value, i.e current market interest rate of corporate bonds is 5% p.a, current market interest rate of the 2-year zero coupon bond held is 4% p.a and current market interest rate of the 3-year zero coupon bonds issued is 3% p.a. What is the bank's leverage adjusted duration gap ? Round your final answer to 2 decimal places.E.g. if the final answer is -3.59 years, type -3.59 in the answer box. If the final answer is 3.59 years, type 3.59 in the box .
Question
ABLE Bank has the following market value balance sheet (in millions, all interests at annual rates and paid annually).Assets 2-year corporate bonds, annual fixed rate at 5% 375 3-year zero coupon bonds, annual fixed rate at 3% 5002-year zero coupon bond, annual coupon rate at 4% 300 Equity 175Note to the balance sheet : All securities are selling at par equal to book value, i.e current market interest rate of corporate bonds is 5% p.a, current market interest rate of the 2-year zero coupon bond held is 4% p.a and current market interest rate of the 3-year zero coupon bonds issued is 3% p.a. What is the bank's leverage adjusted duration gap ? Round your final answer to 2 decimal places.E.g. if the final answer is -3.59 years, type -3.59 in the answer box. If the final answer is 3.59 years, type 3.59 in the box .
Solution
The leverage adjusted duration gap is a measure of the sensitivity of the value of a bank's net worth to changes in interest rates. It is calculated as the difference between the duration of assets and the duration of liabilities, adjusted for the leverage of the bank.
First, we need to calculate the duration of each asset and liability:
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The duration of a 2-year corporate bond with an annual fixed rate of 5% is approximately 1.92 years. (This is calculated using the formula for the duration of a bond with annual coupons: D = [1 + (1 + r)^(-2)] / r, where r is the interest rate.)
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The duration of a 2-year zero coupon bond is exactly 2 years, because the only cash flow occurs at the end of the 2 years.
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The duration of a 3-year zero coupon bond is exactly 3 years, because the only cash flow occurs at the end of the 3 years.
Next, we calculate the weighted average duration of assets (DA) and liabilities (DL):
DA = (375 * 1.92 + 300 * 2) / (375 + 300) = 1.95 years DL = (500 * 3) / 500 = 3 years
The leverage of the bank (L) is calculated as the ratio of assets to equity:
L = (375 + 300) / 175 = 3.86
Finally, we calculate the leverage adjusted duration gap (DGAP) using the formula:
DGAP = DA - (L * DL) = 1.95 - (3.86 * 3) = -9.61 years
So, the bank's leverage adjusted duration gap is -9.61 years.
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