Consider the following balance sheet (in millions of $) for a bank ASSETS CORPOR

Question

Consider the following balance sheet (in millions of $) for a bank ASSETS CORPORATE LOANS DUE IN 7.5 YEARS NOMINAL VALUE LIABILITIES NOMINAL VALUE $650 $140 $790 CERTIFICATES OF DEPOSIT DUE IN 1.5 YEARS EQUITY What is the bank's duration gap (in years)? Answer: Consider a bank with the following balance sheet ASSETS VALUE DURATION LIABILITIES VALUE DURATION Cash 5-yr Loan @ 5% 4-yr Loan @ 6% $10,000 5,000 5,000 0 3 2 4-yr Bond @ LIBOR 3-yr Bond @ 5% 6-yr Bond @ 6% $3,000 5,000 2,000 2 What is the bank's duration gap (in years)? Answer

Explanation / Answer

solution: 1 Bank's Duration Gap (in Years) = Duration of Assets – (Liabilities/Total Assets) Duration of Liabilities = 7.5 – ($650 ÷ $790) × 1.5 = 6.27 years 2 Bank's Duration Gap (in Years) = Weighted Avg Duration of Assets – (Liabilities/TotalAssets)Weighted Avg Duration of Liabilities = 1.25 – ($10,000 ÷ $20,000) × 2.3 = 0.1 Years Total Assets = $20,000 Total liabilities = $10,000 Weighted Avg Duration of Assets = ($10,000/$20,000) × 0 years + ($5,000/$20,000) × 3 years + ($5,000/$20,000) × 2 years = 1.25 Years Weighted Avg Duration of Liabilities = ($3,000/$10,000) × 1 year + ($5,000/$10,000) × 2 years + ($2,000/$10,000) × 5 years = 2.3Years

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