Consider the following bank balance sheet (fixed rates and pure discount securit

Question

Consider the following bank balance sheet (fixed rates and pure discount securities unless indicated otherwise). Interest rates on liabilities are 6 percent and on assets are 8 percent Duration iltions rS Assets Prime-Rate Loans (rates set monthly) 2-Year Car Loans 160 1.0 175 2.0 170 7.0 30-Year Mortgages 505 ? Total Assets (A) Liabilities and Equity Super Now Checking Accounts (rates set monthly) 6-Month Certificates of Deposit 3-Year Certificates of Deposit 200 1.0 140 .5 125 3.0 Total Liabilities (L) 465 Equity (E) 40 Total Liabilities (L) and Equity (E) 505 a. What is the duration of assets, D, and labilities, DL b. Given the duration imbalance of assets and liabilities, what is the loss in market value of assets, liabilities and equity as a result of an interest rate rise by 200 bp? c. Compute the repricing gap for the bank using those assets and liabilities repricing, maturing in 2 years or less or with a duration of 2 years or less. From this information, will the bank benefit or be hurt by a 200 basis point rise in interest rates on assets and liabilities?

Explanation / Answer

Average Duration of Assets:

For each asset, we will calculate the weighted duration by multiplying the duration by the amount of the asset divided by total assets, i.e. $505 billion. Doing this for all the assets and adding them up, we will get the average duration of the assets.

Average Duration of Liabilities:

For each liability, we will calculate the weighted duration by multiplying the duration by the amount of the liability divided by total liabilities (excluding Equity), i.e. $465 billion. Doing this for all the liabilities and adding them up, we will get the average duration of the liabiliti.

Assets Amount ($ Billions) Duration (Years) Weighted Duration (Years) Prime-rate loans 160 1.0 160 * 1.0 / 505 = 0.32 2-year car loans 175 2.0 175 * 2.0 / 505 = 0.69 30-year mortgages 170 7.0 170 * 7.0 / 505 = 2.36 Average Duration of Assets (DA) 3.37

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