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 10 percent and on assets are 12 percent.

a. What is the duration of assets, DA, liabilites, DL, and Equity, E.

b. The bank will benefit or be hurt if all interest rates rise (assume by the

c. Compute the repricing gap for the bank using those assets and liabilities repricing or maturing in 2 years or less. From this information, will the bank be hurt or benefit by a 200 basis point rise in interest rates on assets and liabilities?

d. If the bank gets an additional $100 in a 6-month certificate of deposit, what investments (using the above portfolio possibilities) should it make to control interest rate risk (? y = i?¿1?2 200 basis point change in all interest rates) by changing the duration of its portfolio? State the advantages and disadvantages of using net worth immunization and asset/liability duration as a means of controlling interest rate risk. Define your terms.

Explanation / Answer

Answer: a.) Assets $mn Duration Weighted average Duration Prime rate loans 50 1 0.285714286 2-year car loans 65 1 0.371428571 30 Year mortgages 60 7 2.4 Total assets 175 3.057142857 therefore Duration of asset is sum of weighted average durations on all assets Duration of assets = 3.05714286 Liabilities $mn Duration Weighted average Duration Super now checking accounts 100 1 0.606060606 6-months certificate of deposits 40 0.5 0.121212121 3-months certificate of deposits 25 3 0.454545455 Total Liabilities 165 1.181818182 Equity 10 Generally equity have no duration. So the duration of equity = 0 But Duration of Liablity can be calculated by finding out weighted average duration of Liablities. Therefore Duration of Liabilities = 1.18181818 b.) Lets assume that Interest rate rise from 10% to 11% Change in interest = 11% - 10% = 1% = 0.01 Now find out the change in value of assets by using this duration formula. Change in assets = -duration * (change in interest/(1+ initial interest) Change in assets = -3.057143 * (0.01/(1 + 10%) = -0.02779 or = -2.78% Therefore fall in value of assets is by 2.78 % and hence new value of assets = $175mn -2.78% of $175 mn = $170.14 mn Now find out the change in value of Liabilities by using this duration formula. Change in liabilities = -duration * (change in interest/(1+ initial interest) Change in liabilities = -1.1818 * (0.01/(1 + 10%) = -0.01074 or = -1.074% Therefore fall in value of liabilities is by 1.074 % and hence new value of liabilitiess = $175mn -1.074% of $175 mn = $173.12 mn Hence falll in value of new worth = New assets - New Liabilities = $170.14mn - $173.12mn = $2.98mn

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