Your employer has asked you to examine the interest-rate risk of your bank relat

Question

Your employer has asked you to examine the interest-rate risk of your bank relative to your direct competition. Management is concerned that interest rates will fall by the end of the year and wants to see what would happen to the relative profitability of the firm if the decline actually occurs.

Interest-rate risk depends on each bank's relative position of interest-sensitive assets and liabilities. You begin the analysis by collecting the information and estimates.

What is the average duration for

Assets for your firm?

Assets for your competition?

Liabilities for your firm?

Liabilities for your competition?

What is the duration gap for:

Your firm?

Your competition?

Using the net worth formula if interest rates decline by 3%, what will be the expected change in the market value of net worth for:

Your firm?

Your competition?

Using the net worth formula, if interest rates rise by 3%, what will be the expected change in the market value of net worth for:

Your firm?

Your competition?

What would your firm need to do:

To eliminate the income gap using adjustments to rate-sensitive assets?

To immunize the market value of net worth from interest-rate risk using duration?

Bank Balance Sheet Competition Your Firm Amount Smillions Duration ears Amount Smillions Duration ears 4 0.0 0.0 Reserves and cash items Securities 0.6 1.6 5.0 0.3 1.2 4.0 4 Less than 1 year 1-2 years Greater than 2 years 0.9 4.4 Residential mortgages Variable-rate Fixed-rate (30 years) 0.4 5.5 17 30 30 0.6 1.4 5.4 0.0 Commerical loans 0.9 1.8 6.0 0.0 Less than 1 year 1-2 years 13 31 Greater than 2 years Physical capital 25 10 Liabilities Checkable deposits Money market deposit accounts Savings deposits CDs 1.0 0.5 1.0 14 10 12 6 1.0 0.6 1.0 16 0.4 0.3 1.1 2.9 0.0 12 14 10 10 14 0.6 0.5 1.8 2.2 0.0 Variable-rate Less than 1 year 19 1-2 years Greater than 2 years 15 10 12 39 Fed funds Less than 1 year 1-2 years Greater than 2 years 0.4 1.2 2.9 18 12 31 0.7 1.8 3.8

Explanation / Answer

We would calculate the duration of the asset by using the weighted average method Your Firm Assets Amount($ in millions) Duration(years) weighted duration(years) Reserves and cash Items 3 0 0.0000 Securities Less than 1 yr 4 0.6 0.0240 1-2 years 3 1.6 0.0480 Greater than 2 yrs 7 5 0.3500 Residential Mortgages Variable Rate 9 0.4 0.0360 Fixed Rate(30 yrs) 15 5.5 0.8250 Commercial Loans Less than 1 year 13 0.9 0.1170 1-2 years 31 1.8 0.5580 Greater than 2 years 55 6 3.3000 Physical Capital 10 0 0.0000 Total Duration of assets 5.258 Your Competition Assets Amount($ in millions) Duration(years) weighted duration(years) Reserves and cash Items 4 0 0.0000 Securities Less than 1 yr 5 0.3 0.0150 1-2 years 7 1.2 0.0840 Greater than 2 yrs 9 4 0.3600 Residential Mortgages Variable Rate 21 0.9 0.1890 Fixed Rate(30 yrs) 17 4.4 0.7480 Commercial Loans Less than 1 year 30 0.6 0.1800 1-2 years 22 1.4 0.3080 Greater than 2 years 30 5.4 1.6200 Physical Capital 25 0 0.0000 Total Duration of assets of competitor 3.504 Your Firm Liabilities Amount($ in millions) Duration(years) weighted duration(years) Checkable deposits 10 1 0.1000 Money market deposit accounts 5 0.6 0.0300 savings deposit 12 1 0.1200 CDs Variable-Rate 6 0.4 0.0240 Less than 1 year 19 0.3 0.0570 1-2 years 8 1.1 0.0880 Greater than 2 yrs 15 2.9 0.4350 Fed Funds 10 0 0.0000 Borrowings Less than 1 year 12 0.4 0.0480 1-2 years 9 1.2 0.1080 Greater than 2 yrs 39 2.9 1.1310 Total duration of liabilities 2.1410 Your Competition Liabilities Amount($ in millions) Duration(years) weighted duration(years) Checkable deposits 14 1 0.1400 Money market deposit accounts 9 0.5 0.0450 savings deposit 16 1 0.1600 CDs Variable-Rate 12 0.6 0.0720 Less than 1 year 14 0.5 0.0700 1-2 years 10 1.8 0.1800 Greater than 2 yrs 10 2.2 0.2200 Fed Funds 14 0 0.0000 Borrowings Less than 1 year 18 0.7 0.1260 1-2 years 12 1.8 0.2160 Greater than 2 yrs 31 3.8 1.1780 Total duration of liabilities for your competitor 2.4070 Duration Gap for your firm 5.258-2.1410 3.117 Duration Gap for your competition 3.504-2.4070 1.097 If interest rate declines by 3%, expected change in the net worth Your Firm Change in net worth = change in interest rate + duration 3%-3.117 0.12% Your competition Change in net worth = change in interest rate + duration 3%-1.097 2.10% If interest rate increases by 3%, expected change in the net worth Your Firm Change in net worth = change in interest rate + duration 3%+3.117 6.12% Your competition Change in net worth = change in interest rate + duration 3%+1.097 4.10%

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