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.

1.Using the Macaulay concept of duration, calculate the weighted duration of each asset and liability for both your firm and your competition.

The duration of each asset for

You’re firm: 0,0,10:

Your competition: 0,0,20

The duration for each liability

Your firm: 0, 0, 5

Your competition: 0, 0, 10

2.What is the duration gap for

a.Your firm?

b.Your competition?

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

1. Weighted duration of each asset for both our firm and competitive firm are

0x6/100+10x90/100+0x3/100 = 9 years

0x12/100+20x21/100+0x4/100= 4.2 years

0x9/100+5x15/100= 7.5 years

0x12/100+14x10/100=1.4 years

Net duration of our firm: 9-7.5= 1.5 years

Net duration of a competitive firm: 4.2-1.4 = 2.8 years

2. Duration gap is calculated as interest rate sensitive assets - interest rate sensitive liability

For our firm sensitive assets (variable rate loan)= 9.

For our firm sensitive Liability (variable rate deposit)= 6.

For competitive firm sensitive assets (variable rate loan)= 21.

For competitive firm sensitive Liability (variable rate deposit)= 12. So,

Duration gap of firm = 9-6 = 3.

Duration gap of competitor = 21-12 = 9.

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