CONCEPTS IN THIS CASE interest-rate risk duration gap analysis income gap analys

Question

CONCEPTS IN THIS CASE

interest-rate risk
duration gap analysis
income gap analysis
minimizing risk of market value
interest-rate sensitive assets and liabilities

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.

6.What is the average duration for

a.Assets for your firm?

b.Assets for your competition?

c.Liabilities for your firm?

d.Liabilities for your competition?

7. 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

6.

a. Average duration of assets of the firm is calculated by taking the weighted average of duration of each of the items within the "assets" section

Average duration of assets = ( Amount in reserves and cash * Duration of reserves and cash + Securities less than 1 year * Duration of securities less than 1 year + Securities between 1 and 3 years * Duration of securities between 1 and 3 years + Securities greater than 3 years * Duration of securities greater than 3 year + Variable rate residential mortgages * Duration of variable rate residential mortgages + Fixed rate residential mortgages * Duration of fixed rate residential mortgages + Commercial loans loans less than 1 year * Duration of commercial loans less than 1 year + Commercial loans 1-2 years * Duration of commercial loans 1-2 years + Commercial loans greater than 2 years * Duration of commercial loans greater than 2 years + Physical capital * Duration of physical capital ) / Total assets = ( 3* 0 + 4*0.6 + 3*1.6 + 7*5 + 9*0.4 + 15*5.5 + 13*0.9 + 31*1.8 + 55*6 + 10*0) / (3+4+3+7+9+15+13+31+55+10) = (0+2.4+4.8+35+3.6+82.5+11.7+55.8+330+0)/150 = 3.51 years

b) Average Duration of assets of the competition =( 4*0 + 5*0.3 + 7* 1.2 + 9*4 + 21*0.9 + 17*4.4 + 30*0.6 + 22*1.4 + 30 * 5.4 + 25*0 ) / ( 4+5+7+9+21+17+30+22+30+25) = (0+1.5+8.4+36+18.9+74.8+18+30.8+162+0)/ 170 = 2.061 years

c) Average duration of liabilities of the firm =( Checkable deposits * Duration of checkable deposits + Money market deposit * Duration of money market deposits + Savings deposit * Duration of savings deposit + Variable rate CDs * Duration of variable rate CDs + less than 1 year CDs * Duration of less than 1 year CDs + 1-2 yrs CDs * Duration of 1-2 years CDs + More than 2 years CDs * Duration of more than 2 year CDs + Fed funds * duration of Fed funds + Less than 1 year borrowings * Duration of less than 1 year borrowings + 1-2 year borrowings * Duration of 1-2 years borrowings + Greater than 2 year borrowings * Duration of greater than 2 year borrowings ) / Total liabilities = (10*1 + 5*0.6+12*1+6*0.4+19*0.3+8*1.1 + 15*2.9 + 10*0 + 12*0.4 + 9*1.2+39*2.9)/(10+5+12+6+19+8+15+10+12+9+39) = (10+3+12+2.4+5.7+8.8+43.5+0+4.8+10.8+113.1)/145 = 214.1/145 = 1.48 years

d) Average duration of liabilities of the competition = (14*1+9*0.5+16*1+12*0.6+14*0.5+10*1.8+10*2.2+14*0+18*0.7+12*1.8+31*3.8)/(14+9+16+12+14+10+10+14+18+12+31) = (14+4.5+16+7.2+7+18+22+0+12.6+21.6+117.8) / 160 = 240.7/160 = 1.50 years

7.

a. Duration gap of the firm = Duration of assets - Duration of liabilities = 3.51 - 1.48 = 1.53 years

b. Duration gap of the competition = Duration of assets of competition - Duration of liabilities of competition = 2.061 - 1.50 = 0.56 years

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