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Commercial Bank Behavior. Is Banking Becoming More Competitive?. Recent Bank Mergers. 1990 : ABN and AMRO ($218 billion) 1996 : Chemical Bank and Chase Manhattan ($297 billion) 1996 : Mitsubishi Bank and Bank of Tokyo ($752 billion)

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Commercial bank behavior

Commercial Bank Behavior

Is Banking Becoming More Competitive?


Recent bank mergers
Recent Bank Mergers

1990: ABN and AMRO ($218 billion)

1996: Chemical Bank and Chase Manhattan ($297 billion)

1996: Mitsubishi Bank and Bank of Tokyo ($752 billion)

1997: Union Bank of Switzerland and Swiss Bank ($595 billion)

1997: NationsBank and Barnett ($310 billion)

1998: Royal Bank and Bank of Montreal ($330 billion)

1998: Toronto Dominion and CIBC ($320 billion)

1998: NationsBank and BankAmerica ($570 billion)

1998: Banc One and First Chicago NBD ($240 billion)

1998: Citicorp and Traveler’s ($700 billion)

2003: Bank of America and Fleet ($851billion)

2003: JP Morgan and Bank One ($1trillion)

The last 20 years has seen considerable consolidation in the banking industry…


Consolidation has created a market where a small group of large banks controls a majority of total assets



Concentration ratios
Concentration Ratios banking assets

The concentration ratio is the percentage of market share owned by the largest m firms in the industry (usually 4, 8, 20, 50)


Concentration ratios1
Concentration Ratios banking assets


However while the US is the world’s largest economy, only three of the ten largest banks in the world are American.


The banker’s optimization problem has three dimensions… three of the ten largest banks in the world are American.

As a financial intermediary, a bank must solve the informational problems that exist between borrowers and lenders (moral hazard and adverse selection)

As a portfolio manager, a bank must choose a portfolio composition to minimize risk

As a competitive firm, the bank must choose prices (interest rates) to maximize profits)


As a financial intermediary, a bank must solve the informational problems that exist between borrowers and lenders (moral hazard and adverse selection)

Most of the informational problems that exist between the bank and potential depositors have been solved through regulation and insurance (FDIC), but the bank must still deal with the moral hazard and adverse selection problems associated with its loan customers

  • Diversification

  • Loan Covenants

  • Credit Rationing (Credit Limits)

  • Credit Scoring


Credit scoring is an attempt to estimate loan default rates based on observable characteristics. The most common credit score was developed by Fair/Isaac Co. and is known as your FICO number (300 – 850)

Key Components of FICO Score

These are NOT in a FICO Score

  • How you pay your bills (35%)

  • Amount of Debt/Amount of Available Credit (30%)

  • Length of Credit History (15%)

  • Mix of Credit (Types of Loans) (10%)

  • Applications for new credit (10%)

  • Age

  • Race

  • Employment

  • Income

  • Education

  • Marital Status

To estimate your FICO score, click here


* Interest Rate on a $150,000 , 30 Year Fixed Rate Mortgage based on observable characteristics. The most common credit score was developed by Fair/Isaac Co. and is known as your FICO number (300 – 850)


As a competitive firm, the bank must choose prices (interest rates) to maximize profits)

A bank makes its profits from the spread between the interest rate it charges on loans and the interest rate it pays on deposits

(Interest rate on loans) (Quantity of loans)

– (Quantity of Deposits) (Interest paid on deposits)

Profits

Note: This is ignoring income from fees!


Acme National Bank rates) to maximize profits)

Assets

Liabilities

$5,000 (Cash) - 0%

$100,000 (Checking) - 0%

Profits equal revenues minus costs

$10,000 (Reserves) - 0%

$100,000 (Savings) - 2%

$50,000 (T-Bills) - 4%

$100,000 (1 yr. CD) - 3%

$100,000(5 yr. Loans) – 5%

$65,000 (5 yr. CD) – 4%

$300,000 (30 yr Mort.) – 7%

Assets – Liabilities = $100,000 (Equity)

Profit = .04 ($50,000) + .05 ($100,000) + .07($300,000) = $28,000

- .02($100,000) + .03($100,000) + .04 ($65,000) = $ 7,600

$20,400

However, profits don’t take into account the scale of operations (How large is the bank?)


Acme National Bank rates) to maximize profits)

Assets

Liabilities

$5,000 (Cash) - 0%

$100,000 (Checking) - 0%

$10,000 (Reserves) - 0%

$100,000 (Savings) - 2%

Profit =

$20,400

$50,000 (T-Bills) - 4%

$100,000 (1 yr. CD) - 3%

$100,000(5 yr. Loans) – 5%

$65,000 (5 yr. CD) – 4%

$300,000 (30 yr Mort.) – 7%

Total Assets = $465,000

Assets – Liabilities = $100,000 (Equity)

After Tax Profits

$20,400

Return on Assets (ROA)

=

=

= .044 (4.4%)

Total Assets

$465,000

After Tax Profits

$20,400

Return on Equity (ROE)

=

=

= .20 (20%)

Equity

$100,000


Roe vs roa

Company A rates) to maximize profits)

Assets = 100

Profits = 10

Debt = 20

Equity = 80_________

ROA = 10%

ROE = 12.5%

Company B

Assets = 100

Profits = 10

Debt = 80

Equity = 20_________

ROA = 10%

ROE = 50%

ROE vs. ROA

The more leveraged a firm is, the higher the return to equity for a given ROA. However, a highly leveraged firm carries more risk!


Equity capital to assets in banking
Equity Capital to Assets in Banking rates) to maximize profits)


Return on assets
Return on Assets rates) to maximize profits)


Return on equity
Return on Equity rates) to maximize profits)


Acme National Bank rates) to maximize profits)

Assets

Liabilities

$5,000 (Cash)

$100,000 (Checking)

$10,000 (Reserves)

$100,000 (Savings)

$50,000 (T-Bills)

$100,000 (1 yr. CD)

$100,000(5 yr. Loans)

$65,000 (5 yr. CD)

$300,000 (30 yr Mort.)

Total Assets = $465,000

Assets – Liabilities = $100,000 (Equity)

A Bank also faces two constraints:

Federal Reserve

Cash + Reserves = (Reserve Requirement) (Checkable Deposits)

= (.05)($100,000) = $5,000

Basel Accord

Equity = (.04)(Assets) = (.04)($465,000) = $18,600


Lets assume that you have the only bank in town. You offer one type of loan – a 30 year $100,000 fixed APR mortgage. You offer savings accounts that pay 3% interest per year.


You have monthly fixed costs equal to $20,000. Further, you have annual administrative costs equal to 1% of your total funds raised.

Let Q = Total Number of Loans

.03

.01

Total Monthly Costs

$20,000

+ $100,000

Q

+ $100,000

Q

12

12

Fixed Cost

Interest Cost

Administrative Costs

For example, if you want to create 3 mortgages, you will need to raise $300,000 in deposits that will earn $9,000 per year (3% of $300,000) and incur $3,000 (1% of $300,000) in administrative expenses.

Total Monthly Cost = $20,000 + $750 + $250 = $21,000


Let Q = Total Number of Loans have annual administrative costs equal to 1% of your total funds raised.

.04

Total Monthly Costs

=

$20,000

+ $100,000

Q

12

Fixed Costs

Variable Costs

Cost

Slope = $333.33

$21,000

$20,000

# of Loans

3


You have estimated the demand for mortgages to be as follows:

Q = 155.0 - 624 ( r ) – 90.4 ( UR )

Unemployment Rate

Interest Rate Charged

For example, if you set your mortgage rate at 6% (.06) and the local unemployment rate is 5% (.05), you will be able to sell 113 mortgages

Q = 155.0 - 624 (.06) – 90.4 (.05) = 113

Your total annual revenues would be $100,000 (113)(.06) = $678,000


Q = 115.0 - 624 ( r ) – 90.4 ( UR ) follows:

(Demand)

OR

Interest Rate

115

1

90.4

-

-

r =

Q

UR

(Inverse Demand)

624

624

624

6%

UR = 5%

# of Loans

113

155

1

90.4

-

-

r =

(113)

(.05)

= .06

624

624

624


Q = 155.0 - 624 ( r ) – 90.4 ( UR ) follows:

Interest Rate

6%

UR = 5%

# of Loans

113

Elasticity of Demand refers to the responsiveness of demand to price changes (here, the price is the interest rate)


Revenue Maximization…. follows:

2

Total Revenues = Q($100,000)r =

$100,000

155 r

- 642 r

- 90.4(UR) r

Q = 155 - 624 ( r ) – 90.4 ( UR )

Maximizing Total Revenues involves taking the derivative with respect to the interest rate and setting it equal to zero…

155

- 2 (624) r

- 90.4(UR)

= 0

Solving for r …

155 – 90.4(UR)

r =

2(624)


If the unemployment rate is equal to 5%, the revenue maximizing loan rate is 12.05%

155 – 90.4(.05)

= .1205

r =

2(624)

Revenues = $100,000 (75)(.1205) = $903,750

12.05%

Total Revenues

UR = 5%

# of Loans

75

= 155 - 624 ( .1205 ) – 90.4 (.05 )


Profit Maximization… maximizing loan rate is

r

Total Revenues = Q ($100,000)

12

(Monthly)

155

1

90.4

-

-

r =

Q

UR

624

624

624

2

Total Monthly Revenues

$100,000

$100,000

1

$100,000

90.4

155

-

-

=

Q

Q

UR

Q

12

12

624

12

624

624

2

Total Monthly Revenues

$24,840 - $14,487 UR

160

-

=

Q

Q

12

12


Profit Maximization… maximizing loan rate is

2

Total Monthly Revenues

-

=

$2,070 - $1,207 UR

Q

13.3

Q

Marginal Revenue is the derivative of Total Revenue with respect to Q

$

Marginal Revenues

-

=

$2,070 - $1,207 UR

26.6

Q

$100,000*Demand

MR

Quantity


Profit Maximization… maximizing loan rate is

.04

Total Monthly Costs

=

$20,000

+ $100,000

Q

12

Marginal Cost is the derivative of Total Cost with respect to Q

$

Total Costs

Marginal Costs

=

$333.33

Quantity


Profit Maximization… maximizing loan rate is

Profits = Total Revenues – Total Costs

Maximization Condition

Marginal Revenues = Marginal Costs

-

$2,070 - $1,207 UR

26.6

Q

=

$333.33

UR = .05

Solving for Q

Q

=

63

155

1

90.4

-

-

r =

Q

UR

= .1412 (14. 12%)

624

624

624


Profits = Total Revenues – Total Costs maximizing loan rate is

Total Monthly Revenues = $100,000(63)(.1412)/12 = $74,130

.04

Total Monthly Costs

=

$20,000

+ $100,000

63

= $41,000

$

-

12

Profits =

$33,130

Annual Profit = $397,560

14.1%

MC

$100,000*Demand

MR

Quantity

63



Elasticity of Demand refers to the responsiveness of demand to price changes – as number of banks increases, demand becomes more elastic

Interest Rate

More elastic

Less elastic

Q

This number gets bigger!

Q = 155 - 624 ( r ) – 90.4 ( UR )


  • As Demand Becomes more elastic… to price changes – as number of banks increases, demand becomes more elastic

    • The Spread between price (interest rate) and costs decreases

    • Quantity increases

    • Profits decrease

Interest Rate

r

MC

Demand

MR

Q

Q

This number gets bigger!

Q = 155 - 624 ( r ) – 90.4 ( UR )


As long as there are profits to be made, more banks enter the area. Eventually, price = marginal costs and profits drop to zero.


Banking spreads
Banking Spreads the area. Eventually, price = marginal costs and profits drop to zero.


Banking spreads1
Banking Spreads the area. Eventually, price = marginal costs and profits drop to zero.


As a portfolio manager, a bank must choose a portfolio composition to minimize risk

Acme National Bank

Assets

Liabilities

$5,000 (Cash)

$100,000 (Checking)

$10,000 (Reserves)

$100,000 (Savings)

$50,000 (T-Bills)

$100,000 (1 yr. CD)

$100,000(5 yr. Loans)

$65,000 (5 yr. CD)

$300,000 (30 yr Mort.)

Assets – Liabilities = $100,000 (Equity)

= 21.5% of Assets

Suppose that the yield curve shifts up by 100 basis points:


Acme National Bank composition to minimize risk

Durations are indicated in parentheses

Assets

Liabilities

$5,000 (Cash) (0)

$100,000 (Checking) (0)

$10,000 (Reserves) (0)

$100,000 (Savings) (0)

$50,000 (T-Bills) (1)

$100,000 (1 yr. CD) (1)

$100,000(5 yr. Loans) (3)

$65,000 (5 yr. CD) (5)

$300,000 (30 yr Mort.) (15)

Assets – Liabilities = $100,000 (Equity)

= 21.5% of Assets

$50,000

$100,000

$300,000

Duration (Assets) =

1 +

3 +

15 =10.4

$465,000

$465,000

$465,000

$100,000

$65,000

Duration (Liabilities) =

1 +

5 = 1.16

$365,000

$365,000


Acme National Bank composition to minimize risk

Assets

Liabilities

$5,000 (Cash) (0)

$100,000 (Checking) (0)

$10,000 (Reserves) (0)

$100,000 (Savings) (0)

$50,000 (T-Bills) (1)

$100,000 (1 yr. CD) (1)

$100,000(5 yr. Loans) (3)

$65,000 (5 yr. CD) (5)

$300,000 (30 yr Mort.) (15)

Assets – Liabilities = $100,000 (Equity)

= 21.5% of Assets

Liabilities

Duration Gap = Duration (Assets) – Duration (Liabilities)

Assets

$365,000

= 10.4 – 1.16

= 9.5

$465,000


Acme National Bank composition to minimize risk

Assets

Liabilities

$5,000 (Cash) (0)

$100,000 (Checking) (0)

$10,000 (Reserves) (0)

$100,000 (Savings) (0)

$50,000 (T-Bills) (1)

$100,000 (1 yr. CD) (1)

$100,000(5 yr. Loans) (3)

$65,000 (5 yr. CD) (5)

$300,000 (30 yr Mort.) (15)

Duration Gap = 9.5

Assets – Liabilities = $100,000 (Equity)

= 21.5% of Assets

For every 100 basis point increase in the yield curve, this bank’s equity (as a percentage of assets) drops by 9.5%

How much of an interest rate change can this bank withstand before it inadequately capitalized?


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