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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Is Banking Becoming More Competitive?
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
The 10 largest banks in the US control around 40% of all 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)
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
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
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 (TBills)  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 (TBills)  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
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. ROAThe more leveraged a firm is, the higher the return to equity for a given ROA. However, a highly leveraged firm carries more risk!
Acme National Bank rates) to maximize profits)
Assets
Liabilities
$5,000 (Cash)
$100,000 (Checking)
$10,000 (Reserves)
$100,000 (Savings)
$50,000 (TBills)
$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
Over time, more banks move into the area….. maximizing loan rate is
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 )
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.
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 (TBills)
$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 (TBills) (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 (TBills) (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 (TBills) (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?