Commercial Bank BehaviorCommercial Bank Behavior
Is Banking Becoming More Is Banking Becoming More Competitive?Competitive?
Recent Bank Mergers1990: ABN and AMRO ($218 billion): ABN and AMRO ($218 billion)1996: Chemical Bank and Chase Manhattan ($297 billion): Chemical Bank and Chase Manhattan ($297 billion)1996: Mitsubishi Bank and Bank of Tokyo ($752 billion): Mitsubishi Bank and Bank of Tokyo ($752 billion)1997: Union Bank of Switzerland and Swiss Bank ($595 billion) : Union Bank of Switzerland and Swiss Bank ($595 billion) 1997: NationsBank and Barnett ($310 billion): NationsBank and Barnett ($310 billion)1998: Royal Bank and Bank of Montreal ($330 billion) : Royal Bank and Bank of Montreal ($330 billion) 1998: Toronto Dominion and CIBC ($320 billion) : Toronto Dominion and CIBC ($320 billion) 1998: NationsBank and BankAmerica ($570 billion): NationsBank and BankAmerica ($570 billion)1998: Banc One and First Chicago NBD ($240 billion): Banc One and First Chicago NBD ($240 billion)1998: Citicorp and Traveler’s ($700 billion): Citicorp and Traveler’s ($700 billion)2003: Bank of America and Fleet ($851billion): Bank of America and Fleet ($851billion)2003: JP Morgan and Bank One ($1trillion): JP Morgan and Bank One ($1trillion)
The last 20 years has seen considerable consolidation in the banking industry…
Assets Number of Banks
Share of Banks (%)
Share of Assets (%)
>$25M 1211 14 .4
$25-50M 1851 21.5 1.2
$50-$100M 2179 25.3 2.8
$100-$500M 2693 31.2 9.8
$500M-$1B 296 3.4 3.7
$1-$10B 314 3.6 15.9
<$10B 77 .9 66.1
Total 8621 100 100
Consolidation has created a market where a small group of large banks controls a majority of total assets
Bank Assets (Billions)
Citigroup 1,497
JP Morgan + Bank One 1,097
Bank of America + Fleet 851
Wells Fargo 349
Wachovia 341
Met Life 277
Washington Mutual 268
US Bancorp 180
ABN Amro N America 140
Bank Boston 75
Total 5,075
The 10 largest banks in the US control around 40% of all banking assets
Concentration RatiosConcentration Ratios
0
5
10
15
20
25
30
35
40
45
Banking
C(4)
C(8)
C(20)
The concentration ratio is the percentage of market share owned by the largest m firms in the industry (usually 4, 8, 20, 50)
Concentration RatiosConcentration Ratios
0
10
20
30
40
50
60
70
80
90
100
Banking Apparel Petroluem Finance Automobiles
C(4)
C(8)
C(20)
Bank Assets (Billions)
Citigroup (US) 1,497
JP Morgan + Bank One (US) 1,097
Mizuho Financial Group (Japan) 1,080
Bank of America + First Union (US) 851
UBS (Switzerland) 851
Sumitomo Mitsui (Japan) 844
DeutscheBank (Germany) 795
Mitsubishi Tokyo (Japan) 781
HSBC (UK) 759
BNP Paribas (France) 744
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…
As a competitive firm, the bank must choose prices (interest rates) to maximize profits)
As a portfolio manager, a bank must choose a portfolio composition to minimize risk
As a financial intermediary, a bank must solve the informational problems that exist between borrowers and lenders (moral hazard and adverse selection)
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)
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%)
Key Components of FICO Score
Age
Race
Employment
Income
Education
Marital Status
To estimate your FICO score, click here
Credit Score % of Population
Interest Rate*
499 and below 1 ------
500 - 549 5 9.29%
550 - 599 7 8.53%
600 - 649 11 7.71%
650 - 699 16 6.56%
700 - 749 20 6.02%
750 - 799 29 5.90%
800 - 850 11 5.90%
* Interest Rate on a $150,000 , 30 Year Fixed Rate Mortgage
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!
Assets Liabilities
$50,000 (T-Bills) - 4%
$100,000 (Savings) - 2%
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans) – 5%
$5,000 (Cash) - 0%
$10,000 (Reserves) - 0%
$300,000 (30 yr Mort.) – 7%
$100,000 (Checking) - 0%
$100,000 (1 yr. CD) - 3%
$65,000 (5 yr. CD) – 4%
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
Profits equal revenues minus costs
However, profits don’t take into account the scale of operations (How large is the bank?)
Assets Liabilities
$50,000 (T-Bills) - 4%
$100,000 (Savings) - 2%
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans) – 5%
$5,000 (Cash) - 0%
$10,000 (Reserves) - 0%
$300,000 (30 yr Mort.) – 7%
$100,000 (Checking) - 0%
$100,000 (1 yr. CD) - 3%
$65,000 (5 yr. CD) – 4%
Profit = $20,400
Total Assets = $465,000
Return on Assets (ROA) =After Tax ProfitsTotal Assets
=$20,400
$465,000= .044 (4.4%)
Return on Equity (ROE) =After Tax Profits Equity
=$20,400
$100,000= .20 (20%)
ROE vs. ROAROE vs. ROA
Company ACompany A
Assets = 100Assets = 100
Profits = 10Profits = 10
Debt = 20Debt = 20
Equity = 80_________Equity = 80_________
ROA = 10%
ROE = 12.5%
Company BCompany B
Assets = 100Assets = 100
Profits = 10Profits = 10
Debt = 80Debt = 80
Equity = 20_________Equity = 20_________
ROA = 10%
ROE = 50%
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 BankingEquity Capital to Assets in Banking
7.5
8
8.5
9
9.5
10
1998 1999 2000 2001 2002
State
National
Return on AssetsReturn on Assets
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1998 1999 2000 2001 2002
State
National
Return on EquityReturn on Equity
0
5
10
15
20
1998 1999 2000 2001 2002
State
National
Assets Liabilities
$50,000 (T-Bills)
$100,000 (Savings)
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans)
$5,000 (Cash)
$10,000 (Reserves)
$300,000 (30 yr Mort.)
$100,000 (Checking)
$100,000 (1 yr. CD)
$65,000 (5 yr. CD)
Total Assets = $465,000
A Bank also faces two constraints:
Cash + Reserves = (Reserve Requirement) (Checkable Deposits)
= (.05)($100,000) = $5,000
Equity = (.04)(Assets) = (.04)($465,000) = $18,600
Federal Reserve
Basel Accord
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
$20,000
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
Total Monthly Costs
+ $100,000.0312
Q + $100,000.0112
Q
Let Q = Total Number of Loans
$20,000Total Monthly Costs
+ $100,000.0412
Q
Cost
# of Loans
$20,000
Slope = $333.33
$21,000
3
Fixed CostsVariable Costs
=
You have estimated the demand for mortgages to be as follows:
Q = 155.0 - 624 ( r ) – 90.4 ( UR )
Interest Rate Charged
Unemployment Rate
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 )
# of Loans
Interest Rate
UR = 5%
113
6%
r =
115624
1624
Q90.4624
UR- -
(Demand)
OR
r =
155624
1624
(113)90.4624
(.05)- -
(Inverse Demand)
= .06
33.113
06.624
d
dd Q
P
P
QElasticity of Demand refers to the responsiveness of demand to price changes (here, the price is the interest rate)
Q = 155.0 - 624 ( r ) – 90.4 ( UR )
# of Loans
Interest Rate
UR = 5%
113
6%d
dd
d
dd Q
P
P
Q
PPQ
Q
P
Q
%
%
Revenue Maximization….
Total Revenues = Q($100,000)r =
Q = 155 - 624 ( r ) – 90.4 ( UR )
$100,000 155 r - 642 r2
- 90.4 (UR) r
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 …
r = 155 – 90.4(UR)
2 (624)
r = 155 – 90.4(.05)
2 (624)
If the unemployment rate is equal to 5%, the revenue maximizing loan rate is 12.05%
# of Loans
UR = 5%
75
12.05%
= .1205
= 155 - 624 ( .1205 ) – 90.4 (.05 )
175
1205.624
d
dd Q
P
P
Q
Revenues = $100,000 (75)(.1205) = $903,750
Total Revenues
Profit Maximization…
Total Revenues = Q ($100,000)
r =
155624
1624
Q90.4624
UR- -
Total Monthly Revenues
155624
1624
Q90.4624
UR- - $100,000Q
2
Q=
Total Monthly Revenues
=
$24,840 - $14,487 URQ Q- 160 2
r12
12$100,000
12$100,000
12
12 12
(Monthly)
Total Monthly Revenues
=
$2,070 - $1,207 UR Q Q- 13.32
Profit Maximization…
Quantity
$
$100,000*DemandMR
Marginal Revenue is the derivative of Total Revenue with respect to Q
Marginal Revenues =
Q- 26.6$2,070 - $1,207 UR
$20,000Total Monthly Costs
+ $100,000.0412
Q=
Profit Maximization…
Marginal Cost is the derivative of Total Cost with respect to Q
$
Quantity
Marginal Costs $333.33=
Total Costs
Profit Maximization…
Profits = Total Revenues – Total Costs
UR = .05
Q = 63
Maximization Condition Marginal Revenues = Marginal Costs
$333.33=
r =
155624
1624
Q90.4624
UR- - = .1412 (14. 12%)
Solving for Q
Q- 26.6$2,070 - $1,207 UR
Quantity
$
$100,000*Demand
MC
MR
63
14.1%
Profits = Total Revenues – Total Costs
$20,000Total Monthly Costs
+ $100,000.0412
63=- = $41,000
Total Monthly Revenues = $100,000(63)(.1412)/12 = $74,130
$33,130Profits =
Annual Profit = $397,560
Over time, more banks move into the area…..
dd
d
Q P
P Q
Elasticity of Demand refers to the responsiveness of demand to price changes – as number of banks increases, demand becomes more elastic
Q = 155 - 624 ( r ) – 90.4 ( UR )
Q
Interest Rate
This number gets bigger!
More elastic
Less elastic
dd
d
Q P
P Q
Q = 155 - 624 ( r ) – 90.4 ( UR )
Q
Interest Rate
This number gets bigger!
Demand
MC
MR
As Demand Becomes more elastic…
The Spread between price (interest rate) and costs decreases
Quantity increases
Profits decrease
Q
r
As long as there are profits to be made, more banks enter the area. Eventually, price = marginal costs and profits drop to zero.
Banking SpreadsBanking Spreads
0
2
4
6
8
10
12
14
Jan
-85
Jan
-86
Jan
-87
Jan
-88
Jan
-89
Jan
-90
Jan
-91
Jan
-92
Jan
-93
Jan
-94
Jan
-95
Jan
-96
Jan
-97
Jan
-98
Jan
-99
Jan
-00
Jan
-01
Jan
-02
Jan
-03
Jan
-04
Prime
Fed Funds
Spread
Banking SpreadsBanking Spreads
As a portfolio manager, a bank must choose a portfolio composition to minimize risk
Assets Liabilities
$50,000 (T-Bills)
$100,000 (Savings)
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans)
$5,000 (Cash)
$10,000 (Reserves)
$300,000 (30 yr Mort.)
$100,000 (Checking)
$100,000 (1 yr. CD)
$65,000 (5 yr. CD)
= 21.5% of Assets
Suppose that the yield curve shifts up by 100 basis points:
Assets Liabilities
$50,000 (T-Bills) (1)
$100,000 (Savings) (0)
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans) (3)
$5,000 (Cash) (0)
$10,000 (Reserves) (0)
$300,000 (30 yr Mort.) (15)
$100,000 (Checking) (0)
$100,000 (1 yr. CD) (1)
$65,000 (5 yr. CD) (5)
= 21.5% of Assets
Durations are indicated in parentheses
Duration (Assets) =
Duration (Liabilities) =
$50,000$465,000 1 +
$100,000$465,000 3 +
$300,000$465,000 15 = 10.4
$100,000$365,000 1 +
$65,000$365,000 5 = 1.16
Assets Liabilities
$50,000 (T-Bills) (1)
$100,000 (Savings) (0)
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans) (3)
$5,000 (Cash) (0)
$10,000 (Reserves) (0)
$300,000 (30 yr Mort.) (15)
$100,000 (Checking) (0)
$100,000 (1 yr. CD) (1)
$65,000 (5 yr. CD) (5)
= 21.5% of Assets
Duration Gap = Duration (Assets) – Duration (Liabilities)Liabilities
Assets
= 10.4 – 1.16 $365,000
$465,000= 9.5
Assets Liabilities
$50,000 (T-Bills) (1)
$100,000 (Savings) (0)
Assets – Liabilities = $100,000 (Equity)
Acme National Bank
$100,000(5 yr. Loans) (3)
$5,000 (Cash) (0)
$10,000 (Reserves) (0)
$300,000 (30 yr Mort.) (15)
$100,000 (Checking) (0)
$100,000 (1 yr. CD) (1)
$65,000 (5 yr. CD) (5)
= 21.5% of Assets
Duration Gap = 9.5
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?