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Banking in the USBanking in the US

All Banks in the US are CharteredAll Banks in the US are Chartered

National Banks: Comptroller of the National Banks: Comptroller of the CurrencyCurrency

State Banks: State AuthoritiesState Banks: State AuthoritiesSavings & Loans: Office of Thrift Savings & Loans: Office of Thrift

SupervisionSupervisionCredit Union: National Credit Union Credit Union: National Credit Union

AdministrationAdministration

Federal Reserve MembershipFederal Reserve Membership

National Banks are Required to be members National Banks are Required to be members of the Federal Reserve System (Membership of the Federal Reserve System (Membership is optional for state banks)is optional for state banks) Federal Reserve members are required to Federal Reserve members are required to

purchase stock in the federal reserve system.purchase stock in the federal reserve system. Federal Reserve members provide input to the Federal Reserve members provide input to the

election of Federal Reserve Board Memberselection of Federal Reserve Board Members The Federal Reserve provides emergency loans The Federal Reserve provides emergency loans

(discount window) to all banks.(discount window) to all banks. The Federal Reserve provides check clearing The Federal Reserve provides check clearing

servicesservices

Federal Deposit InsuranceFederal Deposit Insurance

FDIC insured banks are charged 0-27 FDIC insured banks are charged 0-27 cents per $100 of eligible deposits. cents per $100 of eligible deposits.

All deposits up to $100,000 are insured by All deposits up to $100,000 are insured by the FDIC. the FDIC.

Federal reserve members are required to Federal reserve members are required to purchase deposit insurance. purchase deposit insurance.

Bank Supervision/RegulationBank Supervision/Regulation

National BanksNational Banks State Banks (Fed Members) State Banks (Fed Members)

Federal ReserveFederal Reserve Federal Reserve Federal Reserve

OCCOCC State AuthorityState Authority

FDICFDIC FDICFDIC

State Banks (FDIC)State Banks (FDIC) State Banks(Non-FDIC)State Banks(Non-FDIC)

FDICFDIC State AuthorityState Authority

State AuthorityState Authority

Banks, like any other business, exist to earn profitsBanks, like any other business, exist to earn profits

Banks accept deposits and then use those Banks accept deposits and then use those funds to create loansfunds to create loans

Profit = Loans(rl)-Deposits(rs)Profit = Loans(rl)-Deposits(rs)

An ExampleAn Example

Suppose that you raise $10 in initial equity to start a Suppose that you raise $10 in initial equity to start a bank. You use this initial equity to by T-Bills.bank. You use this initial equity to by T-Bills.


AssetsAssetsReserves: Reserves:

Securities: Securities: $10M$10M

Loans Loans

Consumer:Consumer:

Commercial/Industrial:Commercial/Industrial:

Real Estate:Real Estate:

Other:Other:

LiabilitiesLiabilitiesTransaction DepositsTransaction Deposits

Checking:Checking:

Savings: Savings:

Non-Transaction Deposits: Non-Transaction Deposits:

Loans:Loans:

Equity: Equity: $10M$10M


Suppose that you raise $10 in initial equity to start a Suppose that you raise $10 in initial equity to start a bank. bank.

You collect $10M in checking accounts and $20M in You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually. savings accounts pay 2% annually.


AssetsAssetsReserves: Reserves: $30M$30M

Securities: Securities: $10M$10M

Loans Loans

Consumer:Consumer:

Commercial:Commercial:

Real Estate:Real Estate:

Other:Other:


Checking (0%): Checking (0%): $10M$10M

Savings (2%): Savings (2%): $20M$20M


Loans:Loans:



Suppose that you raise $10 in initial equity to start a Suppose that you raise $10 in initial equity to start a bank. bank.

You collect $10M in checking accounts and $20M in You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually. savings accounts pay 2% annually.

The Federal Reserve requires you keep at least 5% in The Federal Reserve requires you keep at least 5% in your vault ($1.5M)your vault ($1.5M)

The remainder you loan out and buy T-BillsThe remainder you loan out and buy T-Bills


AssetsAssetsReserves: Reserves: $2M$2M

Securities (3%): Securities (3%): $15M$15M

Loans Loans

Consumer:Consumer:

Commercial (7%): Commercial (7%): $20M$20M

Real Estate (8%): Real Estate (8%): $3M$3M

Other:Other:





Loans:Loans:



Your Profit after the first year will be:Your Profit after the first year will be:

(.03)$15M + (.07)$20M + (.08)$3M (Interest Income)(.03)$15M + (.07)$20M + (.08)$3M (Interest Income)- (.02) $20M (Interest Cost)(.02) $20M (Interest Cost)- $1,690,000$1,690,000


Suppose that $1M was withdrawn from checking Suppose that $1M was withdrawn from checking accountsaccounts


AssetsAssetsCash Reserves: Cash Reserves: $1M$1M


Loans Loans

Consumer:Consumer:



Other:Other:





Loans:Loans:




Your cash balances are now below the required Your cash balances are now below the required 5% of deposits ($1.450,000). What do you do?5% of deposits ($1.450,000). What do you do?



Your cash balances are now below the required Your cash balances are now below the required 5% of deposits ($1,450,000). What do you do?5% of deposits ($1,450,000). What do you do? Recall a loanRecall a loan Borrow from another bank (federal funds market)Borrow from another bank (federal funds market) Borrow from the federal reserve (discount window)Borrow from the federal reserve (discount window) Sell some securitiesSell some securities




Loans Loans

Consumer:Consumer:



Other:Other:





Loans: Loans: $5M$5M


Equity CapitalEquity Capital

Net Worth (Equity Capital) is the difference Net Worth (Equity Capital) is the difference between a bank’s assets and liabilities between a bank’s assets and liabilities

Banks are required to maintain a minimum Banks are required to maintain a minimum capital adequacy (equity capital >4% of capital adequacy (equity capital >4% of risk weighted assets)risk weighted assets)

Risk weighted assetsRisk weighted assets

Asset Risk Weight

Cash and equivalents 0

Government securities 0

Interbank loans 0.2

Mortgage loans 0.5

Ordinary loans 1.0

Standby letters of credit 1.0

Risk weighted assetsRisk weighted assets

4% of $24M ($960,000) is your required equity4% of $24M ($960,000) is your required equity

Asset Risk Weight

Cash and equivalents: $6M 0 * 6 = 0

Government securities: $15M 0 * 5 = 0

Interbank loans 0.2

Mortgage loans: $8M 0.5 * 8 = $4M

Ordinary loans: $20M 1.0 * 20 = $20M

Standby letters of credit 1.0


Suppose a $10M commercial loan defaultsSuppose a $10M commercial loan defaults




Loans Loans

Consumer:Consumer:



Other:Other:





Loans: Loans: $5M$5M



Suppose a $10M commercial loan defaultsSuppose a $10M commercial loan defaultsWhat do you do now?What do you do now?


Suppose a $10M commercial loan defaultsSuppose a $10M commercial loan defaultsWhat do you do now?What do you do now?

You need to raise equity or shut down!You need to raise equity or shut down!

Bank ProfitabilityBank Profitability

Return on Assets = After Tax Profits/Total Return on Assets = After Tax Profits/Total AssetsAssets

Return to Equity = After Tax Profits/Equity Return to Equity = After Tax Profits/Equity CapitalCapital

ROE = ROA*(Assets/Equity Capital)ROE = ROA*(Assets/Equity Capital)

ROE vs. ROAROE vs. ROA

Company ACompany A

Assets = 100Assets = 100

Profits = 10Profits = 10

Debt = 20Debt = 20

Equity = 80_________Equity = 80_________

ROA = 10%ROA = 10%

ROE = 12.5%ROE = 12.5%

Company BCompany B

Assets = 100Assets = 100

Profits = 10Profits = 10

Debt = 80Debt = 80

Equity = 20_________Equity = 20_________

ROA = 10%ROA = 10%

ROE = 50%ROE = 50%

Equity Capital to AssetsEquity Capital to Assets

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

Key issues in BankingKey issues in Banking

Managing informational problems (moral Managing informational problems (moral hazard, adverse selection)hazard, adverse selection)

Managing LiquidityManaging LiquidityManaging interest rate riskManaging interest rate risk

Asymmetric Information Between Banks & Asymmetric Information Between Banks & BorrowersBorrowers

DiversificationDiversificationCredit ScoringCredit ScoringCollateralCollateralRationing (Credit Limits)Rationing (Credit Limits)Restrictive Covenants & MonitoringRestrictive Covenants & MonitoringPersonal RelationshipsPersonal Relationships

Asymmetric Information Between Banks & Asymmetric Information Between Banks & SaversSavers

FDIC and Government RegulationFDIC and Government RegulationCheckable Deposits as a commitment Checkable Deposits as a commitment

devicedeviceCapital Adequacy ManagementCapital Adequacy Management

Managing LiquidityManaging Liquidity

Banks don’t like holding cash because it Banks don’t like holding cash because it pays no interest, however a bank must pays no interest, however a bank must always be able to meet the cash always be able to meet the cash requirements of its demand depositsrequirements of its demand deposits

This can be handled through excess This can be handled through excess reserves, active participation in the federal reserves, active participation in the federal funds market or through asset & liability funds market or through asset & liability managementmanagement

Interest Rate RiskInterest Rate Risk

A bank’s assets and liabilities are A bank’s assets and liabilities are comprised of payments made or received comprised of payments made or received over time. Therefore, their value depends over time. Therefore, their value depends on the interest rate.on the interest rate.

Present ValuePresent Value

Given some interest rate, the present Given some interest rate, the present value of $X to be paid in N years is:value of $X to be paid in N years is:

PV = $X/(1+i)^NPV = $X/(1+i)^N


Suppose you have a $10,000 loan with an Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to annual interest rate equal to 5%. You agree to pay off the loan in three annual payments.pay off the loan in three annual payments.



P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = ?P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = ?



P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = $10,000P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = $10,000

P = $3,671P = $3,671


Suppose you have a $10,000 loan with an Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to annual interest rate equal to 5%. You agree to pay off the loan in three annual payments of pay off the loan in three annual payments of $3,671. If the current rate of interest is 7%, what $3,671. If the current rate of interest is 7%, what is the present value of this payment stream?is the present value of this payment stream?

PV = $3,671/(1.07) + $3,671/(1.07)^2 + $3,671/(1.07)^3PV = $3,671/(1.07) + $3,671/(1.07)^2 + $3,671/(1.07)^3

= $3,430 + $3,206 + $2,996 = $9,632 = $3,430 + $3,206 + $2,996 = $9,632


The loan originally had a value of $10,000 The loan originally had a value of $10,000 (when the market interest rate was 5%).(when the market interest rate was 5%).

A 2% rise in the interest rate caused the A 2% rise in the interest rate caused the value of the loan to drop to $9,632 (a 4% value of the loan to drop to $9,632 (a 4% decrease)decrease)

Duration & Interest Rate RiskDuration & Interest Rate Risk

The duration of an asset or liability is the The duration of an asset or liability is the “average” payment date.“average” payment date.

The duration of an asset or liability represents an The duration of an asset or liability represents an elasticity with respect to interest rate changeselasticity with respect to interest rate changes

The duration gap is the difference between the The duration gap is the difference between the duration of assets and liabilitiesduration of assets and liabilities

A bank with a positive (negative) duration gap is A bank with a positive (negative) duration gap is hurt by interest rate increases (decreases)hurt by interest rate increases (decreases)

ExampleExample

In the previous example, our loan made In the previous example, our loan made three payments of three payments of $3,671. $3,671.

$3,671/(1.05) = $3,497$3,671/(1.05) = $3,497

$3,671/(1.05)^2 = $3,332$3,671/(1.05)^2 = $3,332

$3,671/(1.05)^3 = $3,171$3,671/(1.05)^3 = $3,171

$10,000$10,000

ExampleExample

In the previous example, our loan made three In the previous example, our loan made three payments of payments of $3,671. $3,671.

$3,497/10,000 = .36 * 1 = .36$3,497/10,000 = .36 * 1 = .36

$3,332/10,000 = .34 * 2 = .68$3,332/10,000 = .34 * 2 = .68

$3,171/10,000 = .32 * 3 = .96$3,171/10,000 = .32 * 3 = .96

2.002.00

%Change in value = (Duration)*(%Change in Interest Rate)%Change in value = (Duration)*(%Change in Interest Rate)

Back to our previous exampleBack to our previous example

AssetsAssetsCash Reserves: Cash Reserves: $6M $6M (0)(0)

Securities (3%): Securities (3%): $15M $15M (5)(5)

Loans Loans

Consumer:Consumer:

Commercial (7%): Commercial (7%): $20M $20M (10)(10)

Real Estate (8%): Real Estate (8%): $3M $3M (15)(15)

Other:Other:


Checking (0%): Checking (0%): $9M $9M (0)(0)

Savings (2%): Savings (2%): $20M $20M (0)(0)


Loans: Loans: $5M$5M (0)(0)


Duration GapDuration Gap

Total Assets = $44MTotal Assets = $44M

(6/44)* 0 = 0(6/44)* 0 = 0

(15/44)* 5 = 1.70(15/44)* 5 = 1.70

(20/44)* 10 = 4.55(20/44)* 10 = 4.55

( 3/44)* 15 = 1.02( 3/44)* 15 = 1.02

7.277.27

Total Liabilities = $34MTotal Liabilities = $34M

(9/34)* 0 = 0(9/34)* 0 = 0

(20/34)* 0 = 1.70(20/34)* 0 = 1.70

( 5/34)* 0 = 2.04( 5/34)* 0 = 2.04

00

Duration GapDuration Gap Total Assets = $44MTotal Assets = $44M

(6/44)* 0 = 0(6/44)* 0 = 0(15/44)* 5 = 1.70(15/44)* 5 = 1.70(20/44)* 10 = 4.55(20/44)* 10 = 4.55( 3/44)* 15 = 1.02( 3/44)* 15 = 1.02

7.277.27

Total Liabilities = Total Liabilities = $34M$34M

(9/34)* 0 = 0(9/34)* 0 = 0(20/34)* 0 = 1.70(20/34)* 0 = 1.70( 5/34)* 0 = 2.04( 5/34)* 0 = 2.04

00

Duration Gap = 7.27 – Duration Gap = 7.27 – 0(34/44)0(34/44)

= 7.27= 7.27

Duration Gap Duration Gap

%Change in Equity/Assets = - (dg)(%change in interest %Change in Equity/Assets = - (dg)(%change in interest

raterate)) dg > 0: Your equity capital falls when interest rates dg > 0: Your equity capital falls when interest rates

riserise dg < 0: Your equity capital rises when interest rates dg < 0: Your equity capital rises when interest rates

riserise


In our example, we had equity equal to (10/44) = In our example, we had equity equal to (10/44) = 22% of assets and a duration gap of 7.27.22% of assets and a duration gap of 7.27.



If interest rates rise by 1%, our equity capital If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets.falls by 7% to 15% of assets.



If interest rates rise by 1%, our equity capital If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets.falls by 7% to 15% of assets.

Recall, we are required to hold equity equal to at Recall, we are required to hold equity equal to at least 4% of assets. Therefore, if interest rates least 4% of assets. Therefore, if interest rates rise by more than (22-4)/7 = 2.5%, we’ll be shut rise by more than (22-4)/7 = 2.5%, we’ll be shut down! What should we do?down! What should we do?

Dealing With Interest Rate RiskDealing With Interest Rate Risk

Duration Gap ManagementDuration Gap ManagementFloating Rate LoansFloating Rate LoansSwapsSwapsFutures & OptionsFutures & Options

The Money MultiplierThe Money Multiplier

While the Fed controls M0 (Cash + While the Fed controls M0 (Cash + Reserves), Banks largely control M1 Reserves), Banks largely control M1 (Cash + Demand Deposits)(Cash + Demand Deposits)

The money multiplier relates change in M1 The money multiplier relates change in M1 to changes in the monetary baseto changes in the monetary base

Change in M1 = mm* Change in M0Change in M1 = mm* Change in M0For example, if the multiplier was equal to 5, every For example, if the multiplier was equal to 5, every

$1 increase in M0 will increase M1 by $5.$1 increase in M0 will increase M1 by $5.

Money MultiplierMoney Multiplier


M0 = Cash (C) + Reserves (R)M0 = Cash (C) + Reserves (R)

M1 = Cash (C) + Demand Deposits (D)M1 = Cash (C) + Demand Deposits (D)

mm = M1/M0 = (C + D)/(C + R)mm = M1/M0 = (C + D)/(C + R)

= = (C/D + 1)(C/D + 1)

(C/D + R/D)(C/D + R/D)


mm = mm = (C/D + 1)(C/D + 1) (C/D + R/D)(C/D + R/D)

D = $650BD = $650BC = $720BC = $720BR = $45BR = $45B

mm = 1.81mm = 1.81