Banking in the US

All Banks in the US are Chartered National Banks: Comptroller of the Currency National Banks: Comptroller of the Currency State Banks: State Authorities State Banks: State Authorities Savings & Loans: Office of Thrift Supervision Savings & Loans: Office of Thrift Supervision Credit Union: National Credit Union Administration Credit Union: National Credit Union Administration

Federal Reserve Membership National Banks are Required to be members of the Federal Reserve System (Membership is optional for state banks) National Banks are Required to be members of the Federal Reserve System (Membership is optional for state banks) Federal Reserve members are required to purchase stock in the federal reserve system. Federal Reserve members are required to purchase stock in the federal reserve system. Federal Reserve members provide input to the election of Federal Reserve Board Members Federal Reserve members provide input to the election of Federal Reserve Board Members The Federal Reserve provides emergency loans (discount window) to all banks. The Federal Reserve provides emergency loans (discount window) to all banks. The Federal Reserve provides check clearing services The Federal Reserve provides check clearing services

Federal Deposit Insurance FDIC insured banks are charged 0-27 cents per $100 of eligible deposits. FDIC insured banks are charged 0-27 cents per $100 of eligible deposits. All deposits up to $100,000 are insured by the FDIC. All deposits up to $100,000 are insured by the FDIC. Federal reserve members are required to purchase deposit insurance. Federal reserve members are required to purchase deposit insurance.

Bank Supervision/Regulation National Banks State Banks (Fed Members) Federal ReserveFederal Reserve OCCState Authority FDICFDIC State Banks (FDIC) State Banks(Non-FDIC) FDICState Authority State Authority

Banks, like any other business, exist to earn profits Banks accept deposits and then use those funds to create loans Banks accept deposits and then use those funds to create loans Profit = Loans(rl)-Deposits(rs) Profit = Loans(rl)-Deposits(rs)

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

An Example AssetsReserves: Securities: $10M LoansConsumer:Commercial/Industrial: Real Estate: Other:Liabilities Transaction Deposits Checking:Savings: Non-Transaction Deposits: Loans: Equity: $10M

An Example Suppose that you raise $10 in initial equity to start a bank. Suppose that you raise $10 in initial equity to start a bank. You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually. You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually.

An Example Assets Reserves: $30M Securities: $10M LoansConsumer:Commercial: Real Estate: Other:Liabilities Transaction Deposits Checking (0%): $10M Savings (2%): $20M Non-Transaction Deposits: Loans: Equity: $10M

An Example Suppose that you raise $10 in initial equity to start a bank. Suppose that you raise $10 in initial equity to start a bank. You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually. You collect $10M in checking accounts and $20M in savings accounts. Checking accounts earn no interest, savings accounts pay 2% annually. The Federal Reserve requires you keep at least 5% in your vault ($1.5M) The Federal Reserve requires you keep at least 5% in your vault ($1.5M) The remainder you loan out and buy T-Bills The remainder you loan out and buy T-Bills

An Example Assets Reserves: $2M Securities (3%): $15M LoansConsumer: Commercial (7%): $20M Real Estate (8%): $3M Other:Liabilities Transaction Deposits Checking (0%): $10M Savings (2%): $20M Non-Transaction Deposits: Loans: Equity: $10M

An Example 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) - $1,690,000

An Example Suppose that $1M was withdrawn from checking accounts Suppose that $1M was withdrawn from checking accounts

An Example Assets Cash Reserves: $1M Securities (3%): $15M LoansConsumer: Commercial (7%): $20M Real Estate (8%): $3M Other:Liabilities Transaction Deposits Checking (0%): $9M Savings (2%): $20M Non-Transaction Deposits: Loans: Equity: $10M

An Example Suppose that $1M was withdrawn from checking accounts Suppose that $1M was withdrawn from checking accounts Your cash balances are now below the required 5% of deposits ($1.450,000). What do you do? Your cash balances are now below the required 5% of deposits ($1.450,000). What do you do?

An Example Suppose that $1M was withdrawn from checking accounts Suppose that $1M was withdrawn from checking accounts Your cash balances are now below the required 5% of deposits ($1,450,000). What do you do? Your cash balances are now below the required 5% of deposits ($1,450,000). What do you do? Recall a loan Recall 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 securities Sell some securities

An Example Assets Cash Reserves: $6M Securities (3%): $15M LoansConsumer: Commercial (7%): $20M Real Estate (8%): $3M Other:Liabilities Transaction Deposits Checking (0%): $9M Savings (2%): $20M Non-Transaction Deposits: Loans: $5M Equity: $10M

Equity Capital Net Worth (Equity Capital) is the difference between a bank’s assets and liabilities Net Worth (Equity Capital) is the difference between a bank’s assets and liabilities Banks are required to maintain a minimum capital adequacy (equity capital >4% of risk weighted assets) Banks are required to maintain a minimum capital adequacy (equity capital >4% of risk weighted assets)

Risk weighted assets AssetRisk Weight Cash and equivalents0 Government securities0 Interbank loans0.2 Mortgage loans0.5 Ordinary loans1.0 Standby letters of credit1.0

Risk weighted assets 4% of $24M ($960,000) is your required equity AssetRisk Weight Cash and equivalents: $6M0 * 6 = 0 Government securities: $15M0 * 5 = 0 Interbank loans0.2 Mortgage loans: $8M0.5 * 8 = $4M Ordinary loans: $20M1.0 * 20 = $20M Standby letters of credit1.0

An Example Suppose a $10M commercial loan defaults Suppose a $10M commercial loan defaults

An Example Assets Cash Reserves: $6M Securities (3%): $15M LoansConsumer: Commercial (7%): $10M Real Estate (8%): $3M Other:Liabilities Transaction Deposits Checking (0%): $9M Savings (2%): $20M Non-Transaction Deposits: Loans: $5M Equity: $0M

An Example Suppose a $10M commercial loan defaults Suppose a $10M commercial loan defaults What do you do now? What do you do now?

An Example Suppose a $10M commercial loan defaults Suppose a $10M commercial loan defaults What 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 Profitability Return on Assets = After Tax Profits/Total Assets Return on Assets = After Tax Profits/Total Assets Return to Equity = After Tax Profits/Equity Capital Return to Equity = After Tax Profits/Equity Capital ROE = ROA*(Assets/Equity Capital) ROE = ROA*(Assets/Equity Capital)

ROE vs. ROA Company A 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%

Equity Capital to Assets

Return on Assets

Return on Equity

Key issues in Banking Managing informational problems (moral hazard, adverse selection) Managing informational problems (moral hazard, adverse selection) Managing Liquidity Managing Liquidity Managing interest rate risk Managing interest rate risk

Asymmetric Information Between Banks & Borrowers Diversification Diversification Credit Scoring Credit Scoring Collateral Collateral Rationing (Credit Limits) Rationing (Credit Limits) Restrictive Covenants & Monitoring Restrictive Covenants & Monitoring Personal Relationships Personal Relationships

Asymmetric Information Between Banks & Savers FDIC and Government Regulation FDIC and Government Regulation Checkable Deposits as a commitment device Checkable Deposits as a commitment device Capital Adequacy Management Capital Adequacy Management

Managing Liquidity Banks don’t like holding cash because it pays no interest, however a bank must always be able to meet the cash requirements of its demand deposits Banks don’t like holding cash because it pays no interest, however a bank must always be able to meet the cash requirements of its demand deposits This can be handled through excess reserves, active participation in the federal funds market or through asset & liability management This can be handled through excess reserves, active participation in the federal funds market or through asset & liability management

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

Present Value Given some interest rate, the present value of $X to be paid in N years is: Given some interest rate, the present value of $X to be paid in N years is: PV = $X/(1+i)^N

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

An Example Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to pay off the loan in three annual payments. Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to pay off the loan in three annual payments. P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = ?

An Example Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to pay off the loan in three annual payments. Suppose you have a $10,000 loan with an annual interest rate equal to 5%. You agree to pay off the loan in three annual payments. P/(1.05) + P/(1.05)^2 + P/(1.05)^3 = $10,000 P = $3,671

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

An Example The loan originally had a value of $10,000 (when the market interest rate was 5%). The loan originally had a value of $10,000 (when the market interest rate was 5%). A 2% rise in the interest rate caused the value of the loan to drop to $9,632 (a 4% decrease) A 2% rise in the interest rate caused the value of the loan to drop to $9,632 (a 4% decrease)

Duration & Interest Rate Risk The duration of an asset or liability is the “average” payment date. The duration of an asset or liability is the “average” payment date. The duration of an asset or liability represents an elasticity with respect to interest rate changes The duration of an asset or liability represents an elasticity with respect to interest rate changes The duration gap is the difference between the duration of assets and liabilities The duration gap is the difference between the duration of assets and liabilities A bank with a positive (negative) duration gap is hurt by interest rate increases (decreases) A bank with a positive (negative) duration gap is hurt by interest rate increases (decreases)

Example In the previous example, our loan made three payments of $3,671. In the previous example, our loan made three payments of $3,671. $3,671/(1.05) = $3,497 $3,671/(1.05)^2 = $3,332 $3,671/(1.05)^3 = $3,171 $10,000 $10,000

Example In the previous example, our loan made three payments of $3,671. In the previous example, our loan made three payments of $3,671. $3,497/10,000 =.36 * 1 =.36 $3,332/10,000 =.34 * 2 =.68 $3,171/10,000 =.32 * 3 = %Change in value = (Duration)*(%Change in Interest Rate)

Back to our previous example Assets Cash Reserves: $6M (0) Securities (3%): $15M (5) LoansConsumer: Commercial (7%): $20M (10) Real Estate (8%): $3M (15) Other:Liabilities Transaction Deposits Checking (0%): $9M (0) Savings (2%): $20M (0) Non-Transaction Deposits: Loans: $5M (0) Equity: $10M

Duration Gap Total Assets = $44M Total Assets = $44M (6/44)* 0 = 0 (15/44)* 5 = 1.70 (20/44)* 10 = 4.55 ( 3/44)* 15 = Total Liabilities = $34M Total Liabilities = $34M (9/34)* 0 = 0 (9/34)* 0 = 0 (20/34)* 0 = 1.70 ( 5/34)* 0 =

Duration Gap Total Assets = $44M Total Assets = $44M (6/44)* 0 = 0 (15/44)* 5 = 1.70 (20/44)* 10 = 4.55 ( 3/44)* 15 = Total Liabilities = $34M Total Liabilities = $34M (9/34)* 0 = 0 (9/34)* 0 = 0 (20/34)* 0 = 1.70 ( 5/34)* 0 = Duration Gap = 7.27 – 0(34/44) = 7.27 = 7.27

Duration Gap %Change in Equity/Assets = - (dg)(%change in interest rate ) %Change in Equity/Assets = - (dg)(%change in interest rate ) dg > 0: Your equity capital falls when interest rates rise dg > 0: Your equity capital falls when interest rates rise dg < 0: Your equity capital rises when interest rates rise dg < 0: Your equity capital rises when interest rates rise

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

Duration Gap In our example, we had equity equal to (10/44) = 22% of assets and a duration gap of In our example, we had equity equal to (10/44) = 22% of assets and a duration gap of If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets. If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets.

Duration Gap In our example, we had equity equal to (10/44) = 22% of assets and a duration gap of In our example, we had equity equal to (10/44) = 22% of assets and a duration gap of If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets. If interest rates rise by 1%, our equity capital falls by 7% to 15% of assets. Recall, we are required to hold equity equal to at least 4% of assets. Therefore, if interest rates rise by more than (22-4)/7 = 2.5%, we’ll be shut down! What should we do? Recall, we are required to hold equity equal to at least 4% of assets. Therefore, if interest rates rise by more than (22-4)/7 = 2.5%, we’ll be shut down! What should we do?

Dealing With Interest Rate Risk Duration Gap Management Duration Gap Management Floating Rate Loans Floating Rate Loans Swaps Swaps Futures & Options Futures & Options

The Money Multiplier While the Fed controls M0 (Cash + Reserves), Banks largely control M1 (Cash + Demand Deposits) While the Fed controls M0 (Cash + Reserves), Banks largely control M1 (Cash + Demand Deposits) The money multiplier relates change in M1 to changes in the monetary base The money multiplier relates change in M1 to changes in the monetary base Change in M1 = mm* Change in M0 Change in M1 = mm* Change in M0 For example, if the multiplier was equal to 5, every $1 increase in M0 will increase M1 by $5. For example, if the multiplier was equal to 5, every $1 increase in M0 will increase M1 by $5.

Money Multiplier

M0 = Cash (C) + Reserves (R) M1 = Cash (C) + Demand Deposits (D) mm = M1/M0 = (C + D)/(C + R) = (C/D + 1) = (C/D + 1) (C/D + R/D) (C/D + R/D)

Money Multiplier mm = (C/D + 1) mm = (C/D + 1) (C/D + R/D) (C/D + R/D) D = $650B C = $720B R = $45B mm = 1.81