Thursday, November 13, 2008

Fractional Reserve Banking: How Required Reserves Keep the Banking System Solvent

How Required Reserves Keep the Banking System Solvent


Reserves are deposits that banks have received but not loaned out. Instead they are kept as currency in the vault of the bank (vault cash) or deposited in the bank’s accounts at the Federal Reserve System.

Banks do not earn a rate of return on reserves. Reserves can be divided into two categories: reserves that the Fed requires banks to hold (required reserves) and any additional reserves the banks choose to hold (excess reserves).

The Federal Reserve System established and controls the required reserve ratio. The required reserve ratio (rr) is the fraction or percentage of deposits that commercial banks are required to hold in the form of reserves. This money can be kept in the vault of the commercial banks (as vault cash) or deposited with the regional Federal Reserve Banks that serve the commercial banks. In the absence of a required reserve ratio, commercial banks might not hold enough reserves. This might cause consumers to lose confidence in the banking system.

To illustrate how the required reserve ratio helps maintain the solvency of the banking system, consider the following example. Suppose a new bank, the Dolphin Bank, is created. Suppose the first depositor, Tracy, deposits 100 dollar bills in the Dolphin Bank and these are placed in the bank’s vault. At the end of this transaction, Tracy has a $100 deposit at the Dolphin Bank (which is a liability for the bank) and the Dolphin Bank has $100 of reserves (cash in the vault, which is an asset for the bank).
Table 3.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)

The Dolphin Bank will not earn any profit if it leaves the $100 in its vault. Banks earn profits by creating loans. Suppose the Dolphin Bank lends the $100 to Brenda. It takes all 100 dollar bills from the vault and gives them to Brenda as a loan. The Dolphin Bank now has no cash in the vault, but its loan to Brenda is an asset for the bank.

Table 4.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves 0
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 100
(owed to the bank by Brenda)


This is not a good situation, however. Suppose Tracy decides to withdraw $10 from her account. Since the bank has no reserves, it does not have any currency in the vault to give Tracy. The bank is now insolvent. A bank is insolvent if it does not have enough cash to provide to the depositors who wish to withdraw their funds. To avoid this situation, the Federal Reserve System requires banks to keep a fraction of their deposits as reserves (vault cash and deposits at the Fed). If the required reserve ratio is .10 (i.e., 10 percent), then the maximum loan the Dolphin Bank could create from a $100 deposit would be $90. Ten dollars would be required to be kept as reserves. The balance sheet of the Dolphin Bank is now illustrated in Table 5.

Table 5.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 10
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 90
(owed to the bank by Brenda)


If Tracy goes to withdraw $10 from her account, the bank will have the currency in the vault. If Tracy withdraws $10, the balance sheet of the Dolphin Bank is:

Table 6.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves 0
(cash in the bank’s vault)
Deposits $ 90
(owed to Tracy by the bank)
Loans $ 90
(owed to the bank by Brenda)



In this scenario, the bank is able to give Tracy the $10 she requests, but the bank no longer has 10% of deposits as reserves. Thus it is normal for banks to hold excess reserves.

Consider again the example of Tracy making an initial $100 deposit at the Dolphin Bank. Suppose the bank keeps $30 of this deposit as reserves and creates loans of $70. Of the $30 in reserves, $10 are required reserves (because 10 percent of $100 is $10) and the remaining $20 are excess reserves. In this case, the balance sheet of the Dolphin Bank is:

Table 7.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 30
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 70
(owed to the bank by Brenda)


Suppose Tracy now withdraws $10 from her account. The bank takes $10 of currency out of the vault and gives it to Tracy and reduces the balance in Tracy’s account to $90. The balance sheet of the Dolphin Bank is now:

Table 8.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 20
(cash in the bank’s vault)
Deposits $ 90
(owed to Tracy by the bank)
Loans $ 70
(owed to the bank by Brenda)


The bank now has $90 of deposits and $20 of reserves. Of the $20, $9 are required reserves (because 10 percent of $90 is $9) and the remaining $11 are excess reserves.

By holding excess reserves, the Dolphin Bank avoided falling short of reserves when Tracy withdrew part of her deposit.

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