Fractional-reserve banking

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Fractional-reserve banking is a banking practice in which banks are required to keep only a fraction of their deposits in reserve with the choice of lending out the remainder while maintaining the obligation to redeem all deposits upon demand. This practice is prevalent worldwide and is considered to be the customary form of banking system.^[1][2]

Contents 1 History 2 Purpose and function 3 How it works 3.1 Money creation 3.1.1 Money multiplier 3.1.1.1 Formula 3.2 Reserve requirements 3.3 Financial ratios 4 Money supplies around the world 5 Limitations for loan creation 5.1 Free banking 5.2 Government regulated systems 5.2.1 Central banks 5.2.2 Use of money multiplier 5.3 Liquidity and capital management for a bank 5.4 Example of a bank balance sheet and financial ratios 5.4.1 Other financial ratios 5.4.2 How the example bank manages its liquidity 6 Criticism 6.1 Business cycle 6.2 Risk 6.3 Effects of an increased money supply 6.4 Inadequate government regulation 7 See also 8 References 9 External links

[edit] History

^[3] At one time, people deposited gold coins and silver coins at goldsmiths, receiving in turn a note for their deposit. Once these notes became a trusted medium of exchange an early form of paper money was born, in the form of the goldsmiths' notes.

As the notes were used directly in trade, the goldsmiths noted that people would never redeem all their notes at the same time, and saw the opportunity to invest coin reserves in interest-bearing loans and bills. This left the goldsmiths with more notes on issue than reserves to pay them with. This generated income—a process that altered their role from passive guardians of bullion charging fees for safe storage, to interest-paying and earning banks. Fractional-reserve banking was born. When creditors (note holders of gold originally deposited) lost faith in the ability of the bank to redeem (pay) their notes, many would try to redeem their notes at the same time, forcing the bank to call in loans or sell bills. This was called a bank run and many early banks either went into insolvency or defaulted on their notes.

[edit] Purpose and function

The Federal Reserve gives a summary of why fractional reserve banking is used and what its effects are:

The fact that banks are required to keep on hand only a fraction of the funds deposited with them is a function of the banking business. Banks borrow funds from their depositors (those with savings) and in turn lend those funds to the banks’ borrowers (those in need of funds). Banks make money by charging borrowers more for a loan (a higher percentage interest rate) than is paid to depositors for use of their money. If banks did not lend out their available funds after meeting their reserve requirements, depositors might have to pay banks to provide safekeeping services for their money. For the economy and the banking system as a whole, the practice of keeping only a fraction of deposits on hand has an important cumulative effect. Referred to as the fractional reserve system, it permits the banking system to create "money".^[4]

[edit] How it works

A demand deposit at a bank (e.g. checking account) or banknote issued by a bank (bank-issued paper money) is essentially a loan to the bank, repayable on demand, which the bank uses to finance its investments in loans and interest bearing securities. The nature of fractional-reserve banking is that there is only a fraction of cash reserves available at the bank needed to repay all of the demand deposits and banknotes issued. The reason people deposit funds at a bank or hold banknotes issued by a bank is to store savings in the form of a demand claim on the bank. One important aspect of fractional-reserve banking is that the note holders and depositors still have a claim to repayment of their funds on demand even though the funds are already largely invested by the bank in interest bearing loans and securities.

For instance, you could ask to withdraw all of the money in your checking account at any time. If all of the depositors of a bank did that at the same time (a bank run), the bank could be in trouble, but this rarely happens.

Fractional-reserve banking works because:

1. Over any typical period of time, redemption demands are largely or wholly offset by new deposits or issues of notes. The bank thus needs only to satisfy the excess amount of redemptions.
2. Only a minority of people will actually choose to withdraw their demand deposits or present their notes for payment at any given time.
3. People usually keep their funds in the bank for a prolonged period of time.
4. There are usually enough cash reserves in the bank to handle net redemptions.

If the net redemption demands are unusually large, the bank will run low on reserves and will be forced to raise new funds from additional borrowings (e.g. by borrowing from the money market or using lines of credit held with other banks), and/or sell assets, to avoid running out of reserves and defaulting on its obligations. If creditors are afraid that the bank is running out of cash, they have an incentive to redeem their deposits as soon as possible, triggering a bank run.

[edit] Money creation

The process of fractional-reserve banking has a cumulative effect of money creation by banks^[4]. In short, there are two types of money in a fractional-reserve banking system^[5][6]:

1. central bank money (physical currency such as coins and paper money)
2. commercial bank money (money created through loans) - sometimes referred to as checkbook money^[7]

When a loan is supplied with central bank money, new commercial bank money is created. As a loan is paid back, the commercial bank money disappears from existence.

The table below displays how loans are funded and how the money supply is affected. It also shows how central bank money is used to create commercial bank money. An initial deposit of $100 of central bank money is lent out 10 times with a fractional-reserve rate of 20%. This means that of the initial $100, 20 percent of it, or $20, is set aside as reserves while the remaining 80 percent, or $80, is loaned out. The recipient of the $80 then spends that money. The receiver of that $80 then deposits it into a bank. The bank then sets aside 20 percent of that $80, or $16, as reserves and lends out the remaining $64. As the process continues, more commercial bank money is created. To simplify the table, a different bank is used for each deposit. In the real world, the money a bank lends may end up in the same bank so it then has more money to lend out.

Table:[8] Fractional-Reserve Lending Cycled 10 times with a 20 percent reserve rate (sources: The Principle of Multiple Deposit Creation[9], Federal Reserve Bank of New York[10], Bank for International Settlements[5])
individual bank	amount deposited	amount lent out	reserves
A	100	80	20
B	80	64	16
C	64	51.20	12.80
D	51.20	40.96	10.24
E	40.96	32.77	8.19
F	32.77	26.21	6.55
G	26.21	20.97	5.24
H	20.97	16.78	4.19
I	16.78	13.42	3.36
J	13.42	10.74	2.68
K	10.74
			total reserves:
			89.26
	total amount deposited:	total amount lent out:	total reserves + last amount deposited:
	457.05	357.05	100
	commercial bank money created + central bank money:	commercial bank money created:	central bank money:
	457.05	357.05	100

Although no new money was physically created in addition to the initial $100 deposit, new commercial bank money is created through loans. The 2 boxes marked in red show the location of the original $100 deposit throughout the entire process. The total reserves plus the last deposit (or last loan, whichever is last) will always equal the original amount, which in this case is $100. As this process continues, more commercial bank money is created. The amounts in each step decrease towards a limit. If a graph is made showing the accumulation of deposits, one can see that the graph is curved and approaches a limit. This limit is the maximum amount of money that can be created with a given reserve rate. When the reserve rate is 20%, as in the example above, the maximum amount of total deposits that can be created is $500 and the maximum amount of commercial bank money that can be created is $400.

For an individual bank, the deposit is considered a liability whereas the loan it gives out and the reserves are considered assets. The deposit will always be equal to the loan plus the reserve, since the loan and reserve are created from the deposit. This is the basis for a bank's balance sheet.

The creation and destruction of commercial bank money occurs through this process. Whether it is created or destroyed depends on what direction the process moves. When loans are given out, the process moves from the top down and money is created. When loans are paid back, the process moves from the bottom to the top and commercial bank money is canceled out, effectively erasing it from existence.

The reserves are not allowed to be used to fund any more loans. The reserves cannot be spent until the loan they back up is paid back. If someone defaults on a loan, the reserves have to remain as reserves until the bank can come up with money to cancel the commercial bank money created by the loan.^{[citation needed]}

This table gives an outline of the makeup of money supplies worldwide. Most of the money in any given money supply consists of commercial bank money^[5]. The value of commercial bank money comes from the fact that it can be exchanged at a bank for central bank money^[5][6].

This is a general outline of how it works. The actual increase in the money supply through this process may be lower, as (at each step) banks may choose to hold reserves in excess of the statutory minimum, borrowers may let some funds sit idle, and some borrowers may choose to hold cash, and there may be delays or frictions in the process.^[11] It may also be higher if the reserve requirement is lower or if there are no reserve requirements^[12]. Government regulations may also be used to limit the money creation process by preventing banks from giving out loans even though the reserve requirements have been fulfilled^[13].

[edit] Money multiplier

The most common mechanism used to measure this increase in the money supply is typically called the money multiplier. It calculates the maximum amount of money that an initial deposit can be expanded to with a given reserve ratio.

[edit] Formula

The money multiplier, m, is the inverse of the reserve requirement, R^[14]:

Example

For example, with the reserve ratio of 20 percent, this reserve ratio, R, can also be expressed as a fraction:

So then the money multiplier, m, will be calculated as:

This number is multiplied by the initial deposit to show the maximum amount of money it can be expanded to.

[edit] Reserve requirements

The reserve requirements are intended to prevent banks from:

1. generating too much money by making too many loans against the narrow money deposit base;
2. having a shortage of cash when large deposits are withdrawn (although the reserve is a legal minimum, it is understood that in a crisis or bank run, reserves may be made available on a temporary basis).

The money creation process is affected by the currency drain ratio (the propensity of the public to hold banknotes rather than deposit them with a commercial bank), and the safety reserve ratio (excess reserves beyond the legal requirement that commercial banks voluntarily hold—usually a small amount). Data for "excess" reserves and vault cash are published regularly by the Federal Reserve in the United States.^[15] In practice, the actual money multiplier varies over time, and may be substantially lower than the theoretical maximum.^[16]

[edit] Financial ratios

In addition to reserve requirements, there are other financial ratios affect how many loans a bank can fund. The capital ratio is one type of ratio. It is also important to note that the term 'reserves' in the reserve ratio generally does not include all liquid assets.^{[citation needed]}

[edit] Money supplies around the world

Main articles: Money supply and Inflation

Fractional-reserve banking forms the basis for several money supplies around the world such as the U.S. dollar money supply and the euro supply of the European Union. The amount of central bank money (currency) in the official money supply statistics is much lower than the total money supply because these are fractional-reserve banking systems. Most of the money in these systems is commercial bank money.

[edit] Limitations for loan creation

The amount of loans that can be given out and thus the amount of commercial bank money that can be created depends on what the bank is permitted to do. In a free banking system, the demand for loans is contingent on the interest rates which are fixed by the lenders who compete against each other. In regulated systems, governments have created central banks that influence interest rates and thus the money supply through the monetary transmission mechanism.

[edit] Free banking

Main article: Free banking

Free banking is a theory of banking in which commercial banks and market forces control the provision of banking services. Under free banking, government central banks and currency boards do not exist, and banking-specific government regulations are either non-existent or not as strict. This system is based on the belief that free markets will properly determine how many loans will be given out. Banks are not bailed out or backed by the government and deposits are not insured by the government. It is believed that this will motivate both the depositors and the bankers to be careful about where money is loaned.

[edit] Government regulated systems

Fractional-reserve banking is the basis for many financial systems throughout the world. Because the nature of fractional-reserve banking involves the possibility of bank runs, central banks have been created throughout the world to address these problems.^[17][3]

[edit] Central banks

Main article: Central bank

Government controls and bank regulations related to fractional-reserve banking have generally been to impose restrictive requirements on note issue and deposit taking on the one hand, and to provide relief from bankruptcy and creditor claims, and/or protect creditors with government funds, when banks defaulted on the other hand. Such measures have included:

1. Minimum required reserve ratios (RRRs)
2. Minimum capital ratios
3. Government bond deposit requirements for note issue
4. 100% Marginal Reserve requirements for note issue, such as the Peels Act 1844 (UK)
5. Sanction on bank defaults and protection from creditors for many months or even years, and
6. Central bank support for distressed banks, and government guarantee funds for notes and deposits, both to counteract bank runs and to protect bank creditors.

[edit] Use of money multiplier

The use of the money multiplier as a tool of monetary policy is declining, as the money multiplier has changed over time and can usually not be directly influenced by central banks: privately owned banks may have different target levels of liquidity and may not be able to control directly the level of deposits attracted or feasible lending opportunities.^[18]

[edit] Liquidity and capital management for a bank

Main articles: Capital requirement and Market liquidity

To avoid defaulting on its obligations, the bank must maintain a minimal reserve ratio that it fixes in accordance with, notably, regulations and its liabilities. In practice this means that the bank sets a reserve ratio target and responds when the actual ratio falls below the target. Such response can be, for instance:

1. Selling or redeeming other assets, or securitization of illiquid assets,
2. Restricting investment in new loans,
3. Borrowing funds (whether repayable on demand or at a fixed maturity),
4. Issuing additional capital instruments, or
5. Reducing dividends.

Because different funding options have different costs, and differ in reliability, banks maintain a stock of low cost and reliable sources of liquidity such as:

1. Demand deposits with other banks
2. High quality marketable debt securities
3. Committed lines of credit with other banks

As with reserves, other sources of liquidity are managed with targets.

The ability of the bank to borrow money reliably and economically is crucial, which is why confidence in the bank's creditworthiness is important to its liquidity. This means that the bank needs to maintain adequate capitalisation and to effectively control its exposures to risk in order to continue its operations. If creditors doubt the bank's assets are worth more than its liabilities, all demand creditors have an incentive to demand payment immediately, a situation known as a run on the bank.

Contemporary bank management methods for liquidity are based on maturity analysis of all the bank's assets and liabilities (off balance sheet exposures may also be included). Assets and liabilities are put into residual contractual maturity buckets such as 'on demand', 'less than 1 month', '2-3 months' etc. These residual contractual maturities may be adjusted to account for expected counter party behaviour such as early loan repayments due to borrowers refinancing and expected renewals of term deposits to give forecast cash flows. This analysis highlights any large future net outflows of cash and enables the bank to respond before they occur. Scenario analysis may also be conducted, depicting scenarios including stress scenarios such as a bank-specific crisis.

[edit] Example of a bank balance sheet and financial ratios

An example of fractional reserve banking, and the calculation of the reserve ratio is shown in the balance sheet below:

Example 2: ANZ National Bank Limited Balance Sheet as at 30 September 2007[citation needed]
ASSETS	NZ$m	LIABILITIES	NZ$m
Cash	201	Demand Deposits	25482
Balance with Central Bank	2809	Term Deposits and other borrowings	35231
Other Liquid Assets	1797	Due to Other Financial Institutions	3170
Due from other Financial Institutions	3563	Derivative financial instruments	4924
Trading Securities	1887	Payables and other liabilities	1351
Derivative financial instruments	4771	Provisions	165
Available for sale assets	48	Bonds and Notes	14607
Net loans and advances	87878	Related Party Funding	2775
Shares in controlled entities	206	[subordinated] Loan Capital	2062
Current Tax Assets	112	Total Liabilities	99084
Other assets	1045	Share Capital	5943
Deferred Tax Assets	11	[revaluation] Reserves	83
Premises and Equipment	232	Retained profits	2667
Goodwill and other intangibles	3297	Total Equity	8703
Total Assets	107787	Total Liabilities plus Net Worth	107787

In this example the (legal tender) cash held by the bank is $201m and the demand liabilities of the bank are $25482m, for a (legal tender) cash reserve ratio of 0.79%.

[edit] Other financial ratios

The key financial ratio used to analyse fractional-reserve banks is the cash reserve ratio, which is the ratio of cash reserves to demand deposits and notes. However, other important financial ratios are also used to analyse the bank's liquidity, financial strength, profitability etc.

For example the ANZ National Bank Limited balance sheet above gives the following financial ratios:

1. The (legal tender) cash reserve ratio is $201m/$25482m, i.e. 0.79%.
2. The central bank notes/balances reserve ratio is $3010m/$25482m, i.e. 11.81%.
3. The liquid assets reserve ratio is ($201m+$2809m+$1797m)/$25482m, i.e. 18.86%.
4. The equity capital ratio is $8703m/107787m, i.e. 8.07%.
5. The tangible equity ratio is ($8703m-$3227m)/10787m, i.e. 5.08%
6. The total capital ratio is ($8703m+$2062m)/$10787m, i.e. 9.98%.

Clearly, then, it is very important how the term 'reserves' is defined for calculating the reserve ratio, and different definitions give different results. Other important financial ratios may require analysis of disclosures in other parts of the bank's financial statements. In particular, for liquidity risk, disclosures are incorporated into a note to the financial statements that provides maturity analysis of the bank's assets and liabilities and an explanation of how the bank manages its liquidity.

[edit] How the example bank manages its liquidity

The ANZ National Bank Limited explains its methods as:^{[citation needed]}

Liquidity risk is the risk that the Banking Group will encounter difficulties in meeting commitments associated with its financial liabilities, e.g. overnight deposits, current accounts, and maturing deposits; and future commitments e.g. loan draw-downs and guarantees. The Banking Group manages its exposure to liquidity risk by maintaining sufficient liquid funds to meet its commitments based on historical and forecast cash flow requirements.

The following maturity analysis of assets and liabilities has been prepared on the basis of the remaining period to contractual maturity as at the balance date. The majority of longer term loans and advances are housing loans, which are likely to be repaid earlier than their contractual terms. Deposits include substantial customer deposits that are repayable on demand. However, historical experience has shown such balances provide a stable source of long term funding for the Banking Group. When managing liquidity risks, the Banking Group adjusts this contractual profile for expected customer behaviour.

Example 2: ANZ National Bank Limited Maturity Analysis of Assets and Liabilities as at 30 September 2007[citation needed]
	Total carrying value	Less than 3 months	3-12 months	1-5 years	Beyond 5 years	No Specified Maturity
Assets
Liquid Assets	4807	4807
Due from other financial institutions	3563	2650	440	187	286
Derivative Financial Instruments	4711					4711
Assets available for sale	48	33	1	13		1
Net loans and advances	87878	9276	9906	24142	44905
Other Assets	4903	970	179			3754
Total Assets	107787	18394	10922	25013	45343	8115
Liabilities
Due to other financial institutions	3170	2356	405	32	377
Deposits and other borrowings	70030	53059	14726	2245
Derivative financial instruments	4932					4932
Other liabilities	1516	1315	96	32	60	13
Bonds and notes	14607	672	4341	9594
Related party funding	2275	2275
Loan capital	2062		100	1653	309
Total liabilities	99084	60177	19668	13556	746	4937
Net liquidity gap	8703	(41783)	(8746)	11457	44597	3178
Net liquidity gap - cumulative	8703	(41783)	(50529)	(39072)	5525	8703

[edit] Criticism

Main article: Criticism of fractional-reserve banking

Although fractional-reserve banking is near universal, it is not without criticism. The primary criticisms relate to the financial risk note holders and depositors bear, and the impact bank notes and demand deposits have on the stock of money, and potentially its value (that is, the effect on inflation and the exchange rate). One proposed alternative to fractional reserve banking is making the practice illegal and classifying the practice as a form of embezzlement, only permitting full-reserve banking and allowing the concurrent issuance of debt-free fiat currency from the Treasury, which is supported by such monetary reformers as Stephen Zarlenga of the American Monetary Institute.

[edit] Business cycle

Main articles: Austrian School and Business cycle#Austrian School

Fractional-reserve banking, by expanding the money supply, implies that interest rates will be different than what they would be in a full-reserve system. Austrian School economists point to the role of the interest rate as the price of investment capital, guiding investment decisions. In their view, the "natural" (free of government influence) interest rate reflects the actual time preference of lenders and borrowers. Government control of the money supply through central banks and regulations allowing fractional-reserve banking disturbs this equilibrium such that the interest rate no longer reflects the real supply of and demand for investment capital. Austrian School economists conclude that, if the interest rate is artificially low, then the demand for loans will be higher than the actual supply of willing lenders, and if the interest rate is artificially high, the opposite situation will occur. This misinformation leads investors to misallocate capital, borrowing and investing either too much or too little in long-term projects. Periodic recessions, then, are seen as necessary "corrections" following periods of fiat credit expansion, when unprofitable investments are liquidated, freeing capital for new investment. One of the proponents of aspects of the business cycle theory, Friedrich von Hayek, was awarded the Nobel Prize in Economics[1], but the theory is not universally accepted; at least one mainstream economist, Paul Krugman, considered it unworthy of serious study.^[19] A few Austrian School economists, such as Pascal Salin, also suggest that a full-reserve banking system should not be enforced and rather simply root for free banking.

[edit] Risk

Main article: Full-reserve banking

In a fractional-reserve banking system, in the event of a bank run, the demand depositors and note holders would attempt to withdraw more money than the bank has in reserves, causing the bank to suffer a liquidity crisis and, ultimately, to perhaps default. In the event of a default, the bank would need to liquidate assets and the creditors of the bank would suffer a loss if the proceeds were insufficient to pay its liabilities. Since public deposits are payable on-demand, liquidation may require selling assets quickly and potentially in large enough quantities to affect the price of those assets. An otherwise solvent bank (whose assets are worth more than its liabilities) may be made insolvent by a bank run. This problem potentially exists for any corporation with debt or liabilities, but is more critical for banks as they rely upon public deposits (which may be redeemable upon demand).

Although an initial analysis of a bank run and default points to the bank's inability to liquidate or sell assets (i.e. because the fraction of assets not held in the form of liquid reserves are held in less liquid investments such as loans), a more full analysis indicates that depositors will cause a bank run only when they have a genuine fear of loss of capital, and that banks with a strong risk adjusted capital ratio should be able to liquidate assets and obtain other sources of finance to avoid default. For this reason, fractional-reserve banks have every reason to maintain their liquidity, even at the cost of selling assets at heavy discounts and obtaining finance at high cost, during a bank run (to avoid a total loss for the contributors of the bank's capital, the shareholders).

Many governments have enforced or established deposit insurance systems in order to protect depositors from the event of bank defaults and to help maintain public confidence in the fractional-reserve system.

Responses to the problem of financial risk described above include:

1. Proponents of prudential regulation, such as minimum capital ratios, minimum reserve ratios, central bank or other regulatory supervision, and compulsory note and deposit insurance, (see Controls on Fractional-Reserve Banking below);
2. Proponents of free banking, who believe that banking should be open to free entry and competition, and that the self-interest of debtors, creditors and shareholders should result in effective risk management; and,
3. Withdrawal restrictions: some bank accounts may place a limit on daily cash withdrawals and may require a notice period for very large withdrawals. Banking laws in some countries may allow restrictions to be placed on withdrawals under certain circumstances, although these restrictions may rarely, if ever, be used;
4. Opponents of fractional reserve banking who insist that notes and demand deposits be 100% reserved.

[edit] Effects of an increased money supply

Fractional reserve banking involves the issue of commercial bank money. According to the quantity theory of money, the expansion of the money supply leads to more money with the same amount of goods, which leads to inflation. Some monetarists believe that the exchange rate or purchasing power of the monetary unit is governed by the quantity of money, including demand deposits and notes, and therefore view fractional reserve banking as a potential cause of inflation. Most schools of economics recognize the link between money supply and inflation; many economists, however, consider the issue of money through the banking system as a mechanism of monetary transmission, which a central bank can influence indirectly by raising or lowering interest rates (although banking regulations may also be adjusted to influence the money supply, depending on the circumstances).

Quantity theorists may either be hostile to fractional reserve banking or supportive of minimum reserve ratios and other government controls on the quantity of money created by commercial banks. The process with which commercial banks practice fractional-reserve banking is explained at deposit creation multiplier.

[edit] Inadequate government regulation

This section does not cite any references or sources. (March 2008) Please help improve this section by adding citations to reliable sources. Unverifiable material may be challenged and removed.

Critics of current bank regulations argue that:

1. Minimum reserve ratios put reserves beyond reach in a time of need;
2. Minimum capital ratios are poor regulators of financial risk, as they ignore other portfolio risk drivers such as scale and diversification and come at a heavy compliance cost;
3. Central bank support and government protection of creditors creates moral hazard and socializes credit risk.

[edit] See also

• Bimetallism
• Bretton Woods system
• Credit money
• Digital gold currency
• Fiat currency
• Full-reserve banking
• Gold standard
• Islamic banking
• Money supply
• Money creation
• Monetary reform
• Seignorage
• Usury
• List of economics topics
• List of finance topics
• List of business ethics, political economy, and philosophy of business topics

[edit] References

• Huerta de Soto, J. (2006), Money, Bank Credit and Economic Cycles, Ludwig von Mises Institute
• Meigs, A.J. (1962), Free reserves and the money supply, Chicago, University of Chicago, 1962.
• Crick, W.F. (1927), The genesis of bank deposits, Economica, vol 7, 1927, pp 191-202.
• Philips, C.A. (1921), Bank Credit, New York, Macmillan, chapters 1-4, 1921,
• Thomson, P. (1956), Variations on a theme by Philips, American Economic Review vol 46, December 1956, pp. 965-970.
• Parliament of Tasmania, Monetary System, Report of Select Committee, With Minutes of Proceedings, 1935.

[edit] External links

• Rothbard, M. N. (1983) The Mystery of Banking, Richardson & Snyder, 1983, pp 87-110
• Narrow banking
• Seignorage and inflation tax
• Schematic diagram to explain the fractional-reserve process
• Fractional reserve banking and usury
• Free banking and fractional reserves: a comment (Pascal Salin)