# Reserve requirement: Wikis

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# Encyclopedia

The reserve requirements (or cash reserve ratio) is a central bank regulation that sets the minimum reserves each bank must hold to customer deposits and notes. It would normally be in the form of fiat currency stored in a bank vault (vault cash), or with a central bank.

The reserve ratio is sometimes used as a tool in the monetary policy, influencing the country's economy, borrowing, and interest rates.[3] Western central banks rarely alter the reserve requirements because it would cause immediate liquidity problems for banks with low excess reserves; they prefer to use open market operations to implement their monetary policy. The People's Bank of China uses changes in reserve requirements as an inflation-fighting tool,[4] and raised the reserve requirement nine times in 2007. As of 2006 the required reserve ratio in the United States was 10% on transaction deposits (component of money supply "M1"), and zero on time deposits and all other deposits.

An institution that holds reserves in excess of the required amount is said to hold excess reserves.

## Effects on money supply

MS = MB * mm

mm = (1 + c) / (c + R)

MS = Money Supply

Mb = Monetary base

mm = money multiplier

c = rate at which people hold cash (as opposed to depositing it)

R = the reserve requirement (the percent of deposits that banks are not allowed to lend)

if banks only have to hold 10% of deposits,they will lend the other 90% of deposits. The person with that loan will then choose to deposit the money from the loan back into the bank at a rate of 'c' (for simplicity say c=0%.) then the bank can again loan 90% of the second deposit which was 90% of the first deposit.

Reserve requirements affect the potential of the banking system to create transaction deposits. If the reserve requirement is 10%, for example, a bank that receives a \$100 deposit may lend out \$90 of that deposit. If the borrower then writes a check to someone who deposits the \$90, the bank receiving that deposit can lend out \$81. As the process continues, the banking system can expand the change in excess reserves of \$90 into a maximum of \$1,000 of money (\$100+\$90+81+\$72.90+...=\$1,000), e.g.\$100/0.10=\$1,000. In contrast, with a 20% reserve requirement, the banking system would be able to expand the initial \$100 deposit into a maximum of (\$100+\$80+\$64+\$51.20+...=\$500), e.g.\$100/0.20=\$500. Thus, higher reserve requirements reduce artificial money creation and help maintain the purchasing power of the currency in use.

Reserve requirements in the US apply only to transaction accounts, which are components of M1, a narrowly defined measure of money. Deposits that are components of M2 and M3 (but not M1), such as savings accounts and time deposits such as CDs, have no reserve requirements and therefore can expand without regard to reserve levels.

Because of the exponential impact that reserve requirements have on the money supply, and the large time lag between their implementation and the corresponding effect of inflation, the Federal reserve does not frequently change reserve requirements for the purpose of affecting monetary policy.

## Reserve ratios

A cash reserve ratio (or CRR) is the percentage of bank reserves to deposits and notes. The cash reserve ratio is also known as the cash asset ratio or liquidity ratio. In the United States, the Board of Governors of the Federal Reserve System requires zero percent (0%) fractional reserves from depository institutions having net transactions accounts of up to \$10.7 million.[1] Depository institutions having over \$10.7 million, and up to \$55.2 million in net transaction accounts must have fractional reserves totaling three percent (3%) of that amount.[1] Finally, depository institutions having over \$55.2 million in net transaction accounts must have fractional reserves totaling ten percent (10%) of that amount.[1] However, under current policy, these numbers do not apply to time deposits from domestic corporations, or deposits from foreign corporations or governments, called "nonpersonal time deposits" and "eurocurrency liabilities," respectively. For these account classes, the fractional reserve requirement is zero percent (0%) regardless of net account value.[1]

The Bank of England holds to a voluntary reserve ratio system. In 1998 the average cash reserve ratio across the entire United Kingdom banking system was 3.1%. Other countries have required reserve ratios (or RRRs) that are statutorily enforced (sourced from Lecture 8, Slide 4: Central Banking and the Money Supply, by Dr. Pinar Yesin, University of Zurich (based on 2003 survey of CBC participants at the Study Center Gerzensee[2]):

Country Required reserve ratio (in %) Note
Australia None
Mexico None
New Zealand None

1999[5]

Sweden None
United Kingdom None
Czech Republic 2.00 Since 7 October
Eurozone 2.00
South Africa 2.50
Switzerland 2.50
Poland 3.00
Chile 4.50
India 5.75 as per RBI (INDIA).
Lithuania 6.00
Pakistan 5.00 Since 1 November 2008
Latvia 8.00
Jordan 8.00
Malawi 15.00
Zambia 8.00
Burundi 8.50
Hungary 8.75
Ghana 9.00
United States 10.00
Sri Lanka 10.00
Bulgaria 12.00 Raised from 8%, effective from 2007-01-09
Croatia 14.00 Down from 17%, effective from 2009-01-14[3]
Costa Rica 15.00
Estonia 15.00
China 16.50 for major Chinese Banks & 13.5 for small median-size banks Up from 16%, effective from 2010-02-25[4]
Hong Kong 18.00
Tajikistan 20.00
Suriname 25.00 Down from 27%, effective from 2007-01-01[5]
Lebanon 30.00 [6]

In some countries, the cash reserve ratios have decreased over time (sourced from IMF Financial Statistic Yearbook):

Country 1968 1978 1988 1998
United Kingdom 20.5 15.9 5.0 3.1
Turkey 58.3 62.7 30.8 18.0
Germany 19.0 19.3 17.2 11.9
United States 12.3 10.1 8.5 10.3

(Ratios are expressed in percentage points.)

Capital adequacy ratio (CAR), also called Capital to Risk (Weighted) Assets Ratio (CRAR)[6], is a ratio of a bank's capital to its risk. National regulators track a bank's CAR to ensure that it can absorb a reasonable amount of loss [7] and are complying with their statutory capital requirements.

## Formula

Capital adequacy ratios ("CAR") are a measure of the amount of a bank's capital expressed as a percentage of its risk weighted credit exposures.

Capital adequacy ratio is defined as

$\mbox{CAR} = \cfrac{\mbox{Capital}}{\mbox{Risk}}$

where Risk can either be weighted assets ($\,a$) or the respective national regulator's minimum total capital requirement. If using risk weighted assets,

$\mbox{CAR} = \cfrac{T_1 + T_2}{a}$ ≥ 8%.[6]

The percent threshold (8% in this case, a common requirement for regulators conforming to the Basel Accords) is set by the national banking regulator.

Two types of capital are measured: tier one capital (T1 above), which can absorb losses without a bank being required to cease trading, and tier two capital (T2 above), which can absorb losses in the event of a winding-up and so provides a lesser degree of protection to depositors.

## Use

Capital adequacy ratio is the ratio which determines the capacity of the bank in terms of meeting the time liabilities and other risk such as credit risk, operational risk, etc. In the most simple formulation, a bank's capital is the "cushion" for potential losses, which protect the bank's depositors or other lenders. Banking regulators in most countries define and monitor CAR to protect depositors, thereby maintaining confidence in the banking system.[6]

CAR is similar to leverage; in the most basic formulation, it is comparable to the inverse of debt-to-equity leverage formulations: CAR uses equity divided by assets instead of debt-to-equity (total debt divided by shareholder's equity or other invested capital). It is important to note that the assets of a bank are its outstanding loans (not the deposits it has taken in). In accounting generally, total assets are by definition equal to debt plus equity. Therefore the capital adequacey ratio is equivalent to the proportion of Capital (generally what shareholders paid to the bank to purchase common stock, but Capital may also include other types of securities issuances) to the "assets" it hold on its books (i.e. the loans that bank customers have to pay back to the bank -- such as a home mortgage). Unlike traditional leverage, however, CAR recognizes that assets can have different levels of risk. The "safer" the asset the more the bank is allowed to discount that asset in its CAR calculation; in other words, banks don't have to hold so much in reserves if their "assets" (the loan dollars owed to them) are very safe (i.e. highly likely to be paid back). For example, if the bank buys and holds a bond from a corporation, there is a better likelihood the corporation will pay off its bond than that a homeowner will pay off his mortgage.

## Risk weighting

Since different types of assets have different risk profiles, CAR primarily adjusts for assets that are less risky by allowing banks to "discount" lower-risk assets. The specifics of CAR calculation vary from country to country, but general approaches tend to be similar for countries that apply the Basel Accords. In the most basic application, government debt is allowed a 0% "risk weighting" - that is, they are subtracted from total assets for purposes of calculating the CAR.

### Risk weighting example

Local regulations establish that cash and government bonds have a 0% risk weighting, and residential mortgage loans have a 50% risk weighting. All other types of assets (loans to customers) have a 100% risk weighting.

Bank "A" has assets totaling 100 units, consisting of:

Bank "A" has deposits of 95 units, all of which are deposits (remember: "deposits" to a bank are its "debt"). By definition, equity is equal to assets minus debt, or 5 units.

Bank A's risk-weighted assets are calculated as follows:

 Total risk Cash 10 * 0% = 0 Government bonds 15 * 0% = 0 Mortgage loans 20 * 50% = 10 Other loans 50 * 100% = 50 Other assets 5 * 100% = 5 Weighted assets 65 Equity 5 CAR (Equity/RWA) 7.69%

Even though Bank "A" would appear to have a debt-to-equity ratio of 95:5, or equity-to-assets of only 5%, its CAR is substantially higher. It is considered less risky because some of its assets are less risky than others.

## Types of capital

The Basel rules recognize that different types of equity are more important than others. To recognize this, different adjustments are made:

1. Tier I Capital: Actual contributed equity plus retained earnings.
2. Tier II Capital: Preferred shares plus 50% of subordinated debt.

Different minimum CAR ratios are applied: minimum Tier I equity to risk-weighted assets may be 4%, while minimum CAR including Tier II capital may be 8%.

There is usually a maximum of Tier II capital that may be "counted" towards CAR, depending on the jurisdiction.