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{{refimprove|date=May 2010}}
The '''reserve requirement''' (or '''cash reserve ratio''') is a [[central bank]] regulation employed by most, but not all, of the world's central banks, that sets the minimum ''fraction'' of customer [[Deposit account|deposits]] and [[Promissory note|notes]] that each [[commercial bank]] must hold as [[bank reserves|reserves]] (rather than lend out). These '''required reserves''' are normally in the form of [[currency|cash]] stored physically in a [[bank vault]] (vault cash) or deposits made with a central bank.
{{main|Character theory}}
In [[group theory]], a branch of [[abstract algebra]], a '''character table''' is a two-dimensional table whose rows correspond to irreducible [[group representation]]s, and whose columns correspond to conjugacy classes of group elements. The entries consist of [[character theory|character]]s, the [[trace (linear algebra)|trace]] of the matrices representing group elements of the column's class in the given row's group representation.  


In [[chemistry]], [[crystallography]], and [[spectroscopy]], [[List of character tables for chemically important 3D point groups|character tables of point groups]] are used to classify ''e.g.'' molecular vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons.
The required reserve ratio is sometimes used as a tool in [[monetary policy]], influencing the country's borrowing and [[interest rate]]s by changing the amount of funds available for banks to make loans with.<ref>[http://www.cbr.ru/eng/analytics/standart_system/print.asp?file=policy_e.html Central Bank of Russia]</ref> Western central banks rarely alter the reserve requirements because it would cause immediate liquidity problems for banks with low [[excess reserves]]; they generally prefer to use [[open market operation]]s (buying and selling government-issued [[Bond (finance)|bonds]]) to implement their monetary policy. The [[People's Bank of China]] uses changes in reserve requirements as an inflation-fighting tool,<ref>{{Cite news| url=http://news.bbc.co.uk/1/hi/business/7089307.stm | work=BBC News | title=China moves to cool its inflation | date=2007-11-11}}</ref> and raised the reserve requirement ten times in 2007 and eleven times since the beginning of 2010.


==Definition and example==
An institution that holds reserves in excess of the required amount is said to hold ''[[excess reserves]]''.
The irreducible complex characters of a [[finite group]] form a '''character table''' which encodes much useful information about the [[group (mathematics)|group]] ''G'' in a compact form.  Each row is labelled by an [[irreducible character]] and the entries in the row are the values of that character on the representatives of the respective [[conjugacy class]] of ''G'' (because characters are [[class function]]s). The columns are labelled by (representatives of) the conjugacy classes of ''G''. It is customary to label the first row by the trivial character, and the first column by (the conjugacy class of) the [[identity element|identity]]. The entries of the first column are the values of the irreducible characters at the identity, the [[Degree of a character|degree]]s of the irreducible characters. Characters of degree ''1'' are known as '''linear characters'''.  


Here is the character table of ''C''<sub>3</sub> = ''<nowiki><u></nowiki>'', the cyclic group with three elements and generator ''u'':
==Effects on money supply==


{| class="wikitable"
===The conventional view===
|-
The economic theory that a reserve requirement can act as a tool of monetary policy is frequently found in economics textbooks. The higher the reserve requirement is set, the theory supposes, the less funds banks will have to loan out{{Citation needed|date=October 2014}}
|&nbsp;
, leading to lower money creation and perhaps ultimately to higher purchasing power of the money previously in use.  The effect is multiplied, because money obtained as loan proceeds can be re-deposited; a portion of those deposits may again be loaned out{{Citation needed|date=October 2014}}, and so on.  The effect on the money supply is governed by the following formulas:
|(1)
 
|(u)
:<math>M_1=MB*m \,</math> : definitional relationship between monetary base ''MB'' (bank reserves plus currency held by the non-bank public) the narrowly defined [[money supply]], <math>M_1</math>,
|(u<sup>2</sup>)
 
|-
:<math>m=\frac{(1+c)}{(c+R)} = \frac{1+\frac{C}{D}}{\frac{C}{D}+R}</math> : derived formula for the [[money multiplier]] ''m'', the factor by which lending and re-lending leads <math>M_1</math> to be a multiple of the monetary base:
|'''1'''
 
|1
where notationally,
|1
 
|1
:<math>c  =</math> the currency ratio: the ratio of the public's holdings of currency (undeposited cash) to the public's holdings of [[demand deposit]]s; and
|-
 
|χ<sub>1</sub>
:<math>R  =</math> the total reserve ratio (the ratio of legally required plus non-required reserve holdings of banks to demand deposit liabilities of banks).
|1
 
|ω
However, in the United States (and other countries except Brazil, China, India, Russia), the reserve requirements are generally not frequently altered to implement monetary policy because of the short-term disruptive  effect on financial markets. {{Citation needed|date=May 2014}}
|ω<sup>2</sup>
 
|-
===The endogenous money view===
|χ<sub>2</sub>
Some economists dispute the conventional theory of the reserve requirement. Criticisms of the conventional theory are usually associated with theories of [[endogenous money]].
|1
 
|ω<sup>2</sup>
Jaromir Benes and Michael Kumhof of the IMF Research Department report that the “deposit multiplier“ of the undergraduate economics textbook, where monetary aggregates are created at the initiative of the central bank, through an initial injection of high-powered money into the banking system that gets multiplied through bank lending, turns the actual operation of the monetary transmission mechanism on its head. Most times when banks ask for replenishment of depleted reserves, the central bank obliges.<ref>Benes, Jaromir, and Michael Kumhof. The chicago plan revisited. International Monetary Fund, 2012.‏ http://www.imf.org/external/pubs/ft/wp/2012/wp12202.pdf</ref> Reserves therefore impose no constraints as the deposit multiplier is simply, in the words of Kydland and Prescott (1990), a myth. And because of this, private banks are almost fully in control of the money creation process.<ref>Benes, Kumhof. http://www.imf.org/external/pubs/ft/wp/2012/wp12202.pdf</ref>
|ω
 
|-
==Required reserves==
|}
 
===United States===
In the United States, a reserve requirement (or '''liquidity ratio''') is a minimum value, set by the Board of Governors of the [[Federal Reserve System]], of the ratio of required reserves to some category of deposits held at depository institutions (e.g., [[commercial bank]] including US branch of a foreign bank, [[savings and loan association]], [[savings bank]], [[credit union]]). The only deposit categories currently subject to reserve requirements are net transactions accounts, mainly checking accounts. The total amount of all net transaction accounts held in USA depository institutions, plus US currency held by the nonbank public, is called [[Money supply#Empirical measures|M1]].
 
A depository institution can satisfy its reserve requirements by holding either [[Bank vault|vault]] cash or [[Bank reserves|reserve deposit]]s. An institution that is a member of the Federal Reserve System must hold its reserve deposits at a Federal Reserve Bank. Nonmember institutions can elect to hold their reserve deposits at a member institution on a pass-through basis.<ref name="federalreserve">[http://www.federalreserve.gov/monetarypolicy/reservereq.htm FRB: Reserve Requirements<!-- Bot generated title -->]</ref>
 
A depository institution's reserve requirements vary by the dollar amount of net transaction accounts held at that institution. Effective January 23, 2014, institutions with net transactions accounts:
* Of less than $13.3 million have no minimum reserve requirement;
* Between $13.3 million and $89.0 million must have a liquidity ratio of 3%;
* Exceeding $89.0 million must have a liquidity ratio of 10%.<ref name="federalreserve" />
The numerical amounts stated above are recalculated annually according to a statutory formula.


where ω is a primitive third root of unity. The character table for general cyclic groups is the [[DFT matrix]].
Effective December 27, 1990, a liquidity ratio of zero has applied to [[Certificate of deposit|CDs]], savings deposits, and [[time deposit]]s, owned by entities other than households, and the Eurocurrency liabilities of depository institutions. Deposits owned by foreign corporations or governments are currently not subject to reserve requirements.<ref name="federalreserve" />
When an institution fails to satisfy its reserve requirements, it can make up its deficiency with reserves borrowed either from a Federal Reserve Bank, or from an institution holding reserves in excess of reserve requirements. Such loans are typically due in 24 hours or less.


The first row of the character table always consists of 1s, and corresponds to the '''[[trivial representation]]''' (the 1-dimensional representation consisting of 1&times;1 matrices containing the entry 1). Further, the character table is always square because (1) irreducible characters are pairwise orthogonal, and (2) no other non-trivial class function is orthogonal to every character. This is tied to the important fact that the irreducible representations of a finite group ''G'' are in bijection with its conjugacy classes. This bijection also follows by showing that the class sums form a basis for the center of the group algebra of ''G'', which has dimension equal to the number of irreducible representations of ''G''.  
An institution's overnight reserves, averaged over some maintenance period, must equal or exceed its average required reserves, calculated over the same maintenance period. If this calculation is satisfied, there is no requirement that reserves be held at any point in time. Hence reserve requirements play only a limited role in money creation in the USA - and since [[quantitative easing]] began in 2008, they have been even less important, as an enormous glut of excess reserves now exists (over the whole system; theoretically, though, individual banks may still run into temporary shortfalls).


==Orthogonality relations==
The [[International Banking Act of 1978]] requires branches of foreign banks operating in the US to follow the same required reserve ratio standards.<ref name=effects>{{cite journal
{{Main|Schur orthogonality relations}}
| last =Ahorny
The space of complex-valued class functions of a finite group G has a natural inner-product:
| first =Joseph
|author2=Saunders, Anthony |author3=Swary, Itzhak
  | title =The Effects of the International Banking Act on Domestic Bank Profitability and Risk
| work =Journal of Money, Credit, and Banking
| publisher =JSTOR
| year =1985
| jstor =1992444}}</ref><ref name=bank>{{cite web
| title =International Banking Act of 1978
| work =Banking Law 101
| url =http://www.csbs.org/bankinglaw101/Wiki%20Pages/International%20Banking%20Act%20of%201978.aspx}}</ref>


:<math>\left \langle \alpha, \beta\right \rangle := \frac{1}{ \left | G \right | }\sum_{g \in G} \alpha(g) \overline{\beta(g)}</math>
===Countries without reserve requirements===
Canada, the UK, New Zealand, Australia and Sweden have no reserve requirements.


where <math>\overline{\beta(g)}</math> means the complex conjugate of the value of <math>\beta</math> on ''g''. With respect to this inner product, the irreducible characters form an orthonormal basis
This does not mean that banks can - even in theory - create money without limit. On the contrary: banks are constrained by [[capital requirements]], which are arguably more important than reserve requirements even in countries that have reserve requirements.
for the space of class-functions, and this yields the orthogonality relation for the rows of the character
table:


:<math>\left \langle \chi_i, \chi_j \right \rangle  = \begin{cases} 0  & \mbox{ if } i \ne j, \\ 1 & \mbox{ if } i = j. \end{cases}</math>
It also does not mean that a commercial bank's overnight reserves can become ''negative'', in these countries. On the contrary: the central bank will ''always'' step in to lend the necessary reserves if necessary so that this does not happen: this is sometimes described as "defending the payment system". Historically, a central bank might once have run out of reserves to lend and so have had to suspend redemptions, but this cannot happen anymore to modern central banks because of the end of the [[gold standard]] worldwide, which means that all nations use a [[fiat currency]].


For <math>g, h \in G</math> the orthogonality relation for columns is as follows:
It is sometimes argued that the requirement not to have a negative reserve balance at the central bank constitutes a reserve requirement of zero. However, mathematically, a requirement to hold zero reserves does not correspond to any ratio; it is more permissive than any ratio. So this can be true only if a broader definition of reserve requirement is adopted. Moreover, such a zero reserve requirement cannot be explained by a theory that holds that monetary policy works by varying the quantity of money using the reserve requirement.


:<math>\sum_{\chi_i} \chi_i(g) \overline{\chi_i(h)} = \begin{cases} \left | C_G(g) \right |, & \mbox{ if } g, h \mbox{ are conjugate } \\ 0 & \mbox{ otherwise.}\end{cases}</math>
Even in the United States, which retains formal (though now mostly irrelevant) reserve requirements, the notion of controlling the money supply by targeting the quantity of base money fell out of favour many years ago, and now the pragmatic explanation of monetary policy refers to targeting the ''interest rate'' to control the broad money supply.


where the sum is over all of the irreducible characters <math>\chi_i</math> of ''G'' and the symbol <math>\left | C_G(g) \right |</math> denotes the order of the centralizer of <math>g</math>.
====United Kingdom====
In the UK the term [[clearing banks]] is sometimes used, meaning banks that have direct access to the clearing system. However, for the purposes of clarity, the term ''commercial banks'' will be used for the remainder of this section.


The orthogonality relations can aid many computations including:
The [[Bank of England]], which is the central bank for the entire [[United Kingdom]], previously held to a voluntary reserve ratio system, with no minimum reserve requirement set. In theory, this meant that commercial banks could retain zero reserves. However, the average cash reserve ratio across the entire [[United Kingdom]] banking system was higher during that period, at about 0.15% {{asof|1999|lc=1}}.<ref name="monetary-economics" />
* Decomposing an unknown character as a linear combination of irreducible characters.
* Constructing the complete character table when only some of the irreducible characters are known.
* Finding the orders of the centralizers of representatives of the conjugacy classes of a group.
* Finding the order of the group.


==Properties==
From 1971 to 1980, the commercial banks all agreed to a reserve ratio of 1.5%. However, in 1981 this requirement was abolished.<ref name="monetary-economics" />
Complex conjugation acts on the character table: since the complex conjugate of a representation is again a representation, the same is true for characters, and thus a character that takes on non-trivial complex values has a conjugate character.


Certain properties of the group ''G'' can be deduced from its character table:
From 1981 to 2009, each commercial bank set out its own monthly voluntary reserve target in a contract with the Bank of England. Both shortfalls and excesses of reserves relative to the commercial bank's own target over an averaging period of one day<ref name="monetary-economics" /> would result in a charge, incentivising the commercial bank to stay near its target, a system known as ''reserves averaging''.


* The order of ''G'' is given by the sum of the squares of the entries of the first column (the degrees of the irreducible characters). (See [[Representation theory of finite groups#Applying Schur's lemma]].) More generally, the sum of the squares of the absolute values of the entries in any column gives the order of the centralizer of an element of the corresponding conjugacy class.
Upon the parallel introduction of quantitative easing and [[interest on excess reserves]] in 2009, banks were no longer required to set out a target, and so were no longer penalised for holding excess reserves; indeed, they were proportionally compensated for holding all their reserves at the Bank Rate (the Bank of England now uses the same interest rate for its bank rate, its deposit rate and its interest rate target).<ref>{{Cite web|url = http://www.bankofengland.co.uk/markets/Pages/sterlingoperations/monetarypolicy.aspx|title = Sterling Operations - Implementation of Monetary Policy|accessdate = 26 August 2013|publisher = Bank of England}}</ref> Indeed, in the absence of an agreed target, the concept of excess reserves does not really apply to the Bank of England any more, so it is technically incorrect to call its new policy "interest on excess reserves".
*All normal subgroups of ''G'' (and thus whether or not ''G'' is simple) can be recognised from its character table. The [[kernel (linear algebra)|kernel]] of a character χ is the set of elements ''g'' in ''G'' for which χ(g) = χ(1); this is a normal subgroup of ''G''. Each normal subgroup of ''G'' is the intersection of the kernels of some of the irreducible characters of ''G''.  
*The derived subgroup of ''G'' is the intersection of the kernels of the linear characters of ''G''. In particular, ''G'' is Abelian if and only if all its irreducible characters are linear.
*It follows, using some results of [[Richard Brauer]] from [[modular representation theory]], that the prime divisors of the orders of the elements of each conjugacy class of a finite group can be deduced from its character table (an observation of [[Graham Higman]]).  


The character table does not in general determine the group [[up to]] [[group isomorphism|isomorphism]]: for example, the [[quaternion group]] ''Q'' and the [[dihedral group]] of 8 elements (''D''<sub>4</sub>) have the same character table. Brauer asked whether the character table, together with the knowledge of how the powers of elements of its conjugacy classes are distributed, determines a finite group up to isomorphism. In 1964, this was answered in the negative by [[E. C. Dade]].
====Canada====
Canada abolished its reserve requirement in 1992.<ref name='monetary-economics'>{{cite book|title=Monetary Economics|edition=2nd|author=Jagdish Handa|publisher=Routledge|year=2008|page=347}}</ref>


The linear characters form a [[character group]], which has important [[number theory|number theoretic]] connections.
===Other countries===
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<ref>[http://www.iew.unizh.ch/study/courses/downloads/lecture8_467.pdf Monetary Macroeconomics by Dr. Pinar Yesin]</ref>):


== Outer automorphisms ==
{| class="wikitable sortable"
The [[outer automorphism]] group acts on the character table by permuting columns (conjugacy classes) and accordingly rows, which gives another symmetry to the table. For example, abelian groups have the outer automorphism <math>g \mapsto -g,</math> which is non-trivial except for [[elementary abelian group|elementary abelian 2-groups]], and outer because abelian groups are precisely those for which conjugation (inner automorphisms) acts trivially. In the example of <math>C_3</math> above, this map sends <math>u \mapsto u^2, u^2 \mapsto u,</math> and accordingly switches <math>\chi_1</math> and <math>\chi_2</math> (switching their values of <math>\omega</math> and <math>\omega^2</math>). Note that this particular automorphism (negative in abelian groups) agrees with complex conjugation.
|- align="center"
! Country !! data-sort-type="number" | Required reserve (in %)!! Note
|- align="right"
|[[Australia]]||None||Statutory Reserve Deposits abolished in 1988, <br>replaced with 1% Non-callable Deposits<ref>"Inquiry into the Australian Banking Industry, Reserve Bank of Australia, January 1991</ref>
|- align="right"
|[[New Zealand]]||None||
1999 [http://www.cnb.cz/m2export/sites/www.cnb.cz/cs/menova_politika/mp_nastroje/download/menove_nastroje.xls]
|- align="right"
|[[Sweden]]||None||
|- align="right"
|[[Eurozone]]||1.00||Effective January 18, 2012.<ref>[https://www.ecb.europa.eu/mopo/implement/mr/html/calc.en.html <en> European Central Bank, minimum reserve requirements]</ref> Down from 2% since Jan 1999.
|- align="right"
|[[Czech Republic]]||2.00||Since October 7, 2009
|- align="right"
||[[Hungary]]||2.00|| Since November 2008
|- align="right"
|[[South Africa]]||2.50||
|- align="right"
|[[Switzerland]]||2.50||
|- align="right"
|[[Latvia]]||3.00||Just after the Parex Bank bailout (24.12.2008), Latvian Central Bank <br>decreased the RRR from 7% (?) down to 3%<ref>{{Cite web | url=http://www.bank.lv/eng/main/all/noract/mon_oper/reserve/reserve_ratio_n21 | title= Minimum Reserve Ratio | work= Bank of Latvia | accessdate=2010-12-29}}</ref>
|- align="right"
|[[Poland]]||3.50||  as of 31 dec 2010 <ref>[http://www.nbp.pl/homen.aspx?f=/en/onbp/informacje/polityka_pieniezna.html Narodowy Bank Polski - Internet Information Service<!-- Bot generated title -->]</ref>
|- align="right"
|[[Romania]]||10.00||  as of 30 jan 2013 for [[Romanian leu|lei]]. And 16% for foreign currency<ref>http://www.bnr.ro/Reserve-requirements-3658.aspx</ref>
|- align="right"
|[[Russia]]||4.00|| Effective April 1, 2011, up from 2.5% in January 2011.<ref>[http://www.cbr.ru/eng/analytics/standart_system/print.asp?file=policy_e.html Central bank of Russia] Required reserve ratio on credit institutions' liabilities to non-resident has been raised to 4.0%</ref>
|- align="right"
|[[Chile]]||4.50||
|- align="right"
|[[India]]||4.00|| January 2013, as per [[Reserve Bank of India|RBI]].<ref>[http://profit.ndtv.com/news/economy/article-we-will-walk-the-path-alone-says-chidambaram-on-growth-challenge-312661?pfrom=home-otherstories] ndtv.com</ref>
|- align="right"
|[[Bangladesh]]||6.00|| Raised from 5.50. Effective from 15 December 2010
|- align="right"
|[[Lithuania]]||6.00||
|- align="right"
|[[Nigeria]]||20.00||Raised from 15.00. Effective from 25 November 2014<ref>http://businessdayonline.com/2014/11/banks-squeezed-further-as-n40bn-may-vanish-from-industry-wide-profits/#.VHbDB51fqUk</ref>
|- align="right"
||[[Pakistan]]||5.00||Since November 1, 2008
|- align="right"
|[[Taiwan]]||7.00||<ref>[http://www.cbc.gov.tw/public/data/EBOOKXLS/P077.pdf Liquidity ratio and liquid reserves of deposit money banks]. Data released by Taiwan's central bank in October 2010.</ref>
|- align="right"
||[[Turkey]]||8.50||Since February 19, 2013
|- align="right"
||[[Jordan]]||8.00||
|- align="right"
|[[Zambia]]||8.00||
|- align="right"
||[[Burundi]]||8.50||
|- align="right"
||[[Ghana]]||9.00||
|- align="right"
||[[Israel]]||9.00||the Required Reserve Ratio is called Minimum Capital Ratio<ref>{{Cite web | url=http://www.bankisrael.gov.il/deptdata/pikuah/nihul_takin/eng/311_et.pdf | title= Minimum capital ratio | work= Bank of Israel | accessdate=2010-12-29}}</ref>
|- align="right"
|[[Mexico]]||10.50||
|- align="right"
|[[Sri Lanka]]||8.00||With effect from 29 April 2011. 8% of total rupee deposit liabilities.
|- align="right"
||[[Bulgaria]]||10.00||Banks shall maintain minimum required reserves to the amount of 10% of the deposit base <br> (effective from December 1, 2008) with two exceptions (effective from January 1, 2009): <br>1. on funds attracted by banks from abroad: 5%; <br>2. on funds attracted from state and local government budgets: 0%.<ref>{{Cite web | url=http://bnb.bg/bnbweb/groups/public/documents/bnb_law/regulations_minimumrequired_en.pdf | title= Ordinance No. 21 of the BNB on the Minimum Required Reserves Maintained with the Bulgarian National Bank by Banks | work= Bulgarian National Bank}}</ref>
|- align="right"
||[[Croatia]]||14.00||Down from 17%, effective from 2009-01-14<ref>[http://www.hnb.hr/propisi/odluke-centralno/h-obvezna%20rezerva.pdf] (in Croatian)</ref>
|- align="right"
|[[Costa Rica]]||15.00||
|- align="right"
|[[Malawi]]||15.00||
|- align="right"
||[[Nepal]]||5.00||From the monetary policy announcement for FY 2011/12 CRR reduced from 5.5% to 5%
|- align="right"
|[[Hong Kong]]||18.00||
|- align="right"
||[[Brazil]]||20.00|| Up from 15%, effective from 2010-12-06 - Ratio is for requirement on term deposits.<ref>[http://www.businessweek.com/news/2010-12-03/brazil-banks-stocks-drop-on-reserve-requirement-raise.html Business week - Brazil reserve requirement raise]</ref><br>RRR for foreign currency positions increased to 43.00 on 2010 July 15 [http://www.businessweek.com/news/2010-07-22/brazil-signals-rate-increases-to-end-as-growth-cools.html]
|- align="right"
||[[China]]||20.50||Ratio is for major [[Chinese banks|Chinese Banks]] on 2012-02-24;<ref>[http://www.fxstreet.com/fundamental/analysis-reports/economics-weekly/2012/02/24/ China cut the required reserve ratio (RRR) for all banks by 50bp] http://www.fxstreet.com on Feb 22nd 2012</ref> down from a 21.5% high in June 2011.<br>Small and medium-size banks have a lower rate of 18.50%.
|- align="right"
||[[Tajikistan]]||20.00||
|- align="right"
||[[Suriname]]||25.00||Down from 27%, effective from 2007-01-01<ref>{{Cite web| url=http://www.cbvs.sr/english/publicaties-reserve.htm | title= Reserve base en Kasreserve | publisher=[[Centrale Bank van Suriname]] | accessdate=2009-12-21}}</ref>
|- align="right"
||[[Lebanon]]||30.00||[http://news.bbc.co.uk/2/hi/middle_east/7764657.stm]
|- align="right"
|}


Formally, if <math>\phi\colon G \to G</math> is an automorphism of ''G'' and <math>\rho \colon G \to \operatorname{GL}</math> is a representation, then <math>\rho^\phi := g \mapsto \rho(\phi(g))</math> is a representation. If <math>\phi = \phi_a</math> is an [[inner automorphism]] (conjugation by some element ''a''), then it acts trivially on representations, because representations are class functions (conjugation does not change their value). Thus a given class of outer automorphisms, it acts on the characters – because inner automorphisms act trivially, the action of the automorphism group Aut descends to the quotient Out.
===Historical changes in reserve ratios===
In some countries, the ''cash reserve ratios'' have decreased over time; in some countries they have increased:<ref>IMF Financial Statistic Yearbook</ref>
{| class="wikitable sortable"
|- align="center"
!Country||1968||1978||1988||1998
|- align="right"
|[[United Kingdom]]||20.5||15.9||5.0||3.1
|- align="right"
|[[Turkey]]||58.3||62.7||30.8||18.0
|- align="right"
|[[Germany]]||19.0||19.3||17.2||11.9
|- align="right"
|[[United States]]||12.3||10.1||8.5||10.3
|- align="right"
|[[India]]<ref>http://www.rbi.org.in/scripts/chro_bankrate.aspx Reserve Bank of India</ref>||3||6||10||10-11
|}
(Ratios are expressed in percentage points.)


This relation can be used both ways: given an outer automorphism, one can produce new representations (if the representation is not equal on conjugacy classes that are interchanged by the outer automorphism), and conversely, one can restrict possible outer automorphisms based on the character table.
==See also==
{{colbegin}}
* [[Bank regulation]]
* [[Basel accord]]s
* [[Capital Requirement]]
* [[Capital adequacy ratio]]
* [[Excess reserves]]
* [[Financial repression]]
* [[Fractional-reserve banking]]
* [[Full-reserve banking]]
* [[Islamic banking]]
* [[Monetary policy of central banks]]
* [[Money creation]]
* [[Money supply]]
* [[Negative interest on excess reserves]]
* [[Statutory Liquidity Ratio]]
* [[Tier 1 capital]]
* [[Tier 2 capital]]
{{colend}}


==References==
==References==
* {{cite book|last=Isaacs|first=I. Martin|title=Character Theory of Finite Groups|date=1976|publisher=Dover}}
{{Reflist|30em}}
* {{MathWorld|title=Character Table|urlname=CharacterTable|author=Rowland, Todd; Weisstein, Eric W}}
 
==External links==
* [http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&tpl=/ecfrbrowse/Title12/12cfr204_main_02.tpl Title 12 of the Code of Federal Regulations (12CFR) PART 204--RESERVE REQUIREMENTS OF DEPOSITORY INSTITUTIONS (REGULATION D)]  (See Section §204.4 for current reserve requirements.)
*[http://www.newyorkfed.org/aboutthefed/fedpoint/fed45.html Reserve Requirements - Fedpoints -  Federal Reserve Bank of New York]
*[http://www.federalreserve.gov/monetarypolicy/reservereq.htm Reserve Requirements - The Federal Reserve Board]
*[http://www.hussmanfunds.com/html/fedirrel.htm Hussman Funds - Why the Federal Reserve is Irrelevant - August 2001]
*[http://www.islamic-finance.com/item113_f.htm Don't mention the reserve ratio]
 
{{Central banks}}
{{Use dmy dates|date=September 2010}}


{{DEFAULTSORT:Character Table}}
{{DEFAULTSORT:Reserve Requirement}}
[[Category:Group theory]]
[[Category:Banking]]
[[Category:Monetary policy]]
[[Category:Financial ratios]]
[[Category:Financial economics]]

Revision as of 00:24, 13 August 2014

The reserve requirement (or cash reserve ratio) is a central bank regulation employed by most, but not all, of the world's central banks, that sets the minimum fraction of customer deposits and notes that each commercial bank must hold as reserves (rather than lend out). These required reserves are normally in the form of cash stored physically in a bank vault (vault cash) or deposits made with a central bank.

The required reserve ratio is sometimes used as a tool in monetary policy, influencing the country's borrowing and interest rates by changing the amount of funds available for banks to make loans with.[1] Western central banks rarely alter the reserve requirements because it would cause immediate liquidity problems for banks with low excess reserves; they generally prefer to use open market operations (buying and selling government-issued bonds) to implement their monetary policy. The People's Bank of China uses changes in reserve requirements as an inflation-fighting tool,[2] and raised the reserve requirement ten times in 2007 and eleven times since the beginning of 2010.

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

Effects on money supply

The conventional view

The economic theory that a reserve requirement can act as a tool of monetary policy is frequently found in economics textbooks. The higher the reserve requirement is set, the theory supposes, the less funds banks will have to loan outPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. , leading to lower money creation and perhaps ultimately to higher purchasing power of the money previously in use. The effect is multiplied, because money obtained as loan proceeds can be re-deposited; a portion of those deposits may again be loaned outPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park., and so on. The effect on the money supply is governed by the following formulas:

 : definitional relationship between monetary base MB (bank reserves plus currency held by the non-bank public) the narrowly defined money supply, ,
 : derived formula for the money multiplier m, the factor by which lending and re-lending leads to be a multiple of the monetary base:

where notationally,

the currency ratio: the ratio of the public's holdings of currency (undeposited cash) to the public's holdings of demand deposits; and
the total reserve ratio (the ratio of legally required plus non-required reserve holdings of banks to demand deposit liabilities of banks).

However, in the United States (and other countries except Brazil, China, India, Russia), the reserve requirements are generally not frequently altered to implement monetary policy because of the short-term disruptive effect on financial markets. Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

The endogenous money view

Some economists dispute the conventional theory of the reserve requirement. Criticisms of the conventional theory are usually associated with theories of endogenous money.

Jaromir Benes and Michael Kumhof of the IMF Research Department report that the “deposit multiplier“ of the undergraduate economics textbook, where monetary aggregates are created at the initiative of the central bank, through an initial injection of high-powered money into the banking system that gets multiplied through bank lending, turns the actual operation of the monetary transmission mechanism on its head. Most times when banks ask for replenishment of depleted reserves, the central bank obliges.[3] Reserves therefore impose no constraints as the deposit multiplier is simply, in the words of Kydland and Prescott (1990), a myth. And because of this, private banks are almost fully in control of the money creation process.[4]

Required reserves

United States

In the United States, a reserve requirement (or liquidity ratio) is a minimum value, set by the Board of Governors of the Federal Reserve System, of the ratio of required reserves to some category of deposits held at depository institutions (e.g., commercial bank including US branch of a foreign bank, savings and loan association, savings bank, credit union). The only deposit categories currently subject to reserve requirements are net transactions accounts, mainly checking accounts. The total amount of all net transaction accounts held in USA depository institutions, plus US currency held by the nonbank public, is called M1.

A depository institution can satisfy its reserve requirements by holding either vault cash or reserve deposits. An institution that is a member of the Federal Reserve System must hold its reserve deposits at a Federal Reserve Bank. Nonmember institutions can elect to hold their reserve deposits at a member institution on a pass-through basis.[5]

A depository institution's reserve requirements vary by the dollar amount of net transaction accounts held at that institution. Effective January 23, 2014, institutions with net transactions accounts:

  • Of less than $13.3 million have no minimum reserve requirement;
  • Between $13.3 million and $89.0 million must have a liquidity ratio of 3%;
  • Exceeding $89.0 million must have a liquidity ratio of 10%.[5]

The numerical amounts stated above are recalculated annually according to a statutory formula.

Effective December 27, 1990, a liquidity ratio of zero has applied to CDs, savings deposits, and time deposits, owned by entities other than households, and the Eurocurrency liabilities of depository institutions. Deposits owned by foreign corporations or governments are currently not subject to reserve requirements.[5]

When an institution fails to satisfy its reserve requirements, it can make up its deficiency with reserves borrowed either from a Federal Reserve Bank, or from an institution holding reserves in excess of reserve requirements. Such loans are typically due in 24 hours or less.

An institution's overnight reserves, averaged over some maintenance period, must equal or exceed its average required reserves, calculated over the same maintenance period. If this calculation is satisfied, there is no requirement that reserves be held at any point in time. Hence reserve requirements play only a limited role in money creation in the USA - and since quantitative easing began in 2008, they have been even less important, as an enormous glut of excess reserves now exists (over the whole system; theoretically, though, individual banks may still run into temporary shortfalls).

The International Banking Act of 1978 requires branches of foreign banks operating in the US to follow the same required reserve ratio standards.[6][7]

Countries without reserve requirements

Canada, the UK, New Zealand, Australia and Sweden have no reserve requirements.

This does not mean that banks can - even in theory - create money without limit. On the contrary: banks are constrained by capital requirements, which are arguably more important than reserve requirements even in countries that have reserve requirements.

It also does not mean that a commercial bank's overnight reserves can become negative, in these countries. On the contrary: the central bank will always step in to lend the necessary reserves if necessary so that this does not happen: this is sometimes described as "defending the payment system". Historically, a central bank might once have run out of reserves to lend and so have had to suspend redemptions, but this cannot happen anymore to modern central banks because of the end of the gold standard worldwide, which means that all nations use a fiat currency.

It is sometimes argued that the requirement not to have a negative reserve balance at the central bank constitutes a reserve requirement of zero. However, mathematically, a requirement to hold zero reserves does not correspond to any ratio; it is more permissive than any ratio. So this can be true only if a broader definition of reserve requirement is adopted. Moreover, such a zero reserve requirement cannot be explained by a theory that holds that monetary policy works by varying the quantity of money using the reserve requirement.

Even in the United States, which retains formal (though now mostly irrelevant) reserve requirements, the notion of controlling the money supply by targeting the quantity of base money fell out of favour many years ago, and now the pragmatic explanation of monetary policy refers to targeting the interest rate to control the broad money supply.

United Kingdom

In the UK the term clearing banks is sometimes used, meaning banks that have direct access to the clearing system. However, for the purposes of clarity, the term commercial banks will be used for the remainder of this section.

The Bank of England, which is the central bank for the entire United Kingdom, previously held to a voluntary reserve ratio system, with no minimum reserve requirement set. In theory, this meant that commercial banks could retain zero reserves. However, the average cash reserve ratio across the entire United Kingdom banking system was higher during that period, at about 0.15% Template:Asof.[8]

From 1971 to 1980, the commercial banks all agreed to a reserve ratio of 1.5%. However, in 1981 this requirement was abolished.[8]

From 1981 to 2009, each commercial bank set out its own monthly voluntary reserve target in a contract with the Bank of England. Both shortfalls and excesses of reserves relative to the commercial bank's own target over an averaging period of one day[8] would result in a charge, incentivising the commercial bank to stay near its target, a system known as reserves averaging.

Upon the parallel introduction of quantitative easing and interest on excess reserves in 2009, banks were no longer required to set out a target, and so were no longer penalised for holding excess reserves; indeed, they were proportionally compensated for holding all their reserves at the Bank Rate (the Bank of England now uses the same interest rate for its bank rate, its deposit rate and its interest rate target).[9] Indeed, in the absence of an agreed target, the concept of excess reserves does not really apply to the Bank of England any more, so it is technically incorrect to call its new policy "interest on excess reserves".

Canada

Canada abolished its reserve requirement in 1992.[8]

Other countries

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[10]):

Country Required reserve (in %) Note
Australia None Statutory Reserve Deposits abolished in 1988,
replaced with 1% Non-callable Deposits[11]
New Zealand None

1999 [1]

Sweden None
Eurozone 1.00 Effective January 18, 2012.[12] Down from 2% since Jan 1999.
Czech Republic 2.00 Since October 7, 2009
Hungary 2.00 Since November 2008
South Africa 2.50
Switzerland 2.50
Latvia 3.00 Just after the Parex Bank bailout (24.12.2008), Latvian Central Bank
decreased the RRR from 7% (?) down to 3%[13]
Poland 3.50 as of 31 dec 2010 [14]
Romania 10.00 as of 30 jan 2013 for lei. And 16% for foreign currency[15]
Russia 4.00 Effective April 1, 2011, up from 2.5% in January 2011.[16]
Chile 4.50
India 4.00 January 2013, as per RBI.[17]
Bangladesh 6.00 Raised from 5.50. Effective from 15 December 2010
Lithuania 6.00
Nigeria 20.00 Raised from 15.00. Effective from 25 November 2014[18]
Pakistan 5.00 Since November 1, 2008
Taiwan 7.00 [19]
Turkey 8.50 Since February 19, 2013
Jordan 8.00
Zambia 8.00
Burundi 8.50
Ghana 9.00
Israel 9.00 the Required Reserve Ratio is called Minimum Capital Ratio[20]
Mexico 10.50
Sri Lanka 8.00 With effect from 29 April 2011. 8% of total rupee deposit liabilities.
Bulgaria 10.00 Banks shall maintain minimum required reserves to the amount of 10% of the deposit base
(effective from December 1, 2008) with two exceptions (effective from January 1, 2009):
1. on funds attracted by banks from abroad: 5%;
2. on funds attracted from state and local government budgets: 0%.[21]
Croatia 14.00 Down from 17%, effective from 2009-01-14[22]
Costa Rica 15.00
Malawi 15.00
Nepal 5.00 From the monetary policy announcement for FY 2011/12 CRR reduced from 5.5% to 5%
Hong Kong 18.00
Brazil 20.00 Up from 15%, effective from 2010-12-06 - Ratio is for requirement on term deposits.[23]
RRR for foreign currency positions increased to 43.00 on 2010 July 15 [2]
China 20.50 Ratio is for major Chinese Banks on 2012-02-24;[24] down from a 21.5% high in June 2011.
Small and medium-size banks have a lower rate of 18.50%.
Tajikistan 20.00
Suriname 25.00 Down from 27%, effective from 2007-01-01[25]
Lebanon 30.00 [3]

Historical changes in reserve ratios

In some countries, the cash reserve ratios have decreased over time; in some countries they have increased:[26]

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
India[27] 3 6 10 10-11

(Ratios are expressed in percentage points.)

See also

Template:Colbegin

Template:Colend

References

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External links

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  1. ↑ Central Bank of Russia
  2. ↑ Template:Cite news
  3. ↑ Benes, Jaromir, and Michael Kumhof. The chicago plan revisited. International Monetary Fund, 2012.‏ http://www.imf.org/external/pubs/ft/wp/2012/wp12202.pdf
  4. ↑ Benes, Kumhof. http://www.imf.org/external/pubs/ft/wp/2012/wp12202.pdf
  5. ↑ 5.0 5.1 5.2 FRB: Reserve Requirements
  6. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

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  7. ↑ Template:Cite web
  8. ↑ 8.0 8.1 8.2 8.3 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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  9. ↑ Template:Cite web
  10. ↑ Monetary Macroeconomics by Dr. Pinar Yesin
  11. ↑ "Inquiry into the Australian Banking Industry, Reserve Bank of Australia, January 1991
  12. ↑ <en> European Central Bank, minimum reserve requirements
  13. ↑ Template:Cite web
  14. ↑ Narodowy Bank Polski - Internet Information Service
  15. ↑ http://www.bnr.ro/Reserve-requirements-3658.aspx
  16. ↑ Central bank of Russia Required reserve ratio on credit institutions' liabilities to non-resident has been raised to 4.0%
  17. ↑ [4] ndtv.com
  18. ↑ http://businessdayonline.com/2014/11/banks-squeezed-further-as-n40bn-may-vanish-from-industry-wide-profits/#.VHbDB51fqUk
  19. ↑ Liquidity ratio and liquid reserves of deposit money banks. Data released by Taiwan's central bank in October 2010.
  20. ↑ Template:Cite web
  21. ↑ Template:Cite web
  22. ↑ [5] (in Croatian)
  23. ↑ Business week - Brazil reserve requirement raise
  24. ↑ China cut the required reserve ratio (RRR) for all banks by 50bp http://www.fxstreet.com on Feb 22nd 2012
  25. ↑ Template:Cite web
  26. ↑ IMF Financial Statistic Yearbook
  27. ↑ http://www.rbi.org.in/scripts/chro_bankrate.aspx Reserve Bank of India
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