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Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts in a particular country or socio - economic context ,  or is easily converted to such a form .  The main functions of money are distinguished as :  a medium of exchange ;  a unit of account ;  a store of value ;  and ,  sometimes ,  a standard of deferred payment .  Any item or verifiable record that fulfills these functions can be considered as money . 
Money is historically an emergent market phenomenon establishing a commodity money ,  but nearly all contemporary money systems are based on fiat money .  Fiat money ,  like any check or note of debt ,  is without use value as a physical commodity .  It derives its value by being declared by a government to be legal tender ;  that is ,  it must be accepted as a form of payment within the boundaries of the country ,  for  " all debts ,  public and private "  . 
The money supply of a country consists of currency  ( banknotes and coins )  and ,  depending on the particular definition used ,  one or more types of bank money  ( the balances held in checking accounts ,  savings accounts ,  and other types of bank accounts )  .  Bank money ,  which consists only of records  ( mostly computerized in modern banking )  ,  forms by far the largest part of broad money in developed countries . 


The word  " money "  is believed to originate from a temple of Juno ,  on Capitoline ,  one of Rome ' s seven hills .  In the ancient world Juno was often associated with money .  The temple of Juno Moneta at Rome was the place where the mint of Ancient Rome was located .  The name  " Juno "  may derive from the Etruscan goddess Uni  ( which means  " the one "  ,   " unique "  ,   " unit "  ,   " union "  ,   " united "  )  and  " Moneta "  either from the Latin word  " monere "   ( remind ,  warn ,  or instruct )  or the Greek word  " moneres "   ( alone ,  unique )  . 
In the Western world ,  a prevalent term for coin - money has been specie ,  stemming from Latin in specie ,  meaning  ' in kind '  . 
The use of barter - like methods may date back to at least 100 , 000 years ago ,  though there is no evidence of a society or economy that relied primarily on barter .  Instead ,  non - monetary societies operated largely along the principles of gift economy and debt .  When barter did in fact occur ,  it was usually between either complete strangers or potential enemies . 
Many cultures around the world eventually developed the use of commodity money .  The Mesopotamian shekel was a unit of weight ,  and relied on the mass of something like 160 grains of barley .  The first usage of the term came from Mesopotamia circa 3000 BC .  Societies in the Americas ,  Asia ,  Africa and Australia used shell money – often ,  the shells of the cowry  ( Cypraea moneta L .  or C .  annulus L .  )  .  According to Herodotus ,  the Lydians were the first people to introduce the use of gold and silver coins .  It is thought by modern scholars that these first stamped coins were minted around 650–600 BC . 
The system of commodity money eventually evolved into a system of representative money .  This occurred because gold and silver merchants or banks would issue receipts to their depositors – redeemable for the commodity money deposited .  Eventually ,  these receipts became generally accepted as a means of payment and were used as money .  Paper money or banknotes were first used in China during the Song Dynasty .  These banknotes ,  known as  " jiaozi "  ,  evolved from promissory notes that had been used since the 7th century .  However ,  they did not displace commodity money ,  and were used alongside coins .  In the 13th century ,  paper money became known in Europe through the accounts of travelers ,  such as Marco Polo and William of Rubruck .  Marco Polo ' s account of paper money during the Yuan Dynasty is the subject of a chapter of his book ,  The Travels of Marco Polo ,  titled  " How the Great Kaan Causeth the Bark of Trees ,  Made Into Something Like Paper ,  to Pass for Money All Over his Country .  "  Banknotes were first issued in Europe by Stockholms Banco in 1661 ,  and were again also used alongside coins .  The gold standard ,  a monetary system where the medium of exchange are paper notes that are convertible into pre - set ,  fixed quantities of gold ,  replaced the use of gold coins as currency in the 17th - 19th centuries in Europe .  These gold standard notes were made legal tender ,  and redemption into gold coins was discouraged .  By the beginning of the 20th century almost all countries had adopted the gold standard ,  backing their legal tender notes with fixed amounts of gold . 
After World War II and the Bretton Woods Conference ,  most countries adopted fiat currencies that were fixed to the US dollar .  The US dollar was in turn fixed to gold .  In 1971 the US government suspended the convertibility of the US dollar to gold .  After this many countries de - pegged their currencies from the US dollar ,  and most of the world ' s currencies became unbacked by anything except the governments '  fiat of legal tender and the ability to convert the money into goods via payment .  According to proponents of modern money theory ,  fiat money is also backed by taxes .  By imposing taxes ,  states create demand for the currency they issue . 
In Money and the Mechanism of Exchange  ( 1875 )  ,  William Stanley Jevons famously analyzed money in terms of four functions :  a medium of exchange ,  a common measure of value  ( or unit of account )  ,  a standard of value  ( or standard of deferred payment )  ,  and a store of value .  By 1919 ,  Jevons ' s four functions of money were summarized in the couplet : 
This couplet would later become widely popular in macroeconomics textbooks .  Most modern textbooks now list only three functions ,  that of medium of exchange ,  unit of account ,  and store of value ,  not considering a standard of deferred payment as it is a distinguished function ,  but rather subsuming it in the others . 
There have been many historical disputes regarding the combination of money ' s functions ,  some arguing that they need more separation and that a single unit is insufficient to deal with them all .  One of these arguments is that the role of money as a medium of exchange is in conflict with its role as a store of value :  its role as a store of value requires holding it without spending ,  whereas its role as a medium of exchange requires it to circulate .  Others argue that storing of value is just deferral of the exchange ,  but does not diminish the fact that money is a medium of exchange that can be transported both across space and time .  The term  " financial capital "  is a more general and inclusive term for all liquid instruments ,  whether or not they are a uniformly recognized tender . 
When money is used to intermediate the exchange of goods and services ,  it is performing a function as a medium of exchange .  It thereby avoids the inefficiencies of a barter system ,  such as the  " coincidence of wants "  problem .  Money ' s most important usage is as a method for comparing the values of dissimilar objects . 
A unit of account  ( in economics )  is a standard numerical monetary unit of measurement of the market value of goods ,  services ,  and other transactions .  Also known as a  " measure "  or  " standard "  of relative worth and deferred payment ,  a unit of account is a necessary prerequisite for the formulation of commercial agreements that involve debt . 
Money acts as a standard measure and common denomination of trade .  It is thus a basis for quoting and bargaining of prices .  It is necessary for developing efficient accounting systems . 
While standard of deferred payment is distinguished by some texts ,  particularly older ones ,  other texts subsume this under other functions .  A  " standard of deferred payment "  is an accepted way to settle a debt – a unit in which debts are denominated ,  and the status of money as legal tender ,  in those jurisdictions which have this concept ,  states that it may function for the discharge of debts .  When debts are denominated in money ,  the real value of debts may change due to inflation and deflation ,  and for sovereign and international debts via debasement and devaluation . 
To act as a store of value ,  a money must be able to be reliably saved ,  stored ,  and retrieved – and be predictably usable as a medium of exchange when it is retrieved .  The value of the money must also remain stable over time .  Some have argued that inflation ,  by reducing the value of money ,  diminishes the ability of the money to function as a store of value . 
In economics ,  money is a broad term that refers to any financial instrument that can fulfill the functions of money  ( detailed above )  .  These financial instruments together are collectively referred to as the money supply of an economy .  In other words ,  the money supply is the number of financial instruments within a specific economy available for purchasing goods or services .  Since the money supply consists of various financial instruments  ( usually currency ,  demand deposits and various other types of deposits )  ,  the amount of money in an economy is measured by adding together these financial instruments creating a monetary aggregate . 
Modern monetary theory distinguishes among different ways to measure the money supply ,  reflected in different types of monetary aggregates ,  using a categorization system that focuses on the liquidity of the financial instrument used as money .  The most commonly used monetary aggregates  ( or types of money )  are conventionally designated M1 ,  M2 and M3 .  These are successively larger aggregate categories :  M1 is currency  ( coins and bills )  plus demand deposits  ( such as checking accounts )  ;  M2 is M1 plus savings accounts and time deposits under  $ 100 , 000 ;  and M3 is M2 plus larger time deposits and similar institutional accounts .  M1 includes only the most liquid financial instruments ,  and M3 relatively illiquid instruments .  The precise definition of M1 ,  M2 etc .  may be different in different countries . 
Another measure of money ,  M0 ,  is also used ;  unlike the other measures ,  it does not represent actual purchasing power by firms and households in the economy .  M0 is base money ,  or the amount of money actually issued by the central bank of a country .  It is measured as currency plus deposits of banks and other institutions at the central bank .  M0 is also the only money that can satisfy the reserve requirements of commercial banks . 
 " Market liquidity "  describes how easily an item can be traded for another item ,  or into the common currency within an economy .  Money is the most liquid asset because it is universally recognised and accepted as the common currency .  In this way ,  money gives consumers the freedom to trade goods and services easily without having to barter . 
Liquid financial instruments are easily tradable and have low transaction costs .  There should be no  ( or minimal )  spread between the prices to buy and sell the instrument being used as money . 
Currently ,  most modern monetary systems are based on fiat money .  However ,  for most of history ,  almost all money was commodity money ,  such as gold and silver coins .  As economies developed ,  commodity money was eventually replaced by representative money ,  such as the gold standard ,  as traders found the physical transportation of gold and silver burdensome .  Fiat currencies gradually took over in the last hundred years ,  especially since the breakup of the Bretton Woods system in the early 1970s . 
Many items have been used as commodity money such as naturally scarce precious metals ,  conch shells ,  barley ,  beads etc .  ,  as well as many other things that are thought of as having value .  Commodity money value comes from the commodity out of which it is made .  The commodity itself constitutes the money ,  and the money is the commodity .  Examples of commodities that have been used as mediums of exchange include gold ,  silver ,  copper ,  rice ,  Wampum ,  salt ,  peppercorns ,  large stones ,  decorated belts ,  shells ,  alcohol ,  cigarettes ,  cannabis ,  candy ,  etc .  These items were sometimes used in a metric of perceived value in conjunction to one another ,  in various commodity valuation or price system economies .  Use of commodity money is similar to barter ,  but a commodity money provides a simple and automatic unit of account for the commodity which is being used as money .  Although some gold coins such as the Krugerrand are considered legal tender ,  there is no record of their face value on either side of the coin .  The rationale for this is that emphasis is laid on their direct link to the prevailing value of their fine gold content .  American Eagles are imprinted with their gold content and legal tender face value . 
In 1875 ,  the British economist William Stanley Jevons described the money used at the time as  " representative money "  .  Representative money is money that consists of token coins ,  paper money or other physical tokens such as certificates ,  that can be reliably exchanged for a fixed quantity of a commodity such as gold or silver .  The value of representative money stands in direct and fixed relation to the commodity that backs it ,  while not itself being composed of that commodity . 
Fiat money or fiat currency is money whose value is not derived from any intrinsic value or guarantee that it can be converted into a valuable commodity  ( such as gold )  .  Instead ,  it has value only by government order  ( fiat )  .  Usually ,  the government declares the fiat currency  ( typically notes and coins from a central bank ,  such as the Federal Reserve System in the US )  to be legal tender ,  making it unlawful not to accept the fiat currency as a means of repayment for all debts ,  public and private . 
Some bullion coins such as the Australian Gold Nugget and American Eagle are legal tender ,  however ,  they trade based on the market price of the metal content as a commodity ,  rather than their legal tender face value  ( which is usually only a small fraction of their bullion value )  . 
Fiat money ,  if physically represented in the form of currency  ( paper or coins )  can be accidentally damaged or destroyed .  However ,  fiat money has an advantage over representative or commodity money ,  in that the same laws that created the money can also define rules for its replacement in case of damage or destruction .  For example ,  the US government will replace mutilated Federal Reserve Notes  ( US fiat money )  if at least half of the physical note can be reconstructed ,  or if it can be otherwise proven to have been destroyed .  By contrast ,  commodity money which has been lost or destroyed cannot be recovered . 
These factors led to the shift of the store of value being the metal itself :  at first silver ,  then both silver and gold ,  and at one point there was bronze as well .  Now we have copper coins and other non - precious metals as coins .  Metals were mined ,  weighed ,  and stamped into coins .  This was to assure the individual taking the coin that he was getting a certain known weight of precious metal .  Coins could be counterfeited ,  but they also created a new unit of account ,  which helped lead to banking .  Archimedes '  principle provided the next link :  coins could now be easily tested for their fine weight of metal ,  and thus the value of a coin could be determined ,  even if it had been shaved ,  debased or otherwise tampered with  ( see Numismatics )  . 
In most major economies using coinage ,  copper ,  silver and gold formed three tiers of coins .  Gold coins were used for large purchases ,  payment of the military and backing of state activities .  Silver coins were used for midsized transactions ,  and as a unit of account for taxes ,  dues ,  contracts and fealty ,  while copper coins represented the coinage of common transaction .  This system had been used in ancient India since the time of the Mahajanapadas .  In Europe ,  this system worked through the medieval period because there was virtually no new gold ,  silver or copper introduced through mining or conquest .  Thus the overall ratios of the three coinages remained roughly equivalent . 
In premodern China ,  the need for credit and for circulating a medium that was less of a burden than exchanging thousands of copper coins led to the introduction of paper money ,  commonly known today as banknotes .  This economic phenomenon was a slow and gradual process that took place from the late Tang Dynasty  ( 618–907 )  into the Song Dynasty  ( 960–1279 )  .  It began as a means for merchants to exchange heavy coinage for receipts of deposit issued as promissory notes from shops of wholesalers ,  notes that were valid for temporary use in a small regional territory .  In the 10th century ,  the Song Dynasty government began circulating these notes amongst the traders in their monopolized salt industry .  The Song government granted several shops the sole right to issue banknotes ,  and in the early 12th century the government finally took over these shops to produce state - issued currency .  Yet the banknotes issued were still regionally valid and temporary ;  it was not until the mid 13th century that a standard and uniform government issue of paper money was made into an acceptable nationwide currency .  The already widespread methods of woodblock printing and then Pi Sheng ' s movable type printing by the 11th century was the impetus for the massive production of paper money in premodern China . 
At around the same time in the medieval Islamic world ,  a vigorous monetary economy was created during the 7th–12th centuries on the basis of the expanding levels of circulation of a stable high - value currency  ( the dinar )  .  Innovations introduced by Muslim economists ,  traders and merchants include the earliest uses of credit ,  cheques ,  promissory notes ,  savings accounts ,  transactional accounts ,  loaning ,  trusts ,  exchange rates ,  the transfer of credit and debt ,  and banking institutions for loans and deposits . 
In Europe ,  paper money was first introduced in Sweden in 1661 .  Sweden was rich in copper ,  thus ,  because of copper ' s low value ,  extraordinarily big coins  ( often weighing several kilograms )  had to be made .  The advantages of paper currency were numerous :  it reduced transport of gold and silver ,  and thus lowered the risks ;  it made loaning gold or silver at interest easier ,  since the specie  ( gold or silver )  never left the possession of the lender until someone else redeemed the note ;  and it allowed for a division of currency into credit and specie backed forms .  It enabled the sale of stock in joint stock companies ,  and the redemption of those shares in paper . 
However ,  these advantages held within them disadvantages .  First ,  since a note has no intrinsic value ,  there was nothing to stop issuing authorities from printing more of it than they had specie to back it with .  Second ,  because it increased the money supply ,  it increased inflationary pressures ,  a fact observed by David Hume in the 18th century .  The result is that paper money would often lead to an inflationary bubble ,  which could collapse if people began demanding hard money ,  causing the demand for paper notes to fall to zero .  The printing of paper money was also associated with wars ,  and financing of wars ,  and therefore regarded as part of maintaining a standing army .  For these reasons ,  paper currency was held in suspicion and hostility in Europe and America .  It was also addictive ,  since the speculative profits of trade and capital creation were quite large .  Major nations established mints to print money and mint coins ,  and branches of their treasury to collect taxes and hold gold and silver stock . 
At this time both silver and gold were considered legal tender ,  and accepted by governments for taxes .  However ,  the instability in the ratio between the two grew over the course of the 19th century ,  with the increase both in supply of these metals ,  particularly silver ,  and of trade .  This is called bimetallism and the attempt to create a bimetallic standard where both gold and silver backed currency remained in circulation occupied the efforts of inflationists .  Governments at this point could use currency as an instrument of policy ,  printing paper currency such as the United States Greenback ,  to pay for military expenditures .  They could also set the terms at which they would redeem notes for specie ,  by limiting the amount of purchase ,  or the minimum amount that could be redeemed . 
By 1900 ,  most of the industrializing nations were on some form of gold standard ,  with paper notes and silver coins constituting the circulating medium .  Private banks and governments across the world followed Gresham ' s Law :  keeping gold and silver paid ,  but paying out in notes .  This did not happen all around the world at the same time ,  but occurred sporadically ,  generally in times of war or financial crisis ,  beginning in the early part of the 20th century and continuing across the world until the late 20th century ,  when the regime of floating fiat currencies came into force .  One of the last countries to break away from the gold standard was the United States in 1971 . 
No country anywhere in the world today has an enforceable gold standard or silver standard currency system . 
Commercial bank money or demand deposits are claims against financial institutions that can be used for the purchase of goods and services .  A demand deposit account is an account from which funds can be withdrawn at any time by check or cash withdrawal without giving the bank or financial institution any prior notice .  Banks have the legal obligation to return funds held in demand deposits immediately upon demand  ( or  ' at call '  )  .  Demand deposit withdrawals can be performed in person ,  via checks or bank drafts ,  using automatic teller machines  ( ATMs )  ,  or through online banking . 
Commercial bank money is created through fractional - reserve banking ,  the banking practice where banks keep only a fraction of their deposits in reserve  ( as cash and other highly liquid assets )  and lend out the remainder ,  while maintaining the simultaneous obligation to redeem all these deposits upon demand .  Commercial bank money differs from commodity and fiat money in two ways :  firstly it is non - physical ,  as its existence is only reflected in the account ledgers of banks and other financial institutions ,  and secondly ,  there is some element of risk that the claim will not be fulfilled if the financial institution becomes insolvent .  The process of fractional - reserve banking has a cumulative effect of money creation by commercial banks ,  as it expands money supply  ( cash and demand deposits )  beyond what it would otherwise be .  Because of the prevalence of fractional reserve banking ,  the broad money supply of most countries is a multiple larger than the amount of base money created by the country ' s central bank .  That multiple  ( called the money multiplier )  is determined by the reserve requirement or other financial ratio requirements imposed by financial regulators . 
The money supply of a country is usually held to be the total amount of currency in circulation plus the total value of checking and savings deposits in the commercial banks in the country .  In modern economies ,  relatively little of the money supply is in physical currency .  For example ,  in December 2010 in the US ,  of the  $ 8853 . 4 billion in broad money supply  ( M2 )  ,  only  $ 915 . 7 billion  ( about 10 %  )  consisted of physical coins and paper money . 
Many digital currencies ,  in particular Flooz and Beenz ,  had gained momentum before the Dot - com bubble of the early 2000s .  Not much innovation occurred until the conception of Bitcoin in 2009 ,  which introduced the concept of a cryptocurrency . 
When gold and silver are used as money ,  the money supply can grow only if the supply of these metals is increased by mining .  This rate of increase will accelerate during periods of gold rushes and discoveries ,  such as when Columbus discovered the New World and brought back gold and silver to Spain ,  or when gold was discovered in California in 1848 .  This causes inflation ,  as the value of gold goes down .  However ,  if the rate of gold mining cannot keep up with the growth of the economy ,  gold becomes relatively more valuable ,  and prices  ( denominated in gold )  will drop ,  causing deflation .  Deflation was the more typical situation for over a century when gold and paper money backed by gold were used as money in the 18th and 19th centuries . 
Modern day monetary systems are based on fiat money and are no longer tied to the value of gold .  The control of the amount of money in the economy is known as monetary policy .  Monetary policy is the process by which a government ,  central bank ,  or monetary authority manages the money supply to achieve specific goals .  Usually the goal of monetary policy is to accommodate economic growth in an environment of stable prices .  For example ,  it is clearly stated in the Federal Reserve Act that the Board of Governors and the Federal Open Market Committee should seek  " to promote effectively the goals of maximum employment ,  stable prices ,  and moderate long - term interest rates .  " 
A failed monetary policy can have significant detrimental effects on an economy and the society that depends on it .  These include hyperinflation ,  stagflation ,  recession ,  high unemployment ,  shortages of imported goods ,  inability to export goods ,  and even total monetary collapse and the adoption of a much less efficient barter economy .  This happened in Russia ,  for instance ,  after the fall of the Soviet Union . 
Governments and central banks have taken both regulatory and free market approaches to monetary policy .  Some of the tools used to control the money supply include : 
In the US ,  the Federal Reserve is responsible for controlling the money supply ,  while in the Euro area the respective institution is the European Central Bank .  Other central banks with significant impact on global finances are the Bank of Japan ,  People ' s Bank of China and the Bank of England . 
For many years much of monetary policy was influenced by an economic theory known as monetarism .  Monetarism is an economic theory which argues that management of the money supply should be the primary means of regulating economic activity .  The stability of the demand for money prior to the 1980s was a key finding of Milton Friedman and Anna Schwartz supported by the work of David Laidler ,  and many others .  The nature of the demand for money changed during the 1980s owing to technical ,  institutional ,  and legal factors and the influence of monetarism has since decreased . 
Counterfeit money is imitation currency produced without the legal sanction of the state or government .  Producing or using counterfeit money is a form of fraud or forgery .  Counterfeiting is almost as old as money itself .  Plated copies  ( known as Fourrées )  have been found of Lydian coins which are thought to be among the first western coins .  Before the introduction of paper money ,  the most prevalent method of counterfeiting involved mixing base metals with pure gold or silver .  A form of counterfeiting is the production of documents by legitimate printers in response to fraudulent instructions .  During World War II ,  the Nazis forged British pounds and American dollars .  Today some of the finest counterfeit banknotes are called Superdollars because of their high quality and likeness to the real US dollar .  There has been significant counterfeiting of Euro banknotes and coins since the launch of the currency in 2002 ,  but considerably less than for the US dollar . 
Money laundering is the process in which the proceeds of crime are transformed into ostensibly legitimate money or other assets .  However ,  in a number of legal and regulatory systems the term money laundering has become conflated with other forms of financial crime ,  and sometimes used more generally to include misuse of the financial system  ( involving things such as securities ,  digital currencies ,  credit cards ,  and traditional currency )  ,  including terrorism financing ,  tax evasion and evading of international sanctions . 
In finance ,  the capital asset pricing model  ( CAPM )  is a model used to determine a theoretically appropriate required rate of return of an asset ,  to make decisions about adding assets to a well - diversified portfolio . 


The model takes into account the asset ' s sensitivity to non - diversifiable risk  ( also known as systematic risk or market risk )  ,  often represented by the quantity beta  ( β )  in the financial industry ,  as well as the expected return of the market and the expected return of a theoretical risk - free asset .  CAPM assumes a particular form of utility functions  ( in which only first and second moments matter ,  that is risk is measured by variance ,  for example a quadratic utility )  or alternatively asset returns whose probability distributions are completely described by the first two moments  ( for example ,  the normal distribution )  and zero transaction costs  ( necessary for diversification to get rid of all idiosyncratic risk )  .  Under these conditions ,  CAPM shows that the cost of equity capital is determined only by beta .  Despite it failing numerous empirical tests ,  and the existence of more modern approaches to asset pricing and portfolio selection  ( such as arbitrage pricing theory and Merton ' s portfolio problem )  ,  the CAPM still remains popular due to its simplicity and utility in a variety of situations . 
The CAPM was introduced by Jack Treynor  ( 1961 ,  1962 )  ,  William F .  Sharpe  ( 1964 )  ,  John Lintner  ( 1965a , b )  and Jan Mossin  ( 1966 )  independently ,  building on the earlier work of Harry Markowitz on diversification and modern portfolio theory .  Sharpe ,  Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics .  Fischer Black  ( 1972 )  developed another version of CAPM ,  called Black CAPM or zero - beta CAPM ,  that does not assume the existence of a riskless asset .  This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM . 
The CAPM is a model for pricing an individual security or portfolio .  For individual securities ,  we make use of the security market line  ( SML )  and its relation to expected return and systematic risk  ( beta )  to show how the market must price individual securities in relation to their security risk class .  The SML enables us to calculate the reward - to - risk ratio for any security in relation to that of the overall market .  Therefore ,  when the expected rate of return for any security is deflated by its beta coefficient ,  the reward - to - risk ratio for any individual security in the market is equal to the market reward - to - risk ratio ,  thus : 
The market reward - to - risk ratio is effectively the market risk premium and by rearranging the above equation and solving for  ,  we obtain the capital asset pricing model  ( CAPM )  . 
where : 
Restated ,  in terms of risk premium ,  we find that : 
which states that the individual risk premium equals the market premium times β . 
Note 1 :  the expected market rate of return is usually estimated by measuring the arithmetic average of the historical returns on a market portfolio  ( e . g .  S&P 500 )  . 
Note 2 :  the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return . 
For the full derivation see Modern portfolio theory . 
CAPM can be modified to include size premium and specific risk .  This is important for investors in privately held companies who often do not hold a well - diversified portfolio .  The equation is similar to the traditional CAPM equation  " with the market risk premium replaced by the product of beta times the market risk premium "  : 
 " where : 
The SML essentially graphs the results from the capital asset pricing model  ( CAPM )  formula .  The x - axis represents the risk  ( beta )  ,  and the y - axis represents the expected return .  The market risk premium is determined from the slope of the SML . 
The relationship between β and required return is plotted on the securities market line  ( SML )  ,  which shows expected return as a function of β .  The intercept is the nominal risk - free rate available for the market ,  while the slope is the market premium ,  E ( Rm ) − Rf .  The securities market line can be regarded as representing a single - factor model of the asset price ,  where Beta is exposure to changes in value of the Market .  The equation of the SML is thus : 
It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk .  Individual securities are plotted on the SML graph .  If the security ' s expected return versus risk is plotted above the SML ,  it is undervalued since the investor can expect a greater return for the inherent risk .  And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed . 
Once the expected / required rate of return  is calculated using CAPM ,  we can compare this required rate of return to the asset ' s estimated rate of return over a specific investment horizon to determine whether it would be an appropriate investment .  To make this comparison ,  you need an independent estimate of the return outlook for the security based on either fundamental or technical analysis techniques ,  including P / E ,  M / B etc . 
Assuming that the CAPM is correct ,  an asset is correctly priced when its estimated price is the same as the present value of future cash flows of the asset ,  discounted at the rate suggested by CAPM .  If the estimated price is higher than the CAPM valuation ,  then the asset is undervalued  ( and overvalued when the estimated price is below the CAPM valuation )  .  When the asset does not lie on the SML ,  this could also suggest mis - pricing .  Since the expected return of the asset at time  is  ,  a higher expected return than what CAPM suggests indicates that  is too low  ( the asset is currently undervalued )  ,  assuming that at time  the asset returns to the CAPM suggested price . 
The asset price  using CAPM ,  sometimes called the certainty equivalent pricing formula ,  is a linear relationship given by
where  is the payoff of the asset or portfolio . 
The CAPM returns the asset - appropriate required return or discount rate—i . e .  the rate at which future cash flows produced by the asset should be discounted given that asset ' s relative riskiness .  Betas exceeding one signify more than average  " riskiness "  ;  betas below one indicate lower than average .  Thus ,  a more risky stock will have a higher beta and will be discounted at a higher rate ;  less sensitive stocks will have lower betas and be discounted at a lower rate .  Given the accepted concave utility function ,  the CAPM is consistent with intuition—investors  ( should )  require a higher return for holding a more risky asset . 
Since beta reflects asset - specific sensitivity to non - diversifiable ,  i . e .  market risk ,  the market as a whole ,  by definition ,  has a beta of one .  Stock market indices are frequently used as local proxies for the market—and in that case  ( by definition )  have a beta of one .  An investor in a large ,  diversified portfolio  ( such as a mutual fund )  ,  therefore ,  expects performance in line with the market . 
The risk of a portfolio comprises systematic risk ,  also known as undiversifiable risk ,  and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk .  Systematic risk refers to the risk common to all securities—i . e .  market risk .  Unsystematic risk is the risk associated with individual assets .  Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio  ( specific risks  " average out "  )  .  The same is not possible for systematic risk within one market .  Depending on the market ,  a portfolio of approximately 30–40 securities in developed markets such as the UK or US will render the portfolio sufficiently diversified such that risk exposure is limited to systematic risk only .  In developing markets a larger number is required ,  due to the higher asset volatilities . 
A rational investor should not take on any diversifiable risk ,  as only non - diversifiable risks are rewarded within the scope of this model .  Therefore ,  the required return on an asset ,  that is ,  the return that compensates for risk taken ,  must be linked to its riskiness in a portfolio context—i . e .  its contribution to overall portfolio riskiness—as opposed to its  " stand alone risk .  "  In the CAPM context ,  portfolio risk is represented by higher variance i . e .  less predictability .  In other words ,  the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor . 
The CAPM assumes that the risk - return profile of a portfolio can be optimized—an optimal portfolio displays the lowest possible level of risk for its level of return .  Additionally ,  since each additional asset introduced into a portfolio further diversifies the portfolio ,  the optimal portfolio must comprise every asset ,   ( assuming no trading costs )  with each asset value - weighted to achieve the above  ( assuming that any asset is infinitely divisible )  .  All such optimal portfolios ,  i . e .  ,  one for each level of return ,  comprise the efficient frontier . 
Because the unsystematic risk is diversifiable ,  the total risk of a portfolio can be viewed as beta . 
All investors : 
In their 2004 review ,  Fama and French argue that  " the failure of the CAPM in empirical tests implies that most applications of the model are invalid "  . 
In economics ,  capital goods ,  real capital ,  or capital assets are already - produced ,  durable goods or any non - financial asset that is used in production of goods or services . 
Adam Smith defines capital as  " That part of a man ' s stock which he expects to afford him revenue "  .  The term  " stock "  is derived from the Old English word for stump or tree trunk .  It has been used to refer to all the moveable property of a farm since at least 1510 .  In Middle Ages France contracted leases and loans bearing interest specified payment . 
How a capital good is maintained or returned to its pre - production state varies with the type of capital involved .  In most cases capital is replaced after a depreciation period as newer forms of capital make continued use of current capital non profitable .  It is also possible that advances make an obsolete form of capital practical again . 
Capital is distinct from land  ( or non - renewable resources )  in that capital can be increased by human labor .  At any given moment in time ,  total physical capital may be referred to as the capital stock  ( which is not to be confused with the capital stock of a business entity )  . 
In a fundamental sense ,  capital consists of any produced thing that can enhance a person ' s power to perform economically useful work—a stone or an arrow is capital for a caveman who can use it as a hunting instrument ,  and roads are capital for inhabitants of a city .  Capital is an input in the production function .  Homes and personal autos are not usually defined as capital but as durable goods because they are not used in a production of saleable goods and services . 
In Marxist political economy ,  capital is money used to buy something only in order to sell it again to realize a financial profit .  For Marx capital only exists within the process of economic exchange—it is wealth that grows out of the process of circulation itself ,  and for Marx it formed the basis of the economic system of capitalism .  In more contemporary schools of economics ,  this form of capital is generally referred to as  " financial capital "  and is distinguished from  " capital goods "  . 


Classical and neoclassical economics regard capital as one of the factors of production  ( alongside the other factors :  land and labour )  .  All other inputs to production are called intangibles in classical economics .  This includes organization ,  entrepreneurship ,  knowledge ,  goodwill ,  or management  ( which some characterize as talent ,  social capital or instructional capital )  . 
This is what makes it a factor of production : 
These distinctions of convenience have carried over to contemporary economic theory .  There was the further clarification that capital is a stock .  As such ,  its value can be estimated at a point in time .  By contrast ,  investment ,  as production to be added to the capital stock ,  is described as taking place over time  (  " per year "  )  ,  thus a flow . 
Marxian economics distinguishes between different forms of capital : 
Earlier illustrations often described capital as physical items ,  such as tools ,  buildings ,  and vehicles that are used in the production process .  Since at least the 1960s economists have increasingly focused on broader forms of capital .  For example ,  investment in skills and education can be viewed as building up human capital or knowledge capital ,  and investments in intellectual property can be viewed as building up intellectual capital .  These terms lead to certain questions and controversies discussed in those articles . 
Detailed classifications of capital that have been used in various theoretical or applied uses generally respect the following division : 
Public and private sector accounting differ in goals ,  time scales and accordingly in accounting .  The ownership and control of some forms of capital may accordingly justify differentiating it in an economic theory .  A blanket term that attempts to characterize all that clearly physical capital that is considered infrastructure and which supports production in unclear or poorly accounted ways is public capital .  This encompasses the aggregate body of all government - owned assets that are used to promote private industry productivity ,  including highways ,  railways ,  airports ,  water treatment facilities ,  telecommunications ,  electric grids ,  energy utilities ,  municipal buildings ,  public hospitals and schools ,  police ,  fire protection ,  courts and still others .  However it is a problematic term insofar as many of these assets can be either publicly or privately owned . 
Separate literatures have developed to describe both natural capital and social capital .  Such terms reflect a wide consensus that nature and society both function in such a similar manner as traditional industrial infrastructural capital ,  that it is entirely appropriate to refer to them as different types of capital in themselves .  In particular ,  they can be used in the production of other goods ,  are not used up immediately in the process of production ,  and can be enhanced  ( if not created )  by human effort . 
There is also a literature of intellectual capital and intellectual property law .  However ,  this increasingly distinguishes means of capital investment ,  and collection of potential rewards for patent ,  copyright  ( creative or individual capital )  ,  and trademark  ( social trust or social capital )  instruments . 
Economist Henry George argued that financial instruments like stocks ,  bonds ,  mortgages ,  promissory notes ,  or other certificates for transferring wealth is not really capital .  Because  " Their economic value merely represents the power of one class to appropriate the earnings of another .  "  and  " their increase or decrease does not affect the sum of wealth in the community "  . 
Some thinkers ,  such as Werner Sombart and Max Weber ,  locate the concept of capital as originating in double - entry bookkeeping ,  which is thus a foundational innovation in capitalism ,  Sombart writing in  " Medieval and Modern Commercial Enterprise "  that :