The Portfolio Theory also known as Modern Portfolio Theory was first developed by Harry Markowitz. He had introduced the theory in his paper ‘Portfolio Selection’ which was published in the Journal of Finance in 1952. In 1990, he along with Merton Miller and William Sharpe won the Nobel Prize in Economic Sciences for the Theory.
The theory suggests a hypothesis on the basis of which, expected return on a portfolio for a given amount of portfolio risk is attempted to be maximized or alternately the risk on a given level of expected return is attempted to be minimized. This is done so by choosing the quantities of various securities cautiously taking mainly into consideration the way in which the price of each security changes in comparison to that of every other security in the portfolio, rather than choosing securities individually. In other words, the theory uses mathematical models to construct an ideal portfolio for an investor that gives maximum return depending on his risk appetite by taking into consideration the relationship between risk and return. According to the theory, each security has its own risks and that a portfolio of diverse securities shall be of lower risk than a single security portfolio. Simply put, the theory emphasizes on the importance of diversifying to reduce risk.
Early on, investors stressed on individually picking high yielding stocks to earn maximum profits. So if one particular industry was offering good returns; an investor would have landed up picking all stocks of his portfolio from the same industry thereby making it a highly unwise act of portfolio management. Although it was intuitively understandable, the Portfolio Theory was the first of its kind to mathematically prove it.
The main outcome of the Portfolio Theory is that with optimum diversification, the risk weight of a portfolio shall be less than the average risk weights of the securities it contains. The Theory uses standard deviation as a substitute to risk and the standard deviation of expected returns is expressed as follows:
√(ΣWa2σa2 + ΣΣWaWbCovab)
Where:
Wa is the size of the portfolio in security a, σa is the standard deviation of the expected return of the security a, and
Covab is the covariance of the expected returns of the securities a and b
With the assumption that the covariance is less than 1 (which is not a practical assumption), it is derived that the weighted average of the standard deviation of the expected returns of the securities shall be more. As such the theory proves that diversification of securities in a portfolio reduces risk.
The Efficient Frontier:
In 1958, James Tobin added to the Portfolio Theory by introducing the Efficient Frontier. According to the theory, every possible combination of securities can be plotted on a graph comprising of the standard deviation of the securities and their expected returns on its two axes. The collection of all such portfolios on the risk-return space defines an area, which is bordered by an upward sloping line. This line is termed as the efficient frontier. The collection of Portfolios which fall on the efficient frontier are the efficient or optimum portfolios that have the lowest amount of risk for a given amount of return or alternately the highest level of return for a given level of risk.
The Two Mutual Fund Theorem
An important outcome of the analysis provided by the theory of the efficient frontier was the Two Mutual Fund Theorem. According to the theorem, a combination of any two portfolios held on the efficient frontier leads to the generation of an efficient portfolio. The two portfolios held on the efficient frontier are the mutual funds as mentioned in the name of the theorem.
 
Portfolio Theory Key Assumptions
The Portfolio Theory is based on many assumptions, most of which weaken the Theory to some degree. The key assumptions of the theory are listed below: * Assumptions from the Efficient Market Hypothesis*: 1. All investors aim to maximize profit and minimize risk. 2. All investors act rationally and are risk averse. 3. All investors receive the same information at the same time.
* The Efficient Market Hypothesis is the basis of all financial models. The term efficient market was first introduced by Fama in 1965 and defined as a market where large numbers of rational and risk averse investors trade actively to maximize profits and minimize risks on the basis of the same information which is freely available to all the investors at the same time. * Other Assumptions: 1. Investors do not need to pay any taxes or transaction costs 2. Investors can buy any security of any size 3. Investors can lend or borrow any amount of securities at the risk free rate 4. Investors are price takers and their actions do not influence prices 5. The correlations between assets are always fixed and constant 6. Return on assets are normally distributed 7. Investors have the exact idea of potential returns
Portfolio Theory Limitations
Although the Theory is popularly used as a tool by investment institutions, the assumptions have received criticisms due to important findings in others areas of study, especially from the field of behavioural economics. For instance, the assumption that all investors act rationally has been proved wrong by behavioural economists. Also, the supposition that all investors have the exact idea of potential returns has been disproved by studies done in the field of behavioural finance as the expectations of investors are normally biased. The theory of all investors being equally informed stands false as the market is quite asymmetrical when it comes to information due to the presence of elements such as insider trading or simply more informed investors. The assumption that investors do not need to pay any taxes or transaction costs also does not hold true. The hypothesis of investors being able to buy securities of any sizes is not practical as some securities have minimum order sizes and securities cannot be bought or sold in fractions. Each investor also has a credit limit and hence he cannot lend or borrow unlimited amounts of shares. The theory that the actions of investors have no impact on the market is also completely flawed as large amounts of sale or purchase of individual securities influence the price of the security or related securities. Also the correlations between assets are never fixed and constant as correlations change with changes in universal relations that exist between fundamental assets. Further, it has also been observed that the return on assets is not always normally distributed due to frequent swings in the market.
Further, the theory mathematically calculates expected values based on past performance to measure the correlations between risk and return. However, past performance is not a guarantee of performance in the future as has been observed by experienced investors. Considering only past performances leads to the leaving out of current scenarios or circumstances that might not have been present during the time when collection of the past data had taken place.
The theory also does not take into account its own impact on the market.
The theory is not practical as it only mathematically represents the future based on historical measurements of values of risk, return and correlation measures. Such an arrangement tends to ignore newer conditions which might not have existed during the time when the historical data was compiled.
Applications of the Portfolio Theory
In spite of its drawbacks, the theory is widely used in financial risk management and has played a key role in the way institutional portfolios are managed today.
The theory is also used by some experts in project portfolios of non-financial instruments.
The theory has also found ground in fields other than finance. In the 1970s the theory was used in the area of regional science to derive the relationship between economic growth and variability. It has also been used in the field of social psychology to concept the model of self. The theory has also been utilized to replicate the uncertainty and relationship between documents in information retrieval.
Conclusion
The Portfolio Theory broadly explains the relationship between risk and reward and has laid the foundation for management of portfolios as it is done today. It emphasizes on the significance of the relationship between securities and diversification to create optimal portfolios and reduce risk. It derives two main conclusions which is of significance even today. The first being that volatility is most dangerous if the time horizon is short and the second being that diversification reduces risk as the risk value of a diversified portfolio is less than the average risk of each of its component securities.
Although the theory was not completely practical due to limitations in its assumptions, it paved the way for today’s method of value at risk measures. The theory has also undergone many attempts to be improvised with more realistic postulates. The Post Modern Portfolio Theory is an extension of the theory. It has taken into consideration two of the main limitations of the original portfolio theory and has designed an improvised model by adopting non-normally distributed, asymmetric measures of risk and recognizing that investors have individual investment objectives and are comfortable with any amounts of return that fulfil their minimum objectives. Although the theory is an improvisation to the older theory, it has its own limitations. The Black Litterman Model is another extension of the Portfolio Theory. One of the problems faced during the application of the original portfolio theory was that when a portfolio is created based on only statistical measures of risk and returns, the results obtained are overly simplistic. This problem was overcome in the Black Litterman Model by simply postulating that the initial expected returns are the basically required returns so as to maintain equilibrium of the portfolio with that of the market.
Definition of 'Efficient Frontier'

A set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal, because they do not provide enough return for the level of risk. Portfolios that cluster to the right of the efficient frontier are also sub-optimal, because they have a higher level of risk for the defined rate of return.

Since the efficient frontier is curved, rather than linear, a key finding of the concept was the benefit of diversification. Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified.

The efficient frontier concept was introduced by Harry Markowitz in 1952 and is a cornerstone of modern portfolio theorySince the efficient frontier is curved, rather than linear, a key finding of the concept was the benefit of diversification. Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified.

The efficient frontier concept was introduced by Harry Markowitz in 1952 and is a cornerstone of modern portfolio theory

The optimal portfolio concept falls under the modern portfolio theory. The theory assumes (among other things) that investors fanatically try to minimize risk while striving for the highest return possible. The theory states that investors will act rationally, always making decisions aimed at maximizing their return for their acceptable level of risk.

The optimal portfolio was used in 1952 by Harry Markowitz, and it shows us that it is possible for different portfolios to have varying levels of risk and return. Each investor must decide how much risk they can handle and than allocate (or diversify) their portfolio according to this decision.

The chart below illustrates how the optimal portfolio works. The optimal-risk portfolio is usually determined to be somewhere in the middle of the curve because as you go higher up the curve, you take on proportionately more risk for a lower incremental return. On the other end, low risk/low return portfolios are pointless because you can achieve a similar return by investing in risk-free assets, like government securities.

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You can choose how much volatility you are willing to bear in your portfolio by picking any other point that falls on the efficient frontier. This will give you the maximum return for the amount of risk you wish to accept. Optimizing your portfolio is not something you can calculate in your head. There are computer programs that are dedicated to determining optimal portfolios by estimating hundreds (and sometimes thousands) of different expected returns for each given amount of risk.
Assumptions[edit]
The framework of MPT makes many assumptions about investors and markets. Some are explicit in the equations, such as the use of Normal distributions to model returns. Others are implicit, such as the neglect of taxes and transaction fees. None of these assumptions are entirely true, and each of them compromises MPT to some degree. * Investors are interested in the optimization problem described above (maximizing the mean for a given variance). In reality, investors have utility functions that may be sensitive to higher moments of the distribution of the returns. For the investors to use the mean-variance optimization, one must suppose that the combination of utility and returns make the optimization of utility problem similar to the mean-variance optimization problem. A quadratic utility without any assumption about returns is sufficient. Another assumption is to use exponential utility and normal distribution, as discussed below. * Asset returns are (jointly) normally distributed random variables. In fact, it is frequently observed that returns in equity and other markets are not normally distributed. Large swings (3 to 6 standard deviations from the mean) occur in the market far more frequently than the normal distribution assumption would predict.[12] While the model can also be justified by assuming any return distribution that is jointly elliptical,[13][14] all the joint elliptical distributions are symmetrical whereas asset returns empirically are not. * Correlations between assets are fixed and constant forever. Correlations depend on systemic relationships between the underlying assets, and change when these relationships change. Examples include one country declaring war on another, or a general market crash. During times of financial crisis all assets tend to become positively correlated, because they all move (down) together. In other words, MPT breaks down precisely when investors are most in need of protection from risk. * All investors aim to maximize economic utility (in other words, to make as much money as possible, regardless of any other considerations). This is a key assumption of theefficient market hypothesis, upon which MPT relies. * All investors are rational and risk-averse. This is another assumption of the efficient market hypothesis. In reality, as proven by behavioral economics, market participants are not alwaysrational or consistently rational. The assumption does not account for emotional decisions, stale market information, "herd behavior", or investors who may seek risk for the sake of risk.Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well. * All investors have access to the same information at the same time. In fact, real markets contain information asymmetry, insider trading, and those who are simply better informed than others. Moreover, estimating the mean (for instance, there is no consistent estimator of the drift of a brownian when subsampling between 0 and T) and the covariance matrix of the returns (when the number of assets is of the same order of the number of periods) are difficult statistical tasks. * Investors have an accurate conception of possible returns, i.e., the probability beliefs of investors match the true distribution of returns. A different possibility is that investors' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, David Hirshleifer, and Avanidhar Subrahmanyam (2001).[15] * There are no taxes or transaction costs. Real financial products are subject both to taxes and transaction costs (such as broker fees), and taking these into account will alter the composition of the optimum portfolio. These assumptions can be relaxed with more complicated versions of the model.[citation needed] * All investors are price takers, i.e., their actions do not influence prices. In reality, sufficiently large sales or purchases of individual assets can shift market prices for that asset and others (via cross elasticity of demand.) An investor may not even be able to assemble the theoretically optimal portfolio if the market moves too much while they are buying the required securities. * Any investor can lend and borrow an unlimited amount at the risk free rate of interest. In reality, every investor has a credit limit. * All securities can be divided into parcels of any size. In reality, fractional shares usually cannot be bought or sold, and some assets have minimum orders sizes. * Risk/Volatility of an asset is known in advance/is constant. In fact, markets often misprice risk (e.g. the US mortgage bubble or the European debt crisis) and volatility changes rapidly.
More complex versions of MPT can take into account a more sophisticated model of the world (such as one with non-normal distributions and taxes) but all mathematical models of finance still rely on many unrealistic premises.
Diagram :

A portfolio that gives maximum return for a given risk,or minimum risk for given return is an efficient porlio.Thus,portfolios are selected as follows:
(a)From the portfolios that have the same return ,the investor will prefer the portfolio with lowerrisk,and[6]
(b)From the portfolios that have the same risk level, an investor will prefer the portfolio withhigh errate of return .Figure1:Risk-Return of Possible Portfolios As the investor is rational ,they would like to havehigher return .And as he is risk averse, he want sto have lowerrisk. [6]
InFig\ure1,the shaded area PVWP includes all the possible securities an investor can invest in.The efficient portfolios are the ones that lie on the boundary of PQVW.Forexample,at risk levelx2,there arethree portfoliosS,T,U. But portfolioS is called the efficient portfolio as it has the highest return,y2, compared to T and U. All the portfolios that lie on the boundary of PQVW are efficient portfolios for a given risklevalel. The boundary PQVW is called the Efficient Frontier .All portfolios that lie below the Efficient Frontier are not good enough because there turn would be lower for the given risk. Portfolios that lie to the righ t of the Efficient Frontier would not be good enough, as there is highe r risk for a given rate ofreturn.All portfolios lying on the boundary of PQVW are called Efficient The Efficient Frontie r is the same for all investors, as all investors want maximum return with the lowest possible risk and they areriskaverse()(

Figure3:TheEfficientPortfolioTheinvestor'soptimalportfolioisfoundatthepointoftangencyoftheefficientfrontierwiththeindifferencecurve.Thispointmarksthehighestlevelofsatisfactiontheinvestorcanobtain.ThisisshowninFigure3.RisthepointwheretheefficientfrontieristangenttoindifferencecurveC3,andisalsoanefficientportfolio.Withthisportfolio,theinvestorwillgethighestsatisfactionaswellasbestrisk-returncombination.Anyotherportfolio,sayX,isn'ttheoptimalportfolioeventhoughitliesonthesameindifferencecurveasitisoutsidetheefficientfrontier.PortfolioYisalsonotoptimalasitdoesnotlieontheindifferencecurve,eventhoughitliesintheportfolioregion.Anotherinvestorhavingothersetsofindifferencecurvesmighthavesomedifferentportfolioashisbest/optimalportfolio.
Allportfoliossofarhavebeenevaluatedintermsofriskysecuritiesonly,anditispossibletoincluedrisk-freesecuritiesinaportfolioaswell.Aportfoliowithrisk-freesecuritieswillenableaninvestortoachieveahigherlevelofsatisfaction.ThishasbeenexplainedinFigure4

Figure4:TheCombinationofRisk-FreeSecuritieswiththeEfficientFrontierandCMLR1istherisk-freereturn,orthereturnfromgovernmentsecurities,asgovernmentsecuritieshavenorisk.R1PXisdrawnsothatitistangenttotheefficientfrontier.AnypointonthelineR1PXshowsacombinationofdifferentproportionsofrisk-freesecuritiesandefficientportfolios.ThesatisfactionaninvestorobtainsfromportfoliosonthelineR1PXismorethanthesatisfactionobtainedfromtheportfolioP.AllportfoliocombinationstotheleftofPshowcombinationsofriskyandrisk-freeassets,andallthosetotherightofPrepresentpurchasesofriskyassetsmadewithfundsborrowedattherisk-freerate.Inthecasethataninvestorhasinvestedallhisfunds,additionalfundscanbeborrowedatrisk-freerateandaportfoliocombinationthatliesonR1PXcanbeobtained.R1PXisknownastheCapitalMarketLine(CML).thislinerepresentstherisk-returntradeoffinthecapitalmarket.TheCMLisanupwardslopingcurve,whichmeansthattheinvestorwilltakehigherriskifthereturnoftheportfolioisalsohigher.TheportfolioPisthemostefficientportfolio,asitliesonboththeCMLandEfficientFrontier,andeveryinvestorwouldprefertoattainthisportfolio,P.ThePportfolioisknownastheMarketPortfolioandisalsothemostdiversifiedportfolio.It

The efficient frontier II
Now that the iso-return lines and the iso-variance ellipses are in place we can use them to identify the efficient frontier. The defintion of the frontier shows us how -
• the locus of points where the iso-return line is tangential to the iso-variance line will be the lowest variance acheivable for each portfolio return.
At any point not satisfying the tangency condition either the variance increases, or the return decreases such that only these points of tangency can be on the efficient frontier. http://www.slideshare.net/ravisingh7543653/portfolio-construction Figure 20: The efficient frontier in a Markowitz diagram
34Along the segement of the line from the global minimum variance portfolio to the w
B
axis the shares are being substituted at a constant rate; for every 1% reduction in the portfolio weight of A, there is a .75% increase in w
B and a .25% increase in w
C.
When w
A = 0 (along the w
B axis) a direct substitution of w
B for w
C occurs until all the portfolio weight is held in the asset with the highest return, w
C
= 1.
When plotted in mean-variance space this frontier takes the familiar shape
Figure 21: The efficient frontier in mean-variance space

Any point to the left of the Xz axis is not attainable because it violates the condition that X1 3 0. Any point below the X1 axis is not attainable because it violates the condition that Xz 3 0. Any
We define an isomean curve to be the set of all points (portfolios) with a given expected return. Similarly an isovariance line is defined to be the set of all points (portfolios) with a given variance of return the isomean curves are a system of parallel straight lines; the isovariance curves are a system of concentric ellipses (
The "center" of the system is the point which minimizes V. We will label this point X. Its expected return and variance we will label E and V. Variance increases as you move away from X. More precisely, if one isovariance curve, C1, lies closer to X than another, Cz, then C1 is associated with a smaller variance than Cz. X, the center of the system of isovariance ellipses, may fall either inside or outside the attainable set. Figure 4 illustrates a case in which
Xfalls inside the attainable set. In this case: Xis efficient.
The point of the isomean line at which V takes on its least value is the point at which the isomean line is tangent to an isovariance curve

As we go along l in either direction from X, V increases. The segment of the critical line from X to the point where the critical line crosses
*direction of increasing E depends on p,. p:. p3
FIG.2
the boundary of the attainable set is part of the efficient set.

In financial markets, an information asymmetry arises between borrowers and lenders because borrowers generally know more about their investment projects than lenders do.
Intermediaries, which specialise in collecting information, evaluating projects and borrowers, and monitoring borrowers. performance, can help overcome the information problem. Financial intermediaries thus exist because there are information and transactions costs that arise from imperfect information between borrowers and lenders.
This implies that the assumptions upon which the Modigliani-Miller theorem is based, and thus the macroeconomic models used by policy makers, do not hold. Conditions in financial and credit markets can affect the real economy; and interest and exchange rates are an incomplete description of the monetary transmission mechanism.

Central banks Mechanism : choose the price at which they lend high-powered money to the inter-bank market. The quantitative effect of a change in the official central bank lending rate on other interest rates, and on financial market conditions more generally, depends on the extent to whicha policy change is anticipated, how the change affects expectations of future policy,interest rates and inflation, and the degree of nominal price rigidities.
Real (inflation expectations adjusted) interest rates reflect the opportunity cost of current expenditure relative to expenditure in some future period, since earning a return in theinterim enables greater consumption or investment at a later date. Changes in real interest rates alter the incentives to consume and invest in the present versus consuming and investing in future.

Movements in short-term interest rates affect longer-term interest rates, at which financial institutions typically lend to and borrow from businesses and consumers, as illustrated by the expectations hypothesis of the term structure of interest rates. The expectations hypothesis states that, for any choice of holding period, the expected return is the same for any combination of bonds of different maturities. For example, the rate of return from holding a one-year note should be the same as holding two successive six-month notes.

Higher real rates directly reduce the profitability of investment projects because of higher financing costs, and indirectly because of the prospect of a slowdown in consumption. A rise in interest rates tends to encourage households to reduce current consumption because the return on saving and the cost of borrowing to finance consumption both increase. Monetary policy may have an additional effect on current consumption by lowering the disposable income of households who are borrowers. A portion of households. Spending is on servicing debt interest. Increases (decreases) in interest rates will raise (lower) the amount of debt servicing required and lower (increase) disposable income. The opposite holds true for households who are savers and the overall net effect on consumption will depend on how much the change in consumption of borrowers is offset by that of savers

Exchange rate movements have a direct impact on the cost of imports and domestic inflation.7 Exchange rate movements also have an indirect impact on inflation through their impact on the demand and supply of tradeable and non-tradeable goods and services. An appreciation of the exchange rate, for example, will lower the rate of growth of the domestic price level, which is a weighted average of tradeables and non-tradeables prices. This is because an appreciation of the exchange rate decreases the domestic price of tradeables (if tradeables prices are determined in foreign currency units by world markets). A decrease in the price of tradeables relative to non-tradeables increases the domestic demand for tradeables (and lowers the domestic supply of tradeable goods and services).8 Moreover, an appreciation of the exchange rate (or decline in the relative price of tradeables to non-tradeables) reduces the domestic demand for non-tradeables and increases the domestic supply of non-tradeables, causing excess supply of nontradeables and a reduction in the price of non-tradeables

Monetary policy affects asset prices more generally. For example, monetary policy directly affects the market value of future cash flows through its effect on the discount factor. The relationship between the market price of a unit future cash flow and interest rates is exp( ) , + = − ⋅ t t k t t PV i k (2) where t ,t+k PV is the present value at time t of a cash flow that matures at time t + k , t i denotes the continuously compounding interest rate at annual rates at time t and t k is the number of years to maturity at time t . The present value (or market price) of the cash flow is inversely related to the yield, i.e. a rise in t i lowers the present value of the cash flow and a decline in t i raises it. This result generalises to all assets (bonds, equities, property, etc.) because the value of all assets can be defined as a combination of expected future cash flows.
Tobin.s q theory provides a mechanism through which monetary policy affects the economy through its effects on the valuation of equities. Tobin (1969) defines q as the market value of firms divided by the replacement cost of capital. The market price of firms will increase with an easing in monetary policy. Tobin.s q rises if this market price of firms increases relative to the replacement cost of capital, i.e. if the cost of new plant and equipment capital declines relative to the market value of firms. Investment spending will rise because firms can purchase new investment goods, which will be valued in the equity market at greater than their purchase cost.9
On the other hand, when q is low, firms will not purchase new investment goods because the market value of firms is low relative to the cost of capital. If companies want to acquire capital when q is low, they can buy another firm cheaply and acquire old capital instead.
As a result, investment spending will be low.
Consumption spending will also be affected by changes in the market value of equities.
This is because equities are typically a component of households. financial wealth. When equities and stock prices fall, because of a tightening in monetary policy, the value of financial wealth decreases, leading to a decline in household consumption. This is because households. consumption spending is determined by their lifetime resources, which consist of current and future human capital, real capital and financial wealth. A tightening in monetary policy that leads to a decline in land and property values or structures and residential housing values also causes households. wealth to decline, while lower interest rates cause an increase in financial wealth.
Interest and exchange rates and asset prices are important channels through which monetary policy affects economic activity and inflation. All, or most of these channels are typically incorporated in macroeconomic models and can operate in conjunction with various degrees of price stickiness. However, in the presence of imperfect information, financial prices are unlikely to be a complete description of the monetary transmission mechanism for the reasons outlined in the introduction. Macroeconomic models that rely solely on the traditional price channels as conduits of monetary policy are likely to omit key channels through which monetary policy can affect activity and inflation. The remainder of this paper examines the role of financial intermediaries and credit in establishing additional channels of monetary policy influence on the real and nominal economy. THEORIES: contributions of Akerlof (1970), Spence (1973) and Rothschild and Stiglitz (1976). Financial intermediaries exist because they can reduce information and transaction costs that arise from an information asymmetry between borrowers and lenders.16 Financial intermediaries thus assist the efficient functioning of markets, and any factors that affect the amount of credit channelled through financial intermediaries can have significantmacroeconomic effects.
There are two strands in the literature that formally explain the existence of financial intermediaries. * The first strand emphasises financial intermediaries. provision of liquidity. * The second strand focuses on financial intermediaries. ability to transform the risk characteristics of assets. In both cases, financial intermediation can reduce the cost of channelling funds between borrowers and lenders, leading to a more efficient allocation of resources

Diamond and Dybvig (1983) analyse the provision of liquidity (the transformation of illiquid assets into liquid liabilities) by banks. * In Diamond and Dybvig.s model, ex ante identical investors (depositors) are risk averse and uncertain about the timing of their futureconsumption needs. Without an intermediary, all investors are locked into illiquid longterm investments that yield high payoffs only to those who consume late. Those who must consume early receive low payoffs because early consumption requires prematureliquidation of long-term investments.

* Banks can improve on a competitive market by providing better risk sharing among agents who need to consume at different (random) times. An intermediary promising investors a higher payoff for early consumption and a lower payoff for late consumption relative to the non-intermediated case enhances risk sharing and welfare. The optimal insurance contract in Diamond and Dybvig.s model is a demand deposit contract, but it has an undesirable equilibrium (bank run), in which all depositors panic and withdraw immediately, including even those who would prefer to leave their deposits in the bank if they were not concerned about the bank failing. Bank runs cause real economic problems because even .healthy. banks can fail, leading to a recall of loans andthe termination of productive investment.

* In Diamond and Dybvig (1983) the illiquidity of assets provides both the rationale for the existence of banks and for their vulnerability to runs.17 A bank run is caused by a shift in expectations. When normal volumes of withdrawals are known and not stochastic, suspension of convertibility of deposits will allow banks both to prevent bank runs and to provide optimal risk sharing by converting illiquid assets into liquid liabilities. In the more general case (with stochastic withdrawals), deposit insurance can rule out runs without reducing the ability of banks to transform assets.18
Financial intermediaries are able to transform the risk characteristics of assets because they can overcome a market failure and resolve an information asymmetry problem. Information asymmetry in credit markets arises because borrowers generally know more about their investment projects than lenders do. The information asymmetry can occur .ex ante. or .ex post.. An ex ante information asymmetry arises when lenders cannot differentiate between borrowers with different credit risks before providing loans and leadsto an adverse selection problem. Adverse selection problems arise when an increase in interest rates leaves a more risky pool of borrowers in the market for funds. Financial intermediaries are then more likely to be lending to high-risk borrowers, because those who are willing to pay high interest rates will, on average, be worse risks. The information asymmetry problem occurs ex post when only borrowers, but not lenders, can observe actual returns after project completion. This leads to a moral hazard problem.

Moral hazard arises when a borrower engages in activities that reduce the likelihood of a loan being repaid. An example of moral hazard is when firms. owners .siphon off. Funds (legally or illegally) to themselves or to associates, for example, through loss-making contracts signed with associated firms.
The problem with imperfect information is that information is a .public good.. If costly privately-produced information can subsequently be used at less cost by other agents, there will be inadequate motivation to invest in the publicly optimal quantity of information
(Hirschleifer and Riley, 1979).
The implication for financial intermediaries is as follows.
Once banks obtain information they must be able to signal their information advantage to lenders without giving away their information advantage. One reason, financial intermediaries can obtain information at a lower cost than individual lenders is that financial intermediation avoids duplication of the production of information. Moreover, there are increasing returns to scale to financial intermediation. Financial intermediaries develop special skills in evaluating prospective borrowers and investment projects. They can also exploit cross-sectional (across customers) information and re-use information over time

Leland and Pyle (1977) formally show that a bank can communicate information to investors about potential borrowers at a lower cost than can individual borrowers. They focus on an ex ante information asymmetry, where entrepreneurs selling shares to the market know the expected returns of their own investment, but other agents find this information costly to observe. This results in a moral hazard problem since firms with low expected returns have an incentive to claim a high expected return so as to increase their market valuation. In Leland and Pyle.s model intermediaries can solve this moral hazard problem by monitoring the actions of firms.
Retained equity can serve as a costly signal of the entrepreneur.s information about a project.19 The value of the firm increases with the share of the firm held by theentrepreneur, and in contrast to Modigliani and Miller (1958), the financial structure of a firm is therefore related to project or firm value.
One problem with the Leland and Pyle analysis is that it assumes the existence of an incentive signalling equilibrium. However, as Campbell and Kracaw (1980) note, if a signalling equilibrium exists, then firms will be properly valued with or without intermediaries or other information producers.

In Diamond.s model, intermediaries are delegated the costly task of monitoring loan contracts. A financial intermediary must choose an incentive contract such that it has incentives to monitor the information, make proper use of it, and make sufficient payments to depositors to attract deposits. Providing these incentives is costly and diversification can reduce these costs.
The optimal contract is a debt contract (an agreement by the borrower to pay the lender a fixed amount) with a non-pecuniary bankruptcy penalty. The intermediary need not be monitored because it bears all penalties for any shortfall of payments. This is because the diversification of the intermediary.s portfolio makes the probability of incurring these penalties very small. The optimal size for a financial intermediary is infinite; costs are lowered indefinitely by diversification, as long as the returns to entrepreneurs are not perfectly correlated.20
Adverse selection increases the likelihood that loans will be made to bad credit risks, while moral hazard lowers the probability that a loan will be repaid. As a result, lenders may decide in some circumstances that they would rather not make a loan and credit rationing may occur. There are two forms of credit rationing: (i) some loan applicants may receive a smaller loan than they applied for at the given interest rate, or (ii) they may not receive a loan at all, even if they offered to pay a higher interest rate.

Jaffee and Russell (1976) develop a theoretical model in which imperfect information and uncertainty can lead to rationing in loan markets, where some agents do not receive the loan they applied for. Their paper analyses the behaviour of a loan market in which borrowers have more information than lenders about the likelihood of default. The key feature in the model is the relationship between default proportions and contract sizes.
There is some minimum loan size at which no default is observed, beyond that, the proportion of individuals who do not default is declining with the contract size.
Since borrowers are identical ex ante, the market interest rate incorporates a premium to take account of the aggregate probability of default. Consequently, borrowers with low default probability pay a premium to support low quality borrowers and credit rationing in the form of the supply of smaller-sized loans than those demanded by the borrowers at a quoted rate may result. High quality borrowers will prefer some rationing if the smaller loan sizes lower the market average default probabilities, thus reducing the premium.
Stiglitz and Weiss (1981) develop a model of credit rationing, where some borrowers receive loans and others do not. They assume that the interest rate directly affects the quality of loans because of an adverse selection effect or moral hazard effect.21 Banks making loans are concerned about the interest rate they receive on a loan, and the riskiness of the loan. For a given loan rate, lenders earn a lower expected return on loans to borrowers with riskier projects than to good quality borrowers.22
The interest rate a bank charges can affect the riskiness of the loans by either sorting prospective borrowers (the adverse selection effect), or by affecting the actions of borrowers (the moral hazard effect). When the price (interest rate) affects the transaction, it may not clear the market. The adverse selection effect of interest rates is a consequence of different borrowers having different probabilities of repaying their loans.
The interest rate an individual is willing to pay may act as a screening device. Those who are willing to pay high interest rates may, on average, be worse risks. They are willing to borrow at high interest rates because they perceive their probability of repaying the loan to be low. As a result there exists an interest rate that maximises the expected return to the bank and beyond which the bank will be unwilling to supply funds, making the supply of loans curve bend backwards.
A change in interest rates can affect the bank.s expected return from loans through the moral hazard effect by changing the behaviour of borrowers. Higher interest rates induce firms to undertake projects with lower probabilities of success but higher payoffs when successful. Increasing the rate of interest increases the relative attractiveness of riskier projects, for which the return to the bank may be lower. As the interest rate rises, the average riskiness of those who borrow increases and the moral hazard effect reinforces the adverse selection problem. Banks therefore have an incentive, in some circumstances, to ration credit rather than to raise interest rates when there is excess demand for loanable funds.

Williamson (1986) develops a model of credit rationing where borrowers are subject to a moral hazard problem. Borrowers are identical ex ante, but some receive loans and others do not. A borrower and lender are asymmetrically informed ex post about the return on the borrower.s investment project, and the borrower will have an incentive to falsely default on the loan. Costly monitoring by lenders of borrowers together with large-scale investment projects imply that there exist increasing returns to scale in lending and borrowing which can be exploited by financial intermediaries. The optimal contract between a lender and a borrower is a debt contract and the lender only monitors in the event of default.23
An increase in the loan interest rate raises the expected return to the lender, but also results in an increase in the probability that the borrower defaults, thus increasing the expected cost of monitoring to the lender. This, in turn, generates an asymmetry in the borrowers. and lenders. payoff functions, which can lead to credit rationing. Because of the asymmetry in the payoff functions it may not be possible for the loan interest rate to adjust to clear the market, so that some borrowers do not receive a loan in equilibrium.
In summary, financial intermediaries play an important role in credit markets because they reduce the cost of channelling funds between relatively uninformed depositors to uses that
21 Stiglitz and Weiss (1981) assume that heterogeneity among entrepreneurs arises from different probability distributions of returns to their projects.
22 This occurs because an unobserved mean-preserving spread in a borrower.s project return distribution reduces the expected payment to lenders under default (Rothschild and Stiglitz, 1970).
23 Unlike in Diamond (1984) monitoring decisions are made ex post and the probability that monitoring occurs is determined endogenously. WP 0 3 / 1 9 A S Y M M E T R I C I N F O R M A T I O N , F I N A N C I A L I N T E R M E D I A T I O N A N D T H E
M O N E T A R Y T R A N S M I S S I O N M E C H A N I S M : A C R I T I C A L R E V I E W 1 3 are information-intensive and difficult to evaluate, leading to a more efficient allocation of resources. Intermediaries specialise in collecting information, evaluating projects, monitoring borrowers. performance and risk sharing. Despite this specialisation, the existence of financial intermediaries does not replicate the credit market outcomes that would occur under a full information environment. The existence of imperfect, asymmetrically-held information causes frictions in the credit market. Changes to the information structure and to variables which may be used to overcome credit frictions
(such as firm collateral and equity) will in turn cause the nature and degree of credit imperfections to alter.
Banks and other intermediaries are .special. where they provide credit to borrowers on terms which those borrowers would not otherwise be able to obtain. Because of the existence of economies of scale in loan markets, small firms in particular may have difficulties obtaining funding from non-bank sources and so are more reliant on bank lending than are other firms. Adverse shocks to the information structure, or to these firms. collateral or equity levels, or to banks. ability to lend, may all impact on firms. access to credit and hence to investment and output

Market microstructure is a branch of finance concerned with the details of how exchange occurs in markets. While the theory of market microstructure applies to the exchange of real or financial assets, more evidence is available on the microstructure of financial markets due to the availability of transactions data from them. The major thrust of market microstructure research examines the ways in which the working processes of a market affects determinants of transaction costs, prices, quotes, volume, and trading behavior.
Contents
[hide] * 1 Definition * 2 Issues * 2.1 Market structure and design * 2.2 Price formation and discovery * 2.3 Transaction cost and timing cost * 2.4 Information and disclosure * 3 References * 4 Further reading * 5 External links
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Definition[edit]
Maureen O’Hara defines market microstructure as “the study of the process and outcomes of exchanging assets under a specific set of rules. While much of economics abstracts from the mechanics of trading, microstructure theory focuses on how specific trading mechanisms affect the price formation process.”[1]
The National Bureau of Economic Research has a market microstructure research group that, it says, “is devoted to theoretical, empirical, and experimental research on the economics of securities markets, including the role of information in the price discovery process, the definition, measurement, control, and determinants of liquidity and transactions costs, and their implications for the efficiency, welfare, and regulation of alternative trading mechanisms and market structures.”[2]
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Issues[edit]
Microstructure deals with issues of market structure and design, price formation and price discovery, transaction and timing cost, information and disclosure, and market maker and investor behavior.
Market structure and design[edit]
This factor focuses on the relationship between price determination and trading rules. In some markets, for instance, assets are traded through dealers who keep an inventory (e.g., new cars), while other markets are dominated by brokers who act as intermediaries (e.g. housing). One of the important questions in microstructure research is how market structure affects trading costs and whether one structure is more efficient than another.
Price formation and discovery[edit]
This factor focuses on the process by which the price for an asset is determined. For example, in some markets prices are formed through an auction process (e.g. eBay), in other markets prices are negotiated (e.g., new cars) or simply posted (e.g. local supermarket) and buyers can choose to buy or not.
Transaction cost and timing cost[edit]
This factor focuses on transaction cost and timing cost and the impact of transaction cost on investment returns and execution methods. Transaction costs include order processing costs, adverse selection costs, inventory holding costs, and monopoly power.
Information and disclosure[edit]
This factor focuses on the market information and transparency and the impact of the information on the behavior of the market participants
.

Informational research in microstructure covers a very wide range of topics.
For the purposes of this article, it is convenient to think of research as falling into four main categories:
(1) Price formation and price discovery, including both static issues such as the determinants of trading costs and dynamic issues such the process by which prices come to impound information over time. Essentially, this topic is concerned with looking inside the &black box' by which latent demands are translated into realized prices and volumes.
(2) Market structure and design issues, including the relation between price formation and trading protocols. Essentially, this topic focuses on how di!erent rules a!ect the black box and hence liquidity and market quality.
(3) Information and disclosure, especially market transparency, i.e., the ability of market participants to observe information about the trading process. This topic deals with how revealing the workings of the black box a!ects the behavior of traders and their strategies.
(4) Informational issues arising from the interface of market microstructure with other areas of "nance including corporate "nance, asset pricing, and international
"nance. Models of the black box allow deeper investigations of traditional issues such as IPO underpricing as well as opening up new avenues for research.

Definition of 'Fama And French Three Factor Model'A factor model that expands on the capital asset pricing model (CAPM) by adding size and value factors in addition to the market risk factor in CAPM. This model considers the fact that value and small cap stocks outperform markets on a regular basis. By including these two additional factors, the model adjusts for the outperformance tendency, which is thought to make it a better tool for evaluating manager performance. | | Investopedia explains 'Fama And French Three Factor Model'Fama and French attempted to better measure market returns and, through research, found that value stocks outperform growth stocks; similarly, small cap stocks tend to outperform large cap stocks. As an evaluation tool, the performance of portfolios with a large number of small cap or value stocks would be lower than the CAPM result, as the three factor model adjusts downward for small cap and value outperformance.

There is a lot of debate about whether the outperformance tendency is due to market efficiency or market inefficiency. On the efficiency side of the debate, the outperformance is generally explained by the excess risk that value and small cap stocks face as a result of their higher cost of capital and greater business risk. On the inefficiency side, the outperformance is explained by market participants mispricing the value of these companies, which provides the excess return in the long run as the value adjusts. |
Definition of 'Multi-Factor Model'

A financial model that employs multiple factors in its computations to explain market phenomena and/or equilibrium asset prices. The multi-factor model can be used to explain either an individual security or a portfolio of securities. It will do this by comparing two or more factors to analyze relationships between variables and the security's resulting performance.

Factors are compared using the following formula:

Ri = ai + βi(m) Rm + βi(1)F1 + βi(2)F2 +…+βi(N)FN + ei

Where:
Ri is the returns of security i
Rm is the market return
F(1,2,3…N) is each of the factors used β is the beta with respect to each factor including the market (m) e is the error term a is the intercept nvestopedia explains 'Multi-Factor Model'

Multi-factor models are used to construct portfolios with certain characteristics, such as risk, or to track indexes. When constructing a multi-factor model, it is difficult to decide how many and which factors to include. One example, the Fama and French model, has three factors: size of firms, book-to-market values and excess return on the market. Also, models will be judged on historical numbers, which might not accurately predict future values.

Multi-factor models can be divided into three categories: macroeconomic, fundamental and statistical models. Macroeconomic models compare a security's return to such factors as employment, inflation and interest. Fundamental models analyze the relationship between a security's return and its underlying financials (such as earnings). Statistical models are used to compare the returns of different securities based on the statistical performance of each security in and of itself.