Modern Portfolio Theory and Capital Asset Pricing Model

Modern Portfolio Theory and capital letter Asset set patternIntroductionThe roof Asset Pricing Model developed by William Sharpe has signifi tin cant similarities with Harry Markowitzs Portfolio theory. In fact, the later is rightly considered as the next logical step from the latter, with twain found on similar foundations.There atomic number 18 also deviances in how each model/theory is calculated, pertaining to gamble considerations.This papers main objective is to happen upon these differences while noblelighting the similarities as well to put things into perspective.The report impart open with an overview of Markowitzs portfolio theory and explain it pass on by means of describing the in effect(p) bourn, the Capital Market Line, lay on the line escaped plus and the Market Portfolio.The report result then switch its attention to the Capital Asset Pricing Model and explain it further through with(predicate) the Security Market Line.The report will then close by outlining the differences between the twain with a view of say the main objective.What will come through in this report is that Markowitzs portfolio theory uses standard aberration as its risk measure and takes into account every risk in an in effect(p) portfolio, while the Capital Asset Pricing Model uses the beta co- efficacious to measure risk and takes into account both efficient and non-efficient portfolios further more(prenominal) it measures the risks of idiosyncratic assets within the portfolio.Modern Portfolio TheoryModern Portfolio Theory (MPT) was introduced by Harry Markowitz, way back in 1952. At a high take it proposes how rational investors use diversification to optimise their enthronization portfolios and give guidance on pricing risky assets.MPT assumes that investors are risk unwilling, i.e. given two assets A and B offering the same anticipate cede, investors will opt for asset A if it is slight risky. In effect, an investor who expects higher turn backs would need to accept more risk. The expected trade-off between risk and extend depends on the individuals level of risk nuisance. The implication of this is a rational investor (a risk averse investor) will not invest in a portfolio if another one exists offering a better risk-return profile (Fabozzi Markowitz, 2002).For any given level of risk, investors will opt for portfolios with higher expected returns instead of those with lower returns.Another assumption under MPT is that investors are only interested in the expected return and the excitability of an investment, as measured by the mean and standard aberrance respectively. Investors do not consider any other characteristics, for example, charges.In effect, based on the assumptions to a higher place, investors are concerned about efficient portfolios.To explain portfolio theory further, let us consider the formula for the expected return and risk of a portfolio under MPT. view two assets A and B formed a portfol io in proportion (X) each, the expected return for that portfolio would beR(p) = X(a)R(a) + X(b)R(b), whereR(p) = expected returns from portfolioR(a) = expected returns from asset AR(b) = expected returns from asset BThe standard deviation or risk of that portfolio would beSD(p) = (XaSDa + XbSDb + 2XaXbRSDaSDb), whereSD(p) = standard deviation of expected returns of portfolioSDa = standard deviation of expected returns of asset ASDb = standard deviation of expected returns of asset BR = correlation coefficient between the expected returns of the two assetsThe efficient frontierUnder MPT, Markowitz examined the efficient frontier curve. The efficient frontier curve gives a graphic presentation of a set of portfolios that offer the maximum come in of return for any given level of risk (McLaney, 2006). According to Markowitz, an efficient investor will opt for an optimum portfolio along the curve, based on their level of risk aversion and their perception of the risk and return kin ( Fabozzi Markowitz, 2002).Figure 1 Efficient Frontier Source www.riskglossary.comThe curve in the diagram above illustrates the efficient frontier. Portfolios on the curve are efficient i.e. they offer maximum expected returns for any given level of risk and minimum risk for any given level of expected returns. The shaded region represents the acceptable level of investments when risk is compared against returns. For every point on the shaded region, there will be at least one portfolio that can be constructed and has a risk and return gibe to that point (www.riskglossary.com)As aforementioned, each portfolio on the efficient frontier curve will have a higher rate of return for the same or lower level of risk or lower risk for an equal or better rate of return when compared with portfolios not on the frontier.It is important to note that the efficient frontier is really made up of portfolios rather than individual assets. This is because portfolios could be diversified, i.e. inve stors can patronise assets which are imperfectly correlated (Fabozzi Markowitz, 2002). This will help to ensure that investors can reduce their risks associated with individual asses by holding other assets a kind of set-off.The Capital Market LineThe Capital Market Line (CML) is a set of risk return combinations that are available by combining the market portfolio with risk free borrowing and lending (www.lse.co.uk/financeglossary). The CML defines the relationship between risk and return for efficient portfolios of risky securities. It specifies the efficient set of portfolios can investor can obtain by combining the portfolio (which contains risk) with a risk free asset.The formula for CML isE (r_c) = r(f) + SD(c)*E(r_m)-r(f)/SD(m)WhereE(r_c) = expected return on portfolio cR(f) = risk free rateSD(c ) = standard deviation of portfolio cE (r_m) = expected return on market portfolioSD(m) = standard deviation of market returnThe CML indicates that the expected return of an effici ent portfolio is equal to the risk-free rate plus a risk premium. Both risk and return increase in a elongately along the CML.Figure 2 Capital Market Line Source www.riskglossary.comIn Figure 2 above, the CML is the line touching the efficient frontier curve. It passes through the risk free rate (assumed to be 5%). The point where the CML forms a tangent with the efficient frontier curve is the point called the super-efficient portfolio.The Risk free asset, Sharpe ratio and the Market PortfolioThe risk free asset pays a risk free rate and has a zero variance in returns, e.g. government short-term securities. When combined with a portfolio of assets the change in return and risk is linear.The Sharpe Ratio is a measure of the additional return to be obtained about a risk free rate for a given portfolio compared with its corresponding risk. On the efficient frontier the portfolio with the highest Sharpe Ratio is known as the market portfolio.The CML is the result of a comparison betw een the market portfolio and the risk free asset. The CML surpasses the efficient frontier with the exception of the point of tangency.The Capital Asset Pricing ModelWhile the CML focuses on the risk and return relationship for efficient portfolios, it would be reclaimable to consider the relationship between expected return and risk for individual assets or securities. The Capital Asset Pricing Model (CAPM) would be used for this.CAPM is an denotation of Markowitzs Portfolio Theory or MPT. It introduces the notions of imperious and specific risks. Let us define eachSystematic risk this is the risk associated with holding the market portfolio of assets private assets are affected by market movementsSpecific risk this risk is unique to an individual asset and represents that portion of an assets return which has no correlation with market movements.CAPM assumes the following (McLaney, 2006, 199)Investors are risk averse and maximise expected utility of wealthThe capital market i s not dominated by any individual investorsInvestors are interested in only two features of a warrantor, its expected returns and its variance or standard deviationThere exists a risk free rate at which all investors may borrow or lend without limit at the same rateThere is an absence of dealing charges, taxes and other imperfectionsAll investors have identical perceptions of each securityThis lends credence to the assertion that CAPM follows a natural progression from MPT. The assumptions are identical with the main difference being how risks are categorised and treated. This will be explored in detail in a later section.Under CAPM, the market place will compensate an investor for taking a self-opinionated risk but not a specific risk. The rationale for this is that specific risks can be avoided or minimised through diversification.The formula for CAPM is as followsr = Rf + Beta x (RM-RF), wherer = expected return on an assetRf = rate of risk free investmentRM = return rate of t he appropriate asset classBeta is the relative risk contribution of an individual security to the overall market portfolio. It measures the security risk relative to the market portfolio and ignores the specific risk. The beta equation is as followsCov (i,M)/(SDm), whereCov (i,M) = covariance between market portfolio and security i(SDm) = variance of the markets returnThe betas for all assets are measured in relation to the market portfolio beta which is 1. In effect, if individual beta is greater than 1, then individual asset has a higher risk than the market risk. If individual beta equals 1, then individual asset risk and market risk are the same. If individual beta is less than 1, then the risk of that individual asset is less than the market risk.The value of beta provides an idea of the level or size of the change in an assets return when a corresponding change in the returns of an overall portfolio is experienced (McLaney, 2006).Beta has come under criticism from academics an d investors who do not prise the value of beta as an appropriate risk measure. However, this is somewhat challenged by actual performance of the betas of portfolios and mutual funds. These are regarded as stable and can be used to predict future betas.Security Market LineCAPM can be applied by using the Security Market Line (SML). SML is a graphical representation showing the linear relationship between systematic risk and expected rates of return for individual assets. In the case of the SML, risk is measured by beta. It plots the expected returns on the y axis and the risk as denoted by beta on the x axis.In other words, the SML expresses the linear relationship between the expected returns on a risky asset and its covariance with market returns. Its formula isFigure 3 CAPM and SMLThe line in the diagram above is the SML.Differences relating to MPT (CML) and CAPM (SML)To explain the differences, it is useful to consider the relationships between risk and return in the perspective of CML and SML. CML compares the relationship from an MPT perspective, while SML does from a CAPM perspective.The main difference pertaining to MPTs relationship with CAPM is pertaining to risk.Under Portfolio theory, CML gives an indication of expected returns in comparison with risk. Here the risk is measured in terms of standard deviation of returns. The rationale for this is CML represents the trade-off for efficient portfolios, i.e. the risk is all systematic risk (McLaney, 2006).The SML on the other hand, indicates the risk/return trade-off, using beta as the measure of risk. In this case, only the systematic risk element of the individual asset is taken into consideration.The reason why CML shows no individual securitys risk profile is because all individual securities have an element of specific risk, implying that they are inefficient. CML only looks at efficient portfolios.The table below summarises the main differences between CML and SMLTable 1 Tabular difference betwee n CML and SMLSummaryAs has been shown above, CAPM has been developed along the lines of Markowitzs Portfolio theory. They both use expected returns and risk as the investors main determinant of their investment decisions. They both assume that investors are risk averse and do not consider anything else other than risk and returns.However, there are some subtle differences which will now be summarised belowUnder Portfolio theory, the CML measures risk by standard deviation or total risk. The SML measures risk by beta or systematic risk under CAPM it ignores specific risksThe CML graph is interested in providing information on efficient portfolios only. The SML graph on the other hand provides insight into both efficient and non-efficient portfolio and securitiesREFERENCES AND BIBLIOGRAPHYBooksBodie, et al (2006) Investments (7th edition), McGraw-Hill/Irwin, capital of the United KingdomElton, E et al (2003) Modern Portfolio Theory and Investment Analysis, Wiley, LondonFabozzi, F. M arkowitz, H. (2002) Theory and Practice of Investment Management, Wiley, LondonMcLaney, E. (2006) Business Finance Theory and Practice (7th edition), Prentice Hall, LondonOneill, W.J. (2002) How to Make Money in Stocks, (3rd edition), McGraw-Hill, LondonInternet Sourceswww.lse.co.ukwww.riskglossary.comwww.wikipedia.com