1、1,Econ 906 Corporate Finance,The Capital Asset Pricing Model(CAPM)Readings:#Copeland/Weston Ch 7,BM Ch 9,GT Ch 5-6 Roll,Richard W.“A Critique of the Asset Pricing Theorys Tests;#Part I:#On Past and Potential Testability of the Theory”,Journal of Financial Economics 4,no.2(1977),pp 129-176Kothari,S.P
2、.,et al.,“Another Look at the Cross-Section of Expected Stock Returns”,Journal of Finance,50,no.1(1995),pp 185-224.,2,Learning outcomes,Make distinction between CML and SMLIdentifying the efficiency frontier and minimum variance portfolioAnalysing the relationship between risk and returnAssessing em
3、pirical tests of the CAPM and the limitations of the model,3,Introduction,The CAPM show that the equilibrium rates of return on all risky assets are a function of their covariance with the market portfolioThe APT on the other hand considers that the return on any risky asset is a linear combination
4、of various factors that affect asset returns.The APT is more general than the CAPM since it allows numerous factors to explain the equilibrium return on a risky asset.,4,CAPM Assumptions,Investors base their investment decision on a single-period analysis.Markets are frictionless(borrowing rate equa
5、ls lending rate)and information is costless and simultaneously available to all investors.There are no market imperfections such as taxes,regulations,or restrictions on short-selling.Investors are risk-averse,and they care only about mean and variance of their portfolio returns.Investors have homoge
6、neous expectation which means that all investors reach the same conclusions about the mean and standard deviations of all feasible portfolios.Risk-less rate of interest exists such that investors may borrow or lend unlimited amounts at the risk-free rate.,5,Capital Market Line,Return,Risk,Efficient
7、Portfolio,Risk Free Return=,Market Return=rm,6,Security Market Line,Efficient Portfolio,BETA,Return,Market Return=rm,Risk Free Return=,1.0,Security Market Line(SML),7,The Efficient Frontier,The top half of the mean-variance plot for mean-variance efficient portfolio is known as the efficient frontie
8、r of risky stocks.The efficient frontier is the most efficient trade-off between mean and variance.A more efficient portfolio weighting scheme can earn a higher mean return and has the same variance to a given portfolio or alternatively the same mean and a lower variance.The efficient frontier can b
9、e generated by holding risk-free asset and one“key”portfolio(known as tangency portfolio).,8,The Efficiency of the Market Portfolio,So long as investors have homogeneous expectations,they will all perceive the same minimum variance opportunity set.Hence,even in the absence of risk-free asset,they wi
10、ll all select efficient portfolios regardless of their individual risk tolerance.Given that all individuals hold positive proportions of their wealth in efficient portfolios,then the market portfolio must be efficient because:#(1)The market is simply the sum of all individual holdings and,(2)The ind
11、ividual holdings are efficientTherefore,in theory,when all investors have homogeneous expectations,the market portfolio must be efficient.,9,The Feasible Set,10,The Relation Between the Mean-Standard Deviation Diagram and a Mean-Beta Diagram,11,Capital Asset Pricing Model,Assumptions of the CAPM:#1.
12、Investors care only about the mean and variance of their portfolios returns.2.Markets are frictionless:#no taxes,no transactions costs etc3.Investors have homogeneous beliefs,which means that all investors reach the same conclusions about the means and standard deviations of all feasible portfolios-
13、investors will not be trying to outsmart one another and“beat the market”by actively managing their portfolios,12,Market Portfolio,The market portfolio is the portfolio that provides the highest possible risk premium per unit of risk,or the greatest possible gain from diversification.In practice a m
14、arket index such as FTSE All Share Index may serve as a proxy for the market portfolio.Graphically,the market portfolio is the portfolio for which the line that is tangential to the efficient frontier and passes through the risk-less assets return point representing the steepest slope.This line is k
15、nown as the Capital Market Line(CML).,13,Capital Market Line,The tangency portfolio represents the unique optimal portfolio that contains no investment in the risk free asset.The line connecting the return of risk-free asset with the tangency portfolio is known as the Capital Market Line(CML).The CM
16、L is represented by the following equation:#,14,Capital Market Line cntd.,Where and are the mean and standard deviation of the tangency portfolios return respectively and is the return on the risk-free asset.As the CML is the steepest sloped line available from combining a risk-free investment with any risky investment,it plots the set of mean-variance efficient portfolios that can be achieved by combining the risky stocks with a risk-free investment.,15,Relation Between Risk and Return,The ratio of th
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