第十章 收益和风险 CAPMcziv.pptx
McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-0Chapter Outline10.1 Individual Securities10.2 Expected Return,Variance,and Covariance10.3 The Return and Risk for Portfolios10.4 The Efficient Set for Two Assets10.5 The Efficient Set for Many Securities10.6 Diversification:An Example10.7 Riskless Borrowing and Lending10.8 Market Equilibrium10.9 Relationship between Risk and Expected Return(CAPM)10.10 Summary and ConclusionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-110.1 Individual SecuritiesThe characteristics of individual securities that are of interest are the:Expected ReturnVariance and Standard DeviationCovariance and CorrelationMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-210.2 Expected Return,Variance,and Covariance Consider the following two risky asset world.There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-310.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-410.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-510.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-610.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-710.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-810.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-910.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1010.2 Expected Return,Variance,and CovarianceMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1110.3 The Return and Risk for PortfoliosNote that stocks have a higher expected return than bonds and higher risk.Let us turn now to the risk-return tradeoff of a portfolio that is 50%invested in bonds and 50%invested in stocks.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1210.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1310.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1410.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1510.3 The Return and Risk for PortfoliosThe expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1610.3 The Return and Risk for PortfoliosThe variance of the rate of return on the two risky assets portfolio is where BS is the correlation coefficient between the returns on the stock and bond funds.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1710.3 The Return and Risk for PortfoliosObserve the decrease in risk that diversification offers.An equally weighted portfolio(50%in stocks and 50%in bonds)has less risk than stocks or bonds held in isolation.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1810.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50%in stocks and 50%in bonds 100%bonds100%stocksMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-1910.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50%in stocks and 50%in bonds 100%bonds100%stocksMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2010.4 The Efficient Set for Two Assets100%stocks100%bondsNote that some portfolios are“better”than others.They have higher returns for the same level of risk or less.These compromise the efficient frontier.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-21Two-Security Portfolios with Various Correlations 100%bondsreturn 100%stocks=0.2=1.0=-1.0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-22Portfolio Risk/Return Two Securities:Correlation EffectsRelationship depends on correlation coefficient-1.0 +1.0The smaller the correlation,the greater the risk reduction potentialIf =+1.0,no risk reduction is possibleMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-23Portfolio Risk as a Function of the Number of Stocks in the PortfolioNondiversifiable risk;Systematic Risk;Market RiskDiversifiable Risk;Nonsystematic Risk;Firm Specific Risk;Unique Riskn In a large portfolio the variance terms are effectively diversified away,but the covariance terms are not.Thus diversification can eliminate some,but not all of the risk of individual securities.Portfolio riskMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2410.5 The Efficient Set for Many SecuritiesConsider a world with many risky assets;we can still identify the opportunity set of risk-return combinations of various portfolios.return PIndividual AssetsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2510.5 The Efficient Set for Many SecuritiesGiven the opportunity set we can identify the minimum variance portfolio.return Pminimum variance portfolioIndividual AssetsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2610.5 The Efficient Set for Many SecuritiesThe section of the opportunity set above the minimum variance portfolio is the efficient frontier.return Pminimum variance portfolioefficient frontierIndividual AssetsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-27Optimal Risky Portfolio with a Risk-Free Asset In addition to stocks and bonds,consider a world that also has risk-free securities like T-bills100%bonds100%stocksrfreturn McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2810.7 Riskless Borrowing and LendingNow investors can allocate their money across the T-bills and a balanced mutual fund100%bonds100%stocksrfreturn Balanced fundCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-2910.7 Riskless Borrowing and LendingWith a risk-free asset available and the efficient frontier identified,we choose the capital allocation line with the steepest slope return Pefficient frontierrfCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-3010.8 Market EquilibriumWith the capital allocation line identified,all investors choose a point along the linesome combination of the risk-free asset and the market portfolio M.In a world with homogeneous expectations,M is the same for all investors.return Pefficient frontierrfMCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-31The Separation Property The Separation Property states that the market portfolio,M,is the same for all investorsthey can separate their risk aversion from their choice of the market portfolio.return Pefficient frontierrfMCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-32The Separation Property Investor risk aversion is revealed in their choice of where to stay along the capital allocation linenot in their choice of the line.return Pefficient frontierrfMCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-33Market EquilibriumJust where the investor chooses along the Capital Asset Line depends on his risk tolerance.The big point though is that all investors have the same CML.100%bonds100%stocksrfreturn Balanced fundCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-34Market EquilibriumAll investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate.100%bonds100%stocksrfreturn Optimal Risky PorfolioCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-35The Separation PropertyThe separation property implies that portfolio choice can be separated into two tasks:(1)determine the optimal risky portfolio,and(2)selecting a point on the CML.100%bonds100%stocksrfreturn Optimal Risky PorfolioCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-36Optimal Risky Portfolio with a Risk-Free Asset By the way,the optimal risky portfolio depends on the risk-free rate as well as the risky assets.100%bonds100%stocksreturn First Optimal Risky PortfolioSecond Optimal Risky PortfolioCML0CML1McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-37Definition of Risk When Investors Hold the Market PortfolioResearchers have shown that the best measure of the risk of a security in a large portfolio is the beta(b)of the security.Beta measures the responsiveness of a security to movements in the market portfolio.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-38Estimating b with regressionSecurity ReturnsSecurity ReturnsReturn on Return on market%market%Ri=a a i+b biRm+eiSlope=b biCharacteristic LineCharacteristic LineMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-39Estimates of b for Selected StocksStockBetaBank of America1.55Borland International2.35Travelers,Inc.1.65Du Pont1.00Kimberly-Clark Corp.0.90Microsoft1.05Green Mountain Power0.55Homestake Mining0.20Oracle,Inc.0.49McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-40The Formula for BetaClearly,your estimate of beta will depend upon your choice of a proxy for the market portfolio.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-4110.9 Relationship between Risk and Expected Return(CAPM)Expected Return on the Market:Expected return on an individual security:Market Risk PremiumThis applies to individual securities held within well-diversified portfolios.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-42Expected Return on an Individual SecurityThis formula is called the Capital Asset Pricing Model(CAPM)Assume bi=0,then the expected return is RF.Assume bi=1,thenExpected return on a security=Risk-free rate+Beta of the securityMarket risk premiumMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-43Relationship Between Risk&Expected ReturnExpected returnb b1.0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-44Relationship Between Risk&Expected ReturnExpected returnb b1.5McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-4510.10 Summary and ConclusionsThis chapter sets forth the principles of modern portfolio theory.The expected return and variance on a portfolio of two securities A and B are given byBy varying wA,one can trace out the efficient set of portfolios.We graphed the efficient set for the two-asset case as a curve,pointing out that the degree of curvature reflects the diversification effect:the lower the correlation between the two securities,the greater the diversification.The same general shape holds in a world of many assets.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-4610.10 Summary and ConclusionsThe efficient set of risky assets can be combined with riskless borrowing and lending.In this case,a rational investor will always choose to hold the portfolio of risky securities represented by the market portfolio.Then with borrowing or lending,the investor selects a point along the CML.return Pefficient frontierrfMCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.10-4710.10 Summary and ConclusionsThe contribution of a security to the risk of a well-diversified portfolio is proportional to the covariance of the securitys return with the markets return.This contribution is called the beta.The CAPM states that the expected return on a security is positively related to the securitys beta:
