【精品】investments 投资学 （博迪bodie, kane, marcuschap008 index models精品ppt课件.ppt

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1、INVESTMENTS 投资学（博迪BODIE,KANE,MARCUS）Chap008 Index ModelsINVESTMENTS|BODIE,KANE,MARCUSReduces the number of inputs for diversificationEasier for security analysts to specializeAdvantages of the Single Index ModelINVESTMENTS|BODIE,KANE,MARCUS i=response of an individual securitys return to the common

2、factor,m.Beta measures systematic risk.m=a common macroeconomic factor that affects all security returns.The S&P 500 is often used as a proxy for m.ei=firm-specific surprisesSingle Factor ModelINVESTMENTS|BODIE,KANE,MARCUSSingle-Index ModelRegression Equation:Expected return-beta relationship:INVEST

3、MENTS|BODIE,KANE,MARCUSSingle-Index Model Risk and covariance:Variance=Systematic risk and Firm-specific risk:Covariance=product of betas x market index risk:INVESTMENTS|BODIE,KANE,MARCUSINVESTMENTS|BODIE,KANE,MARCUSINVESTMENTS|BODIE,KANE,MARCUSFigure 8.1 The Variance of an Equally Weighted Portfoli

4、o with Risk Coefficient pINVESTMENTS|BODIE,KANE,MARCUSFigure 8.2 Excess Returns on HP and S&P 500INVESTMENTS|BODIE,KANE,MARCUSFigure 8.3 Scatter Diagram of HP,the S&P 500,and HPs Security Characteristic Line(SCL)INVESTMENTS|BODIE,KANE,MARCUSTable 8.1 Excel Output:Regression Statistics for the SCL of

5、 Hewlett-PackardINVESTMENTS|BODIE,KANE,MARCUSTable 8.1 InterpretationCorrelation of HP with the S&P 500 is 0.7238.The model explains about 52%of the variation in HP.HPs alpha is 0.86%per month(10.32%annually)but it is not statistically significant.HPs beta is 2.0348,but the 95%confidence interval is

6、 1.43 to 2.53.INVESTMENTS|BODIE,KANE,MARCUSFigure 8.4 Excess Returns on Portfolio AssetsINVESTMENTS|BODIE,KANE,MARCUSAlpha and Security Analysis1.Use macroeconomic analysis to estimate the risk premium and risk of the market index.2.Use statistical analysis to estimate the beta coefficients of all s

7、ecurities and their residual variances,2(ei).INVESTMENTS|BODIE,KANE,MARCUSAlpha and Security Analysis3.Establish the expected return of each security absent any contribution from security analysis.4.Use security analysis to develop private forecasts of the expected returns for each security.INVESTME

8、NTS|BODIE,KANE,MARCUSSingle-Index Model Input ListRisk premium on the S&P 500 portfolioEstimate of the SD of the S&P 500 portfolion sets of estimates ofBeta coefficientStock residual variancesAlpha valuesINVESTMENTS|BODIE,KANE,MARCUSOptimal Risky Portfolio of the Single-Index ModelMaximize the Sharp

9、e ratioExpected return,SD,and Sharpe ratio:INVESTMENTS|BODIE,KANE,MARCUSOptimal Risky Portfolio of the Single-Index ModelCombination of:Active portfolio denoted by AMarket-index portfolio,the passive portfolio denoted by MINVESTMENTS|BODIE,KANE,MARCUSOptimal Risky Portfolio of the Single-Index Model

10、Modification of active portfolio position:WhenINVESTMENTS|BODIE,KANE,MARCUSThe Information RatioThe Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio(the passive strategy):INVESTMENTS|BODIE,KANE,MARCUSThe Information RatioThe contribution of the active

11、portfolio depends on the ratio of its alpha to its residual standard deviation.The information ratio measures the extra return we can obtain from security analysis.INVESTMENTS|BODIE,KANE,MARCUSFigure 8.5 Efficient Frontiers with the Index Model and Full-Covariance MatrixINVESTMENTS|BODIE,KANE,MARCUS

12、Table 8.2 Portfolios from the Single-Index and Full-Covariance ModelsINVESTMENTS|BODIE,KANE,MARCUSIs the Index Model Inferior to the Full-Covariance Model?Full Markowitz model may be better in principle,butUsing the full-covariance matrix invokes estimation risk of thousands of terms.Cumulative erro

13、rs may result in a portfolio that is actually inferior to that derived from the single-index model.The single-index model is practical and decentralizes macro and security analysis.INVESTMENTS|BODIE,KANE,MARCUSBeta Book:Industry Version of the Index ModelUse 60 most recent months of price data Use S

14、&P 500 as proxy for MCompute total returns that ignore dividendsEstimate index model without excess returns:INVESTMENTS|BODIE,KANE,MARCUSBeta Book:Industry Version of the Index ModelThe average beta over all securities is 1.Thus,our best forecast of the beta would be that it is 1.Also,firms may become more“typical”as they age,causing their betas to approach 1.Adjust beta because:INVESTMENTS|BODIE,KANE,MARCUSTable 8.4 Industry Betas and Adjustment Factors