最新investments 投资学 （博迪bodie, kane, marcuschap008 index models(共28张ppt课件).pptx

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1、INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 8Index Models第一页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUS Reduces the number of inputs for diversification Easier for security analysts to specializeAdvantages of the Single

2、 Index Model8-2第二页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUS i = response of an individual securitys return to the common 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 surpri

3、sesSingle Factor Model( )iiiirE rme8-3第三页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSSingle-Index Model Regression Equation: Expected return-beta relationship: tetRtRiMiiiMiiiRERE8-4第四页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSSingle-Index Model Risk and covariance: Variance = Systematic risk and Firm-spe

4、cific risk: Covariance = product of betas x market index risk:2222( )iiMie 2( ,)ijijMCov r r 8-5第五页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSSingle-Index Model Correlation = product of correlations with the market index222( ,)( ,)( ,)ijMiMjMijiMjMijiMjMCorr r rCorr r rxCorr r r 8-6第六页，共二十八页。INVESTMENT

5、S | BODIE, KANE, MARCUSIndex Model and Diversification Variance of the equally weighted portfolio of firm-specific components: When n gets large, 2(ep) becomes negligible and firm specific risk is diversified away.2222111()( )( )nPiieeenn8-7第七页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSFigure 8.1 The V

6、ariance of an Equally Weighted Portfolio with Risk Coefficient p8-8第八页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSFigure 8.2 Excess Returns on HP and S&P 5008-9第九页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSFigure 8.3 Scatter Diagram of HP, the S&P 500, and HPs Security Characteristic Line (SCL) tetRtRHPPSH

7、PHPHP500&8-10第十页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSTable 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-Packard8-11第十一页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSTable 8.1 Interpretation Correlation of HP with the S&P 500 is 0.7238. The model explains about 52% of the variation in

8、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 1.43 to 2.53.8-12第十二页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSFigure 8.4 Excess Returns on Portfolio Assets8-13第十三页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUS

9、Alpha 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 securities and their residual variances, 2 (ei).8-14第十四页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSAlpha and Security A

10、nalysis3.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.8-15第十五页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSSingle-Index Model Input List Risk premium on the S&P

11、500 portfolio Estimate of the SD of the S&P 500 portfolio n sets of estimates of Beta coefficient Stock residual variances Alpha values8-16第十六页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSOptimal Risky Portfolio of the Single-Index Model Maximize the Sharpe ratio Expected return, SD, and Sharpe ratio:111

12、1122111222222211()()()()( )()nnPPMPiiMiiiinnPPMPMiiiiiiPPPE RE RwE RwewweE RS 8-17第十七页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSOptimal Risky Portfolio of the Single-Index Model Combination of: Active portfolio denoted by A Market-index portfolio, the passive portfolio denoted by M8-18第十八页，共二十八页。INVES

13、TMENTS | BODIE, KANE, MARCUSOptimal Risky Portfolio of the Single-Index ModelModification of active portfolio position: When0*01 (1)AAAAwww*01,AAAww8-19第十九页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSThe Information Ratio The Sharpe ratio of an optimally constructed risky portfolio will exceed that of t

14、he index portfolio (the passive strategy):222()APMAess8-20第二十页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSThe Information Ratio The contribution of the active portfolio depends on the ratio of its alpha to its residual standard deviation. The information ratio measures the extra return we can obtain fro

15、m security analysis.8-21第二十一页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSFigure 8.5 Efficient Frontiers with the Index Model and Full-Covariance Matrix8-22第二十二页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSTable 8.2 Portfolios from the Single-Index and Full-Covariance Models8-23第二十三页，共二十八页。INVESTMENTS | BODIE

16、, KANE, MARCUSIs the Index Model Inferior to the Full-Covariance Model? Full Markowitz model may be better in principle, but Using the full-covariance matrix invokes estimation risk of thousands of terms. Cumulative errors may result in a portfolio that is actually inferior to that derived from the

17、single-index model. The single-index model is practical and decentralizes macro and security analysis.8-24第二十四页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSBeta Book: Industry Version of the Index Model Use 60 most recent months of price data Use S&P 500 as proxy for M Compute total returns that ignore d

18、ividends Estimate index model without excess returns: *ebrarm8-25第二十五页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSBeta Book: Industry Version of the Index Model The 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:8-26第二十六页，共二十八页。INVESTMENTS | BODIE, KANE, MARCUSTable 8.4 Industry Betas and Adjustment Factors8-27第二十七页，共二十八页。内容(nirng)总结CHAPTER 8。Expected return-beta relationship:。Risk and covariance:。Adjust beta because:。8-27第二十八页，共二十八页。