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CHAPTER 8

CHAPTER 8. Index Models. Reduces the number of inputs for diversification Easier for security analysts to specialize. Advantages of the Single Index Model. ß i = index of a securities’ particular return to the factor m = Unanticipated movement related to security returns

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CHAPTER 8

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  1. CHAPTER 8 Index Models

  2. Reduces the number of inputs for diversification Easier for security analysts to specialize Advantages of the Single Index Model

  3. ßi = index of a securities’ particular return to the factor m = Unanticipated movement related to security returns ei = Assumption: a broad market index like the S&P 500 is the common factor. Single Factor Model

  4. Single-Index Model Regression Equation: Expected return-beta relationship:

  5. Single-Index Model Continued Risk and covariance: Total risk = Systematic risk + Firm-specific risk: Covariance = product of betas x market index risk: Correlation = product of correlations with the market index

  6. Index Model and Diversification Portfolio’s variance: Variance of the equally weighted portfolio of firm-specific components: When n gets large, becomes negligible

  7. Figure 8.1 The Variance of an Equally Weighted Portfolio with Risk Coefficient βp in the Single-Factor Economy

  8. Figure 8.2 Excess Returns on HP and S&P 500 April 2001 – March 2006

  9. Figure 8.3 Scatter Diagram of HP, the S&P 500, and the Security Characteristic Line (SCL) for HP

  10. Table 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-Packard

  11. Figure 8.4 Excess Returns on Portfolio Assets

  12. Alpha and Security Analysis Macroeconomic analysis is used to estimate the risk premium and risk of the market index Statistical analysis is used to estimate the beta coefficients of all securities and their residual variances, σ2 ( e i ) Developed from security analysis

  13. Alpha and Security Analysis Continued The market-driven expected return is conditional on information common to all securities Security-specific expected return forecasts are derived from various security-valuation models The alpha value distills the incremental risk premium attributable to private information Helps determine whether security is a good or bad buy

  14. Single-Index Model Input List Risk premium on the S&P 500 portfolio Estimate of the SD of the S&P 500 portfolio n sets of estimates of Beta coefficient Stock residual variances Alpha values

  15. Optimal Risky Portfolio of the Single-Index Model Maximize the Sharpe ratio Expected return, SD, and Sharpe ratio:

  16. Optimal Risky Portfolio of the Single-Index Model Continued Combination of: Active portfolio denoted by A Market-index portfolio, the (n+1)th asset which we call the passive portfolio and denote by M Modification of active portfolio position: When

  17. The Information Ratio The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy):

  18. Figure 8.5 Efficient Frontiers with the Index Model and Full-Covariance Matrix

  19. Table 8.2 Comparison of Portfolios from the Single-Index and Full-Covariance Models

  20. Table 8.3 Merrill Lynch, Pierce, Fenner & Smith, Inc.: Market Sensitivity Statistics

  21. Table 8.4 Industry Betas and Adjustment Factors

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