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Ch10 Index Models

# Ch10 Index Models - Index Models Chapter 10 Advantages...

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Index Models Chapter 10

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Advantages Reduces the number of inputs for diversification. Easier for security analysts to specialize.
Single Factor model r i = E(R i ) + ß i F + e ß i = index of a securities’ particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Assumption: a broad market index like the S&P500 is the common factor.

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Single factor model (r i - r f ) = i + ß i (r m - r f ) + e i α Risk Prem Market Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero ß i (r m - r f ) = the component of return due to movements in the market index (r m - r f ) = 0 e i = firm specific component, not due to market movements r α
Risk premium Let: R i = (r i - r f ) R m = (r m - r f ) Risk premium R i = α i + ß i (R m ) + e i

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Security Characteristic Line Excess Returns (i) SCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excess returns on market index R i = α i + ß i R m + e i . .
Example Jan. Feb. . . Dec Mean Std Dev 5.41 -3.44 . . 2.43 -.60 4.97 7.24 .93 . . 3.90 1.75 3.32 Excess Mkt. Ret. Excess GM Ret.

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Regression result Estimated coefficient Std error of estimate Variance of residuals = 12.601 Std dev of residuals = 3.550

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Ch10 Index Models - Index Models Chapter 10 Advantages...

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