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Index Models
Chapter 10
Advantages of the Single Index Model
Reduces the number of inputs for diversification.
Easier for security analysts to specialize.
1102
Single Factor Model
ri = E(Ri) + ßiF + e
ßi = 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.
1103
Single Index Model
(ri rf) = i + ßi(rm rf) + ei
Risk Prem Market Risk Prem or Index Risk Prem
i
= the stock’s expected return if the
market’s excess return is zero (rm rf) = 0
ßi(rm rf) = the component of return due to
movements in the market index
ei = firm specific component, not due to market
movements
1104
Risk Premium Format
Let: Ri = (ri rf) Risk premium Rm = (rm rf) format
Ri = i + ßi(Rm) + ei
1105
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