Predicted return

eGMt RGMt ( GMRMt GM)

These residuals are estimates of the monthly unexpected firm-specific component of the rate of return on GM stock. Hence we can estimate the firm-specific variance by5

1 12 2(eGM) 10 et 12.60 t 1

The standard deviation of the firm-specific component of GMs return, (eGM), is 12.60 3.55% per month, equal to the standard deviation of the regression residual.

5 Because the mean of et is zero, e2 is the squared deviation from its mean. The average value of e2 is therefore the estimate of the t t variance of the firm-specific component. We divide the sum of squared residuals by the degrees of freedom of the regression, n 2 12 2 10, to obtain an unbiased estimate of 2(e).

III. Equilibrium In Capital

Markets

10. Single−Index and

Multifactor Models

The McGraw−Hill

Companies, 2001

CHAPTER 10 Single-Index and Multifactor Models 299

The Index Model and Diversification

The index model, first suggested by Sharpe,6 also offers insight into portfolio diversifica- tion. Suppose that we choose an equally weighted portfolio of n securities. The excess rate of return on each security is given by

Ri i iRM ei Similarly, we can write the excess return on the portfolio of stocks as RP P PRM eP (10.5) We now show that, as the number of stocks included in this portfolio increases, the part of