the excess return (over the risk-free rate) on the market index, whereas the vertical axis measures the excess return on the asset in ques- tion (GM stock in our example). A pair of excess returns (one for the market index, one for GM stock) constitutes one point on this scatter diagram. The points are numbered 1 through 12, representing excess returns for the S&P 500 and GM for each month from January through December. The single-index model states that the relationship between the excess returns on GM and the S&P 500 is given by   RGMt GM GMRMt eGMt   Note the resemblance of this relationship to a regression equation. In a single-variable regression equation, the dependent variable plots around a straight line with an intercept and a slope . The deviations from the line, e, are assumed to be mutually uncorrelated as well as uncorrelated with the independent variable. Because these assumptions are identical to those of the index model we can look at the index model as a regression model. The sensitivity of GM to the market, measured by GM, is the slope of the regression line. The intercept of the regression line is GM, representing the average firm-specific return when the markets excess return is zero. Deviations of particular ob- servations from the regression line in any period are denoted eGMt, and called residuals. Each of these residuals is the difference between the actual stock return and the return that would be predicted from the regression equation describing the usual relationship between the stock and the market; therefore, residuals measure the impact of firm-specific events during the particular month. The parameters of interest, , , and Var(e), can be estimated using standard regression techniques. Estimating the regression equation of the single-index model gives us the security characteristic line (SCL), which is plotted in Figure 10.1. (The regression results and raw III. Equilibrium In Capital Markets 10. Single−Index and Multifactor Models The McGraw−Hill Companies, 2001           298 PART III Equilibrium in Capital Markets     Table 10.1 Characteristic Line for GM Stock