It is possible (although unlikely) that even in the multifactor economy, only exposure to market risk will be "priced," that is, carry a risk premium, so that only the usual single-index beta would matter for expected stock returns. Even in this case, however, portfolio managers interested in analyzing the risks to which their portfolios are exposed still would do better to use a multifactor model that can capture the multiplicity of risk sources. III. Equilibrium In Capital Markets 10. Single−Index and Multifactor Models The McGraw−Hill Companies, 2001           E X C E L A P P L I C A T I O N       ESTIMATING BETA COEFFICIENTS   The spreadsheet Betas, which you will find on the Online Learning Center (www.mhhe.com/bkm), contains 60 months returns for 10 individual stocks. Returns are calculated over the five years ending in December 2000. The spreadsheet also contains re- turns for S&P 500 Index and the observed risk-free rates as measured by the one-year Trea- sury bill. With this data, monthly excess returns for the individual securities and the market as measured by the S&P 500 Index can be used with the regression module in Excel. The spreadsheet also contains returns on an equally weighted portfolio of the individual securi- ties. The regression module is available under Tools Data Analysis. The dependent variable is the security excess return. The independent variable is the market excess return. A sample of the output from the regression is shown below. The estimated beta coeffi- cient for American Express is 1.21, and 48% of the variance in returns for American Express can be explained by the returns on the S&P 500 Index.   A B C D E F   1 SUMMARY OUTPUT AXP   2   3 Regression Statistics   4 Multiple R 0.69288601   5 R Square 0.48009103