Chapter 11, Problem 2CC

Beta is often estimated by linear regression. A model often used is called the market model, which is:

R_t – R_ft = α_i + β_i [R_Mt – R_ft] + ε_t

In this regression, R_t is the return on the stock and R_ft is the risk-free rate for the same period. R_Mt is the return on a stock market index such as the S&P 500 index, α_i is the regression intercept, and β_i is the slope (and the stock’s estimated beta). ε_t represents the residuals for the regression. What do you think is the motivation for this particular regression? The intercept, α_i, is often called Jensen’s alpha. What does it measure? If an asset has a positive Jensen’s alpha, where would it plot with respect to the SML? What is the financial interpretation of the residuals in the regression?