Chapter 13, Problem 2M

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

  $R_t-R_{ft}={\text{α}}_i+{\text{β}}_i[R_{Mt}-R_{ft}]+{\text{ε}}_t$

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?