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

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. i is the regression intercept, and i is the slope (and the stock's estimated beta). t represents the residuals for the regression. What do you think is the motivation for this particular regression? The intercept, 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?