Suppose that some data have been collected on the excess returns on a fund manager’s portfolio (‘fund XXX’) together with the excess returns on a market index, as shown in Table 3.1.

Table 3.1 Sample data on fund XXX to motivate OLS estimation The fund manager has some intuition that the beta (in the CAPM framework) on this fund is positive, and she therefore wants to find whether there appears to be a relationship between x and y given the data. Again, the first stage could be to form a scatter plot of the two Figure 3.6 Scatter plot of excess returns on fund XXX versus excess returns on the market portfolio Clearly, there appears to be a positive, approximately linear relationship between x and y, although there is not much data on which to base this conclusion! Plugging the five observations in to make up the formulae given in equations (3.5) and (3.4) would lead to the estimates and The fitted line would be written as (3.7)
where xt is the excess return of the market portfolio over the risk-free rate (i.e., rm – rf), also known as the market risk premium.