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The Characteristic Line

We are now in a position to compare the expected return for an individual stock with the expected return for the market portfolio. In our comparison, it is useful to deal with returns in excess of the risk-free rate, which acts as a benchmark against which the risky asset returns are contrasted. The excess retrrrr is simply the expected return less the risk-free return.

The solid blue line is known as the security's characteristic line; it depicts the expected relationship between excess returns for the stock and excess returns for the market portfolio. The expected relationship may be based on past experience, in which case actual excess returns for the stock and for the market portfolio would be plotted on the graph, and a regression line best characterizing the historical relationship would be drawn. Such a situation is illustrated by the scatter diagram shown in the figure. Each point represents the excess return of the stock and that of the S&P 500 Index for a given month in the past (60 months in total). From these returns the monthly risk-free rate is subtracted to obtain excess returns.

For our example stock, we see that, when returns on the market portfolio are high, returns on the stock tend to be high as well. Instead of using historical return relationships, one might obtain future return estimates from security analysts who follow the stock. Because this approach is usually restricted to investment organizations with a number of security analysts, we illustrate the relationship assuming the use of historical data.