Statistical and Graphical Example

Example 8: Using scatter plots to demonstrate beta coefficients

 

The graphic below shows four scatter diagrams. The coordinates of each plotted point shows the intersection of a particular stock's monthly rate of return combined with the monthly rate of return on the S&P 500 index. You can see all plots slope upward to the right indicating a positive relationship between the market return and the return on the stock. Each stock's beta coefficient is given in the graphic. For example, we see Phillip Morris with a beta of 1.69. This means that a 10% change in the S&P would lead to a 16.9% increase in the return on Phillip Morris. The term "characteristic line" is just another term for the regression line described above. Of the four stocks, Coca Cola with a beta of 0.88 would be considered the least risky of all four.

Pay particular attention to the dispersion of the points about the regression line. The less dispersion the better the "fit" and the higher the R-square value will be (as will be discussed). The distance between the regression line and any coordinate is a measure of the diversifiable risk remaining in a market portfolio containing a given stock.

 

 

return to top | previous page | next page