In words the beta is the covariance of a security with the market divided by

# In words the beta is the covariance of a security

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In words, the beta is the covariance of a security with the market, divided by the variance of the market. Because we calculated both covariance and variance in earlier chapters, calculating beta involves no new material. Measuring Company Betas The basic method of measuring company betas is to estimate: using = 1,2,…, observations. Problems
1. Betas may vary over time. 2. The sample size may be inadequate. 3. Betas are influenced by changing financial leverage and business risk. Solutions 1. Problems 1 and 2 can be moderated by more sophisticated statistical techniques. 2. Problem 3 can be lessened by adjusting for changes in business and financial risk. 3. Look at average beta estimates of several comparable firms in the industry It is instructive to see how betas are determined for actual real-world companies. Figure 13.3 plots monthly returns for four large firms against monthly returns on the Standard & Poor’s (S&P) 500 Index. Using a standard regression technique, we fit a straight line through data points. The result is called the “characteristic” line for the security. The slope of the characteristic line is beta. Though we have not shown it in the table, we can also determine the intercept (commonly called alpha) of the characteristic line by regression. Figure 13.3 Plots of Five Years of Monthly Returns (2003-2007) on Four Individual Securities against Five Years of Monthly Returns on the Standard & Poor’s (S&P) 500 Index
We use five years of monthly data for each plot. Although this choice is arbitrary, it is in line with calculations performed in the real world. Practitioners know that the accuracy of the beta coefficient is suspect when too few observations are used. Conversely, because firms may change their industry over time, observations from the distant past are out of date. We stated in a previous chapter that the average beta across all stocks in an index is 1. Of course, this need not be true for a subset of the index. For example, of the four securities in our figure, two have betas above 1 and two have betas below 1. Because beta is a measure of the risk of a single security for someone holding a large, diversified portfolio, our results indicate that Microsoft has relatively low risk and Amazon.com has relatively high risk. We have stated that the beta of a firm is likely to change if the firm changes its industry. It is also interesting to ask the reverse question: Does the beta of a firm stay the same if its industry stays the same? Take the case of American Airlines, now called AMR Corporation, which has remained in the same industry for many decades. Figure 13.4 plots the returns on AMR and the returns on the S&P 500 for four successive five-year periods. As can be seen from the figure, AMR’s beta varies from period to period. However, this movement in beta is probably nothing more than random variation.

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