# Question

The beta of a stock is found by running a regression with the monthly return on a market index as the explanatory variable and the monthly return on the stock as the dependent variable. The beta of the stock is then the slope of this regression line.

a. Explain why most stocks have a positive beta.

b. Explain why a stock with a beta with absolute value greater than one is more volatile than the market index and a stock with a beta less than one (in absolute value) is less volatile than the market index.

c. Use the data in the file P10_45.xlsx to estimate the beta for each of the four companies listed: Caterpillar, Goodyear, McDonalds, and Ford. Use the S&P 500 as the market index.

d. For each of these companies, what percentage of the variation in its returns is explained by the variation in the market index? What percentage is unexplained by variation in the market index?

e. Verify (using Excel’s COVAR and VARP functions) that the beta for each company is given by

Covariance between Company and Market / Variance of Market

Also, verify that the correlation between each company’s returns and the market’s returns is the square root of R2.

a. Explain why most stocks have a positive beta.

b. Explain why a stock with a beta with absolute value greater than one is more volatile than the market index and a stock with a beta less than one (in absolute value) is less volatile than the market index.

c. Use the data in the file P10_45.xlsx to estimate the beta for each of the four companies listed: Caterpillar, Goodyear, McDonalds, and Ford. Use the S&P 500 as the market index.

d. For each of these companies, what percentage of the variation in its returns is explained by the variation in the market index? What percentage is unexplained by variation in the market index?

e. Verify (using Excel’s COVAR and VARP functions) that the beta for each company is given by

Covariance between Company and Market / Variance of Market

Also, verify that the correlation between each company’s returns and the market’s returns is the square root of R2.

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