Consider the daily percent changes of McDonald’s stock price and those of the Dow Jones Industrial Average for trading days in the months of January and February 2010, as shown in Table 11.3.5.
a. Draw a scatterplot of McDonald’s daily percent changes against the Dow Jones percent changes.
b. Describe the relationship you see in this scatterplot.
c. Find the correlation between these percent changes. Does this agree with your impression from the scatterplot?
d. Find the coefficient of determination. (You may just square the correlation.) Interpret this number as “variation explained.” In financial terms, it represents the proportion of non-diversifiable risk in McDonald’s. For example, if it were 100%, McDonald’s stock would track the market perfectly, and diversification would introduce nothing new.
e. Find the proportion of diversifiable risk. This is just 1 – R2 (or 100% minus the percentage of non-diversifiable risk). This indicates the extent to which you can diversify away the risk of McDonald’s stock by investing part of your portfolio in the Dow Jones Industrial stocks.
f. Find the regression equation to explain the percent change in McDonald’s stock from the percent change in the Dow Jones Index. Identify the stock’s so-called beta, a measure used by market analysts, which is equal to the slope of this line. According to the capital asset pricing model, stocks with large beta values tend to give larger expected returns (on average, over time) than stocks with smaller betas.
g. Find the 95% confidence interval for the slope coefficient.
h. Test at the 5% level to see whether or not the daily percent changes of McDonald’s and of the Dow Jones Index are significantly associated.
i. Test at the 5%level to see whether the beta of McDonald’s is significantly different from 1, which represents the beta of a highly diversified portfolio.

  • CreatedNovember 11, 2015
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