Consider the daily percent changes of McDonald’s stock price andthose of the Dow
Jones Industrial Average for trading days in the months of Julyand August 1987.
Data can be found in the Excel file S4.XLSX (Mc-Dow) in theExcel directory.
a. Draw a scatterplot of McDonald’s daily percent changesagainst the Dow Jones
percent changes.
b. Describe the relationship you see in this scatterplot.
c. Find the correlation between these percent changes. Does thisagree with your
impression of the scatterplot?
d. Find the coefficient of determination (you may just squarethe correlation).
Interpret this number as “variation explained”. In financialterms, it represents
the proportion of non-diversifiable risk in McDonald’s. Forexample, if it were
100%, McDonald’s stock would track the market perfectly, anddiversification
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 extentto which you
can diversify away the risk of McDonald's stock by investingpart of your
portfolio in the Dow Jones Industrial stocks.
f. Find the regression equation to predict the percent change inMcDonald's stock
from the percent change in the Dow Jones Index. Identify thestock's so-called
beta, a measure used by market analysts, which is equal to theslope of this
line. According to the capital asset pricing model, stocks withlarge 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 slopecoefficient.
h. Test at the 5% level to see whether or not the daily percentchanges of
McDonald's and of the Dow Jones Index are significantlyassociated.
i. Test at the 5% level to see whether the beta of McDonald's issignificantly
different from 1, which represents the beta of a highlydiversified portfolio
| McDonald’s stock vs Dow Jones |
| |
| Dow Jones | McDonald’s |
| 0.47 | 1.12 |
| 1.41 | -0.29 |
| 0.70 | 0.83 |
| 0.69 | 0.58 |
| -0.69 | -0.52 |
| -1.38 | 0.20 |
| -2.34 | -0.12 |
| 1.44 | 1.16 |
| -0.24 | 0.10 |
| 0.47 | 0.53 |
| -1.18 | 0.52 |
| -1.19 | -0.89 |
| 0.72 | -0.80 |
| 0.72 | 0.09 |
| 0.95 | 0.07 |
| 0.94 | 0.54 |
| 0.93 | 0.35 |
| 0.92 | 1.04 |
| 0.92 | 0.78 |
| 0.45 | 1.10 |
| 0.23 | 0.18 |
| -1.35 | -0.58 |
| -1.14 | -0.41 |
| 2.08 | 0.78 |
| 3.17 | 1.07 |
| -0.66 | -0.09 |
| 1.99 | 1.69 |
| 3.03 | 1.69 |
| -0.84 | -0.42 |
| 1.48 | 0.83 |
| -0.63 | -0.23 |
| 2.31 | 0.56 |
| -0.21 | -1.70 |
| -2.06 | 0.42 |
| 0.84 | 1.54 |
| 0.00 | 0.10 |
| -2.08 | -0.46 |
| 2.34 | 0.94 |
| -0.21 | 0.76 |
| -1.67 | -0.99 |
| -2.33 | -1.33 |
| 1.08 | 0.89 |
