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The Annual Returns of Wonder Widgets,Inc Find the Following for Wonder Widgets:
A

Question 15

Essay

The annual returns of Wonder Widgets,Inc.and the S&P 500 Composite Index over the last ten years were as follows:
 Year  Wonder Widgets  S&P 500115%8.5%210%4.0%312%14.0%420%15.0%520%14.0%615%26.0%725%37.0%830%24.0%910%7.0%103%6.5%\begin{array} { r c c } \text { Year } & \text { Wonder Widgets } & \text { S\&P } 500 \\\hline 1 & - 15 \% & - 8.5 \% \\2 & 10 \% & 4.0 \% \\3 & 12 \% & 14.0 \% \\4 & 20 \% & 15.0 \% \\5 & - 20 \% & - 14.0 \% \\6 & - 15 \% & - 26.0 \% \\7 & 25 \% & 37.0 \% \\8 & 30 \% & 24.0 \% \\9 & - 10 \% & - 7.0 \% \\10 & 3 \% & 6.5 \%\end{array}
Find the following for Wonder Widgets:
a. Beta ( β\beta W, slope of regression line)
b. Alpha ( α\alpha W, intercept of regression line)
c. Unsystematic variance ( σ\sigma 2W - β\beta 2W σ\sigma 2m)
d. Correlation coefficient (  The annual returns of Wonder Widgets,Inc.and the S&P 500 Composite Index over the last ten years were as follows:  \begin{array} { r c c }  \text { Year } & \text { Wonder Widgets } & \text { S\&P } 500 \\ \hline 1 & - 15 \% & - 8.5 \% \\ 2 & 10 \% & 4.0 \% \\ 3 & 12 \% & 14.0 \% \\ 4 & 20 \% & 15.0 \% \\ 5 & - 20 \% & - 14.0 \% \\ 6 & - 15 \% & - 26.0 \% \\ 7 & 25 \% & 37.0 \% \\ 8 & 30 \% & 24.0 \% \\ 9 & - 10 \% & - 7.0 \% \\ 10 & 3 \% & 6.5 \% \end{array}  Find the following for Wonder Widgets: a. Beta ( \beta <sub>W</sub>, slope of regression line) b. Alpha ( \alpha <sub>W</sub>, intercept of regression line) c. Unsystematic variance ( \sigma <sup>2</sup><sub>W</sub> - \beta <sup>2</sup><sub>W</sub> \sigma <sup>2</sup><sub>m</sub>) d. Correlation coefficient  (    ) )

Correct Answer:

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a.Beta: blured image = 0.89
b.Alpha: blured image = ...

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