Returns for the Alcoff Company over the last 3 years are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.) $$\begin{array} { l l }
\text { Year } & { Retur } \
2010&21.00 \%\
2009 & - 12.50 \% \
2008 & 25.00 \%
\end{array}$$
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

Question

Returns for the Alcoff Company over the last 3 years are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.) $$\begin{array} { l l } 
\text { Year } & { Retur } \
 2010&21.00 \%\
2009 & - 12.50 \% \
2008 & 25.00 \%
\end{array}$$
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

Quizplus · Accepted Answer

This is a relatively technical problem. It should be used only if calculations are emphasized in class or on a take-home exam where students have time to look up formulas or to use Excel or their calculator functions.
 $\begin{array}{lccc}
 \text { Year } & \underline { \text { Return } } &\text { from Mean }&\text { Deviation }\
2010 & 21.00 \% & 9.83 \% & 0.97 \% \
2009 & -12.50 \% & -23.67 \% & 5.60 \% \
2008 & \underline{25.00 \%} & 13.83 \% & \underline{1.91 \%} \
\text { Expected return } & \underline{11.17 \%} & & \underline{\underline{8.48 \%}}&  \text {Sum sqd
deviations......
$ \mathrm{Sum} / \mathrm{N}-1 $ }\
&&&4.24\%
\end{array}$
$
\mathrm{SQRT}=\alpha=20.59 \%
$$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $ $ 20.59 \% $ with Excel

Returns for the Alcoff Company Over the Last 3 Years Year Retur201021.00%2009−12.50%200825.00%\begin{array} { l l } \text { Year } & { Retur } \\ 2010&21.00 \%\\2009 & - 12.50 \% \\2008 & 25.00 \%\end{array} Year 201020092008​Retur21.00%−12.50%25.00%​

Returns for the Alcoff Company Over the Last 3 Years $\begin{array} { l l } \text { Year } & { Retur } \\ 2010&21.00 \%\\2009 & - 12.50 \% \\2008 & 25.00 \%\end{array}$