Macro Corporation has had the following returns for the past three years: -10 percent, 10 percent, and 30 percent.Use the following formulas to calculate the standard deviation of the returns: Variance = expected value of $\left( r _ { m } \right)$ $\left( \tilde { r } _ { m } - r _ { m } \right) ^ { 2 }$ Standard deviation of . $\tilde { r } _ { m } = \sqrt { \text { variance } \left( r _ { m } \right) }$
A)10.00 percent
B)16.33 percent
C)18.21 percent
D)30.00 percent

Question

Quizplus · Accepted Answer

First, we need to calculate the expected value of the returns ($r_m$):
\begin{align*}
r_m &= \frac{-10\% + 10\% + 30\%}{3} \
&= 10\%
\end{align*}

Next, we can calculate the variance of the returns using the formula:
\begin{align*}
\text{variance}(r_m) &= \frac{(-10\% - 10\%)^2 + (10\% - 10\%)^2 + (30\% - 10\%)^2}{3} \
&= 0.24
\end{align*}

Finally, we can calculate the standard deviation of the returns using the formula:
\begin{align*}
\text{standard deviation}(r_m) &= \sqrt{\text{variance}(r_m)} \
&= \sqrt{0.24} \
&\approx 0.1633 \
&\approx 16.33\%
\end{align*}

Therefore, the best choice is B because it is the closest option to the calculated standard deviation of 16.33%.

Macro Corporation Has Had the Following Returns for the Past (rm)\left( r _ { m } \right)(rm​)

Macro Corporation Has Had the Following Returns for the Past $\left( r _ { m } \right)$