The probabilities of different returns on a stock over the year are: $$\begin{array} {cc }
\text { Probability } & \text { Return } \
10 \% & - 5 \% \
15 \% & 0 \% \
20 \% & 5 \% \
30 \% & 10 \% \
25 \% & 20 \%
\end{array}$$

The standard deviation of the return on the stock is about_____ percent.

Question

The probabilities of different returns on a stock over the year are: $$\begin{array} {cc } 
\text { Probability } & \text { Return } \
10 \% & - 5 \% \
15 \% & 0 \% \
20 \% & 5 \% \
30 \% & 10 \% \
25 \% & 20 \%
\end{array}$$

The standard deviation of the return on the stock is about_____ percent.

Quizplus · Accepted Answer

To calculate the standard deviation, we need to first calculate the expected return (E(r)) and the variance.
E(r) = (0.1*-0.05)+(0.15*0)+(0.2*0.05)+(0.3*0.1)+(0.25*0.2) = 0.0975 or 9.75%
Variance = (0.1*(-0.05-0.0975)^2)+(0.15*(0-0.0975)^2)+(0.2*(0.05-0.0975)^2)+(0.3*(0.1-0.0975)^2)+(0.25*(0.2-0.0975)^2) = 0.0162
Standard deviation = square root of variance = 0.127 or 12.7%
Since the answer choices are in rounded percentages, the closest choice is B) 8.

The Probabilities of Different Returns on a Stock Over the Year