Andre is considering an investment in Bristol Inc.and has gathered the following information.What is the expected standard deviation for a share of the firm's stock? $$\begin{array} { | l | c | c | }
\hline \text { State of the } & \begin{array} { c }
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c }
\text { Conditional Expected Return } \
\text { Bristol Inc. }
\end{array} \
\hline \text { Renomy } & .40 & - 10 \% \
\hline \text { Steady } & .20 & 10 \% \
\hline \text { Boom } & .40 & 45 \% \
\hline
\end{array}$$
A)614.00%
B)24.78%
C)20.13%
D)5.14%

Question

Andre is considering an investment in Bristol Inc.and has gathered the following information.What is the expected standard deviation for a share of the firm's stock? $$\begin{array} { | l | c | c | } 
\hline \text { State of the } & \begin{array} { c } 
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c } 
\text { Conditional Expected Return } \
\text { Bristol Inc. }
\end{array} \
\hline \text { Renomy } & .40 & - 10 \% \
\hline \text { Steady } & .20 & 10 \% \
\hline \text { Boom } & .40 & 45 \% \
\hline
\end{array}$$
A)614.00%
B)24.78%
C)20.13%
D)5.14%

Quizplus · Accepted Answer

To calculate the expected standard deviation, first, we need to find the expected return and then calculate the variance before taking the square root to get the standard deviation.1. Calculate the expected return (E[R]):$$E[R] = (0.40 \times -10\%) + (0.20 \times 10\%) + (0.40 \times 45\%) = -4\% + 2\% + 18\% = 16\%$$2. Calculate the variance ($\sigma^2$):$$ \sigma^2 = 0.40 \times (-10\% - 16\%)^2 + 0.20 \times (10\% - 16\%)^2 + 0.40 \times (45\% - 16\%)^2 $$$$ \sigma^2 = 0.40 \times (-26\%)^2 + 0.20 \times (-6\%)^2 + 0.40 \times (29\%)^2 $$$$ \sigma^2 = 0.40 \times 0.0676 + 0.20 \times 0.0036 + 0.40 \times 0.0841 $$$$ \sigma^2 = 0.02704 + 0.00072 + 0.03364 = 0.0614 $$3. Calculate the standard deviation ($\sigma$):$$ \sigma = \sqrt{0.0614} \approx 0.2478 \text{ or } 24.78\% $$Therefore, the expected standard deviation for a share of Bristol Inc.'s stock is approximately 24.78%.

Andre Is Considering an Investment in Bristol Inc A)61400% B)24

Andre Is Considering an Investment in Bristol Inc A)61400%
B)24