Richard has two investment opportunities.He can invest in The Sunglasses Company or The Umbrella Company.What is the expected return and standard deviation of each company? $$\begin{array} { | l | c | c | c | }
\hline \begin{array} { l }
\text { State of the } \
\text { Economy }
\end{array} & \begin{array} { c }
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c }
\text { Expected Retum Sunglasses } \
\text { Company }
\end{array} & \begin{array} { c }
\text { Expected Return } \
\text { Umbrella Company }
\end{array} \
\hline \text { Sunny } & .50 & 25 \% & 0 \% \
\hline \text { Rainy } & .50 & 0 \% & 25 \% \
\hline
\end{array}$$
A)The expected return for each company is 12.50% and the standard deviation for each company is 0.00%.
B)The expected return for each company is 12.50% and the standard deviation for each company is 12.50%.
C)The expected return for each company is 12.50% and the standard deviation for each company is 156.25%.
D)The expected return for each company is 12.50% and the standard deviation for each company is 25.00%.

Question

Richard has two investment opportunities.He can invest in The Sunglasses Company or The Umbrella Company.What is the expected return and standard deviation of each company? $$\begin{array} { | l | c | c | c | } 
\hline \begin{array} { l } 
\text { State of the } \
\text { Economy }
\end{array} & \begin{array} { c } 
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c } 
\text { Expected Retum Sunglasses } \
\text { Company }
\end{array} & \begin{array} { c } 
\text { Expected Return } \
\text { Umbrella Company }
\end{array} \
\hline \text { Sunny } & .50 & 25 \% & 0 \% \
\hline \text { Rainy } & .50 & 0 \% & 25 \% \
\hline
\end{array}$$
A)The expected return for each company is 12.50% and the standard deviation for each company is 0.00%.
B)The expected return for each company is 12.50% and the standard deviation for each company is 12.50%.
C)The expected return for each company is 12.50% and the standard deviation for each company is 156.25%.
D)The expected return for each company is 12.50% and the standard deviation for each company is 25.00%.

Quizplus · Accepted Answer

The expected return for both companies is calculated as the average of the returns under both states of the economy, which is $(25\% + 0\%)/2 = 12.5\%$. The standard deviation is calculated based on the deviation of each state's return from the expected return, which in this case is $12.5\%$, leading to a standard deviation of $12.5\%$.

Richard Has Two Investment Opportunities A)The Expected Return for Each Company Is 12