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

Question

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

Quizplus · Accepted Answer

The expected return of the portfolio is calculated as the weighted average of the returns of the individual investments. Since Richard is investing 50% in each company, the expected return is (0.5 * 25% + 0.5 * 0%) for sunny and (0.5 * 0% + 0.5 * 25%) for rainy, both resulting in 12.5%. The standard deviation is 0.00% because the returns perfectly offset each other in different states, eliminating variability.

Richard Has Two Investment Opportunities A)The Expected Return for the Portfolio Is 12