GenLabs has been a hot stock the last few years, but is risky. The expected returns for GenLabs are highly dependent on the state of the economy as follows:
$\begin{array} { l l l }
\underline{\text { State of Economy }} & \underline{\text { Probability }} & \underline{ \text { GenLabs Returns } }\
\text { Depression } & . \mathbf { 0 5 } & \mathbf { - 5 0 \% } \
\text { Recession } & .10 & \mathbf { - 1 5 \% } \
\text { Mild Slowdown } & .20 & \mathbf { 5 \% } \
\text { Normal } & .30 & \mathbf { 1 5 \% } \
\text { Broad Expansion } & .20 & \mathbf { 2 5 } \% \
\text { Strong Expansion } & .15 & \mathbf { 4 0 \% }
\end{array}$
-The variance of GenLabs returns is:
A).0207
B).0428
C).0643
D).0733
E)None of the above.

Question

GenLabs has been a hot stock the last few years, but is risky. The expected returns for GenLabs are highly dependent on the state of the economy as follows:
$\begin{array} { l l l } 
 \underline{\text { State of Economy }} &  \underline{\text { Probability }} & \underline{ \text { GenLabs Returns } }\
 \text { Depression } & . \mathbf { 0 5 } & \mathbf { - 5 0 \% } \
\text { Recession } & .10 & \mathbf { - 1 5 \% } \
\text { Mild Slowdown } & .20 & \mathbf { 5 \% } \
\text { Normal } & .30 & \mathbf { 1 5 \% } \
\text { Broad Expansion } & .20 & \mathbf { 2 5 } \% \
\text { Strong Expansion } & .15 & \mathbf { 4 0 \% }
\end{array}$
-The variance of GenLabs returns is:
A).0207
B).0428
C).0643
D).0733
E)None of the above.

Quizplus · Accepted Answer

First, we need to calculate the expected return of GenLabs:
$$E(R)=0.5(-50\%)+0.10(-15\%)+0.20(5\%)+0.30(15\%)+0.20(25\%)+0.15(40\%)=11.5\%$$
Next, we need to calculate the variance of the returns:
$$Var(R)=(0.5(-50\%-11.5\%)^2+0.10(-15\%-11.5\%)^2+0.20(5\%-11.5\%)^2+0.30(15\%-11.5\%)^2+0.20(25\%-11.5\%)^2+0.15(40\%-11.5\%)^2)$$
Solving this equation results in:
$$Var(R)=0.0428$$
Therefore, the answer is B.

GenLabs Has Been a Hot Stock the Last Few Years