GenLabs has been a hot share the last few years,but is risky.The expected returns for GenLabs are highly dependent on the state of the economy as follows: $\begin{array}{|l|l|l|}
\hline
\text { State of Economy } & \text { Probability } & \text { GenLabs Retums } \
\hline \text { Depression } & .05 & -50 \% \
\hline \text { Recession } & .10 & -15 \% \
\hline \text { MildSlowdown } & .20 & 5 \% \
\hline \text { Normal } & .30 & 15 \% \
\hline \text { Broad Expansion } & .20 & 25 \% \
\hline \text { StrongExpansion } & .15 & 40 \%\
\hline
\end{array}$ The variance of GenLabs returns is
A).0207
B).0428
C).0643
D).0733
E)None of the above.

Question

Quizplus · Accepted Answer

To calculate the variance, we need to use the formula:

$Var(X) = \sum_i p_i(x_i - \mu)^2$

where $p_i$ is the probability of state i, $x_i$ is the return in state i, and $\mu$ is the expected return.

Using the data given, we can calculate the expected return as follows:

$\mu = 0.05(-50\%) + 0.1(-15\%) + 0.2(5\%) + 0.3(15\%) + 0.2(25\%) + 0.15(40\%) = 14\%$

Using this, we can now calculate the variance:

$Var(X) = 0.05(-50\% - 14\%)^2 + 0.1(-15\% - 14\%)^2 + 0.2(5\% - 14\%)^2 + 0.3(15\% - 14\%)^2 + 0.2(25\% - 14\%)^2 + 0.15(40\% - 14\%)^2 = 0.0428$

Therefore, the answer is B.

GenLabs Has Been a Hot Share the Last Few Years,but