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: $\begin{array}{|l|l|l|}
\hline \text { State of Economy } & \text { Probability } & \text { GenLabs Returns } \
\hline \text { Depression } & .05 & -50 \% \
\hline \text { Recession } & .10 & -15 \% \
\hline \text { Mild Slowdown } & .20 & 5 \% \
\hline \text { Normal } & .30 & 15 \% \
\hline \text { Broad Expansion } & .20 & 25 \% \
\hline \text { StrongExpansion } & .15 & 40 \%\
\hline
\end{array}$ The standard deviation of GenLabs returns is
A).0845
B).2069
C).3065
D).3358
E)None of the above.

Question

Quizplus · Accepted Answer

To calculate the standard deviation of GenLabs returns, we need to first calculate the expected return and then use it to calculate the variance and standard deviation. The expected return is calculated as follows:

Expected Return = (0.05 x (-50%)) + (0.10 x (-15%)) + (0.20 x 5%) + (0.30 x 15%) + (0.20 x 25%) + (0.15 x 40%)
Expected Return = 13.5%

The variance is calculated as follows:

Variance = (0.05 x (-50% - 13.5%)^2) + (0.10 x (-15% - 13.5%)^2) + (0.20 x (5% - 13.5%)^2) + (0.30 x (15% - 13.5%)^2) + (0.20 x (25% - 13.5%)^2) + (0.15 x (40% - 13.5%)^2)
Variance = 0.0445

And the standard deviation is the square root of the variance:

Standard Deviation = √0.0445
Standard Deviation = 0.210725

Therefore, the answer is B) 0.2069 (rounded to four decimal places).

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