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 standard deviation of GenLabs returns is
A).0845
B).2069
C).3065
D).3358
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 standard deviation of GenLabs returns is
A).0845
B).2069
C).3065
D).3358
E)None of the above

Quizplus · Accepted Answer

To find the standard deviation of GenLabs returns, we need to calculate the variance first. We can use the following formula:
Variance = P(Depression)(Return-Expected Return)^2 + P(Recession)(Return-Expected Return)^2 + P(Mild Slowdown)(Return-Expected Return)^2 + P(Normal)(Return-Expected Return)^2 + P(Broad Expansion)(Return-Expected Return)^2 + P(Strong Expansion)(Return-Expected Return)^2
Where P stands for probability and the expected return is the weighted average of individual returns:
Expected return = P(Depression)(-50%) + P(Recession)(-15%) + P(Mild Slowdown)(5%) + P(Normal)(15%) + P(Broad Expansion)(25%) + P(Strong Expansion)(40%)
Plugging in the numbers, we get:
Expected return = (0.5)(-50%) + (0.1)(-15%) + (0.2)(5%) + (0.3)(15%) + (0.2)(25%) + (0.15)(40%) = 9.75%
Now, we can calculate the variance using the formula above, which gives us:
Variance = (0.5)(-50%-9.75%)^2 + (0.1)(-15%-9.75%)^2 + (0.2)(5%-9.75%)^2 + (0.3)(15%-9.75%)^2 + (0.2)(25%-9.75%)^2 + (0.15)(40%-9.75%)^2 = 0.04288
Finally, we can take the square root of the variance to get the standard deviation:
Standard deviation = sqrt(Variance) = sqrt(0.04288) = 0.2069
Therefore, the answer is B.

GenLabs Has Been a Hot Stock the Last Few Years