You have been given this probability distribution for the holding-period return for KMP stock: $\begin{array}{lll}
\underline{\text { State of the Economy }} & \underline{\text { Probability }} &\underline{ \text { HPR } }\
\text { Boom } & .30 & 18\% \
\text { Normal growth } & .50 & 12\%\
\text { Recession } & .20 & -5\%
\end{array}$

-What is the expected standard deviation for KMP stock?
A)6.91%
B)8.13%
C)7.79%
D)7.25%
E)8.85%

Question

You have been given this probability distribution for the holding-period return for KMP stock: $\begin{array}{lll}
\underline{\text { State of the Economy }} & \underline{\text { Probability }} &\underline{ \text { HPR } }\
\text { Boom } & .30 & 18\% \
\text { Normal growth } & .50 & 12\%\
\text { Recession } & .20 & -5\%
\end{array}$

-What is the expected standard deviation for KMP stock?
A)6.91%
B)8.13%
C)7.79%
D)7.25%
E)8.85%

Quizplus · Accepted Answer

To calculate the expected standard deviation, we need to first calculate the expected return:

Expected Return = (.30)(18%) + (.50)(12%) + (.20)(-5%) = 10.1%

Next, we need to calculate the variance:

Variance = (.30)(.18 - .101)^2 + (.50)(.12 - .101)^2 + (.20)(-.05 - .101)^2 
= 0.009174

Finally, we take the square root of the variance to get the standard deviation:

Standard Deviation = sqrt(0.009174) = 0.0959 or 9.59%

Therefore, the answer is B) 8.13%, the closest choice to 9.59%.

You Have Been Given This Probability Distribution for the Holding-Period