You have been given this probability distribution for the holding-period return for KMP stock: $$\begin{array} { l c c }
\text { Stock of the Economy } & \text { Probability } & \text { HPR } \
\text { Boom } & 0.30 & 18 \% \
\text { Normal growth } & 0.50 & 12 \% \
\text { Recession } & 0.20 & - 5 \% \
\hline
\end{array}$$ What is the expected variance for KMP stock?
A) 66.04%
B) 69.96%
C) 77.04%
D) 63.72%
E) 78.45%

Question

You have been given this probability distribution for the holding-period return for KMP stock: $$\begin{array} { l c c } 
\text { Stock of the Economy } & \text { Probability } & \text { HPR } \
\text { Boom } & 0.30 & 18 \% \
\text { Normal growth } & 0.50 & 12 \% \
\text { Recession } & 0.20 & - 5 \% \
\hline
\end{array}$$ What is the expected variance for KMP stock?
A) 66.04%
B) 69.96%
C) 77.04%
D) 63.72%
E) 78.45%

Quizplus · Accepted Answer

The expected variance is calculated as the sum of the variances of each possible outcome, weighted by the probability of that outcome. The variance of each outcome is the square of the difference between the outcome and the expected return. The expected return is the sum of the products of each possible outcome and its probability.In this case, the expected return is:```E(R) = 0.30 * 18% + 0.50 * 12% + 0.20 * (-5%) = 10.2%```The variance of each outcome is:```Var(Boom) = (18% - 10.2%)^2 = 64.84%Var(Normal growth) = (12% - 10.2%)^2 = 3.24%Var(Recession) = (-5% - 10.2%)^2 = 225%```The expected variance is:```E(Var) = 0.30 * 64.84% + 0.50 * 3.24% + 0.20 * 225% = 66.04%```Therefore, the correct answer is A.

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