You have been given this probability distribution for the holding-period return for a stock: $\begin{array}{lll}
\underline{\text { State of the Economy} } &\underline{ \text { Probability} } & \underline{\text { HPR } }\
\text { Boom } & .40 & 22\% \
\text { Normal growth } & .35 & 11\%\
\text { Recession } & .25 & -9 \%
\end{array}$

-What is the expected variance for the stock?
A)142.07%
B)189.96%
C)177.04%
D)128.17%
E)None of the above

Question

You have been given this probability distribution for the holding-period return for a stock: $\begin{array}{lll}
\underline{\text { State of the Economy} } &\underline{ \text { Probability} } & \underline{\text { HPR } }\
\text { Boom } & .40 & 22\% \
\text { Normal growth } & .35 & 11\%\
\text { Recession } & .25 & -9 \%
\end{array}$

-What is the expected variance for the stock?
A)142.07%
B)189.96%
C)177.04%
D)128.17%
E)None of the above

Quizplus · Accepted Answer

The expected variance is calculated using the formula: $\sum (p_i \times (r_i - \text{expected return})^2)$. First, calculate the expected return: $0.4 \times 0.22 + 0.35 \times 0.11 + 0.25 \times (-0.09) = 0.1045$. Then, calculate the variance: $0.4 \times (0.22 - 0.1045)^2 + 0.35 \times (0.11 - 0.1045)^2 + 0.25 \times (-0.09 - 0.1045)^2 = 0.0149$ or 1.49%. None of the given options match this result.

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