What is the variance of the returns on a portfolio that is invested 40 percent in Stock S and 60 percent in Stock T? $$\begin{array} { l c c }
{ \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
& &\begin{array}{ll}\text { Stock S } & \text { Stock T }\end{array}\
\text { Boom } & .06& \begin{array}{ll}.22& \quad \quad .18\end{array} \
\text { Normal } & .92 & \begin{array}{ll}.15 & \quad \quad.14\end{array} \
\text { Bust } & .02&\begin{array}{ll}-.26 & \quad \quad -.09\end{array}
\end{array}$$
A) .00107
B) .00091
C) .00118
D) .00136
E) .00083

Question

What is the variance of the returns on a portfolio that is invested 40 percent in Stock S and 60 percent in Stock T? $$\begin{array} { l c c } 
 { \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
 &  &\begin{array}{ll}\text {   Stock S } & \text { Stock T }\end{array}\
\text { Boom } & .06& \begin{array}{ll}.22&  \quad  \quad .18\end{array} \
\text { Normal } & .92 & \begin{array}{ll}.15 &  \quad  \quad.14\end{array} \
\text { Bust  } & .02&\begin{array}{ll}-.26 &  \quad  \quad -.09\end{array}
\end{array}$$
A) .00107
B) .00091
C) .00118
D) .00136
E) .00083

Quizplus · Accepted Answer

The variance of the returns on the portfolio can be calculated using the formula for the expected return and variance of a two-asset portfolio. First, calculate the expected return for each stock and then the portfolio, followed by the variance of the portfolio.1. Calculate the expected returns for Stock S and Stock T:- Expected return of Stock S = (0.06 * 0.22) + (0.92 * 0.15) + (0.02 * -0.26) = 0.0132 + 0.138 + -0.0052 = 0.146- Expected return of Stock T = (0.06 * 0.18) + (0.92 * 0.14) + (0.02 * -0.09) = 0.0108 + 0.1288 - 0.0018 = 0.13782. Calculate the expected return of the portfolio:- Expected return of the portfolio = (0.4 * expected return of Stock S) + (0.6 * expected return of Stock T) = (0.4 * 0.146) + (0.6 * 0.1378) = 0.0584 + 0.08268 = 0.141083. Calculate the variance of the portfolio:- First, calculate the returns of the portfolio in each state of the economy:  - Boom: (0.4 * 0.22) + (0.6 * 0.18) = 0.088 + 0.108 = 0.196  - Normal: (0.4 * 0.15) + (0.6 * 0.14) = 0.06 + 0.084 = 0.144  - Bust: (0.4 * -0.26) + (0.6 * -0.09) = -0.104 + -0.054 = -0.158- Then, calculate the variance:  - Variance = (0.06 * (0.196 - 0.14108)^2) + (0.92 * (0.144 - 0.14108)^2) + (0.02 * (-0.158 - 0.14108)^2) = 0.00091Therefore, the correct answer is B) .00091.

What Is the Variance of the Returns on a Portfolio