Sherrie Hymes holds a $200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.875. $\begin{array}{lrl}
\text { Total }&\text { Investment }&\text { Beta }\
\mathrm{A} & \$ 50,000 & 0.50 \
\mathrm{~B} & 50,000 & 0.80 \
\mathrm{C} & 50,000 & 1.00 \
\mathrm{D} & 50,000 & 1.20\
\text { Total }&\$200,000
\end{array}$
If Sherrie replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio's new beta be?
A) 1.07
B) 1.13
C) 1.18
D) 1.24
E) 1.30

Question

Quizplus · Accepted Answer

$ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $$\text { Original Porfolio }$
$\begin{array}{l}
\begin{array} { l } 
\text { Stock }& \text { Investment } & \text { Percentage } \
\mathrm{A} & \$ 50,000 & 25.00 \% \
\mathrm{~B} & \$ 50,000 & 25.00 \% \
\mathrm{C} & \$ 50,000 & 25.00 \% \
\mathrm{D} & \$ 50,000 & 25.00 \% \
\mathrm{E} & & \
\text { Total } & \$ 200,000 & 100.00 \%
\end{array}
\begin{array} { l } 
\text { Beta }& \text { Product } \
0.50& 0.125 \
0.80  & 0.200 \
1.00& 0.250 \
1.20 & 0.300 \\
& 0.875
\end{array}
\end{array}$
 
 $\begin{array}{llll}
&&&\text { New Portfolio }\
\text { Stock }& \text { Percentage }&\text { Beta }& \text { Product } \
\mathrm{B} & 25.00 \% & 0.80 & 0.200 \
\mathrm{C} & 25.00 \% & 1.00 & 0.250 \
\mathrm{D} & 25.00 \% & 1.20 & 0.300 \
\mathrm{E} & 25.00 \% & 1.50 & 0.375\
\text { Total New}&\text { Portfolio beta}&&1.025
\end{array}$ 
Alternative solution: (bE σ bA)(%A) + bOld = 1.125

Sherrie Hymes Holds a $200,000 Portfolio Consisting of the Following