Paul McLaren holds the following portfolio: $\begin{array}{lll}
Stock&Investment&Beta\
A&\$ 150,000 & 1.40 \
B&50,000 & 0.80 \
C&100,000 & 1.00 \
D&75,000 & 1.20\
Total&\$ 375,000 \
\end{array}$
Paul plans to sell Stock A and replace it with Stock E, which has a beta of 0.75. By how much will the portfolio beta change?

Question

Quizplus · Accepted Answer

$\begin{array}{l}
\begin{array} { l } 
&&&Origina\
Stock& Investment& Percentage& Beta\
A&\$ 150,000 &  40.00 \% & 1.400 \
B&\$ 50,000 &  13.33 \% & 0.800 \
C&\$ 100,000 &  26.67 \% & 1.000 \
D&\$ 75,000 & 20.00 \% & 1.200\
\end{array}
\begin{array} { l ll} 
&New &\
Product& Beta&Product\
0.560 & 0.750 & 0.300 \
0.107 & 0.800 & 0.107 \
0.267 & 1.000 & 0.267 \
0.240 & 1.200 & 0.240 \
\end{array}
\end{array}$
 
Change in beta = New σ Old = σ0.260 Alternative solution: (bE σ bA) × %A = σ0.260

Paul McLaren Holds the Following Portfolio Paul Plans to Sell Stock a and Replace It with \\B&50,000

Paul McLaren Holds the Following Portfolio Paul Plans to Sell Stock a and Replace It with \\
B&50,000