Paul McLaren holds the following portfolio: $\begin{array}{crr}
\text { Stock } & \text { Investment } &\text { Beta }\
\mathrm{A} & \$ 150,000&1.40 \
\mathrm{~B} & 50,000&0.80 \
\mathrm{C} & 100,000 &1.00\
\mathrm{D} & 75,000&1.20 \
\text { Total } & \$ 375,000
\end{array}$
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?
A) $0.190
B) $0.211
C) $0.234
D) $0.260
E)$0.286

Question

Paul McLaren holds the following portfolio: $\begin{array}{crr}
\text { Stock } &  \text { Investment } &\text { Beta }\
\mathrm{A} &  \$ 150,000&1.40 \
\mathrm{~B} &  50,000&0.80 \
\mathrm{C} &  100,000 &1.00\
\mathrm{D} &  75,000&1.20 \
\text { Total } & \$ 375,000
\end{array}$
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?
A) $0.190
B) $0.211
C) $0.234
D) $0.260
E)$0.286

Quizplus · Accepted Answer

$\begin{array}{l}
\begin{array} { l } 
&&&Original\
\text { Stock } & \text { Investment }& \text { Percentage } \
\text { A } & \$ 150,000  & 40.00 \% \
\text { B } & \$ 50,000   & 13.33 \% \
\text { C } & \$ 100,000  & 26.67 \% \
\text { D } & \$ 75,000 & 20.00 \% \
\text { Total } & \$ 375.000 & 100.00 \% \
\end{array}
\begin{array} { l } 
Beta\
1.400\
0.800\
1.000\
1.200\
&Old. b=\
\end{array}
\begin{array} { l } 
&&New\
\text { Product } &  \text { Beta } & \text { Product } \
0.560 & 0.750 & 0.300 \
0.107 &  0.800 & 0.107 \
0.267 &  1.000 & 0.267 \
\underline{0.240} &  1.200 & \underline{0.240} \
\underline{1.173} &  \text { New b } & \underline{0.913}
\end{array}
\end{array}$
 
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