Sherrie Hymes holds a $200,000 portfolio consisting of the following stocks.The portfolio's beta is 0.875. $$\begin{array} { c r r }
\text { Stock } & \text { Investment } & \text { Beta } \
\hline \text { A } & \$ 50,000 & 0.50 \
\text { B } & 50,000 & 0.80 \
\text { C } & 50,000 & 1.00 \
\text { D } & 50,000 & 1.20 \
\text { Total } &\underline{ \$ 200,000} &
\end{array}$$ 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

Sherrie Hymes holds a $200,000 portfolio consisting of the following stocks.The portfolio's beta is 0.875. $$\begin{array} { c r r } 
\text { Stock } & \text { Investment } & \text { Beta } \
\hline \text { A } & \$ 50,000 & 0.50 \
\text { B } & 50,000 & 0.80 \
\text { C } & 50,000 & 1.00 \
\text { D } & 50,000 & 1.20 \
\text { Total } &\underline{ \$ 200,000} &
\end{array}$$ 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

Quizplus · Accepted Answer

To calculate the new portfolio beta after replacing Stock A with Stock E, we first find the weighted average of the original portfolio's beta and then adjust it for the change. The original calculation of the portfolio's beta is based on the weighted contributions of each stock's beta, which correctly sums up to 0.875 as given. When Stock A (beta of 0.50) is replaced with Stock E (beta of 1.50), the change in the portfolio's beta is calculated as follows:Original beta contribution of Stock A = 0.50 * ($50,000 / $200,000) = 0.125New beta contribution of Stock E = 1.50 * ($50,000 / $200,000) = 0.375The difference due to the replacement = 0.375 - 0.125 = 0.25Therefore, the new portfolio beta = original portfolio beta + difference = 0.875 + 0.25 = 1.125Since the options are given to two decimal places, the correct answer is rounded to 1.13.

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