Consider a value-weighted market index that includes the following two companies. On Day 1 you form a portfolio to mimic the index. (In other words, to earn the same return as the index.) $$\begin{array} { | c | c | c | c | c | }
\hline & \text { Company 1 } & \text { Company 1 } & \text { Company 2 } & \text { Company 2 } \
\hline \text { Day } & \text { Price } & \text { \# of Shares } & \text { Price } & \text { \# of Shares } \
\hline 1 & \$ 6.62 & 200 & \$ 10.00 & 750 \
\hline \mathbf { 2 } & \$ 7.24 & 200 & \$ 10.54 & 750 \
\hline
\end{array}$$ What is the portfolio weight on Company 1, and what is the return on the portfolio from Day 1 to Day 2? (Weight %, Return %)
A)14%, 5%
B)14%, 6%
C)15%, 6%
D)15%, 7%
E)16%, 5%

Question

Consider a value-weighted market index that includes the following two companies. On Day 1 you form a portfolio to mimic the index. (In other words, to earn the same return as the index.) $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Company 1 } & \text { Company 1 } & \text { Company 2 } & \text { Company 2 } \
\hline \text { Day } & \text { Price } & \text { \# of Shares } & \text { Price } & \text { \# of Shares } \
\hline 1 & \$ 6.62 & 200 & \$ 10.00 & 750 \
\hline \mathbf { 2 } & \$ 7.24 & 200 & \$ 10.54 & 750 \
\hline
\end{array}$$ What is the portfolio weight on Company 1, and what is the return on the portfolio from Day 1 to Day 2? (Weight %, Return %)
A)14%, 5%
B)14%, 6%
C)15%, 6%
D)15%, 7%
E)16%, 5%

Quizplus · Accepted Answer

The market value of Company 1 on Day 1 is $6.62 * 200 = $1,324, and for Company 2, it is $10.00 * 750 = $7,500. The total market value is $1,324 + $7,500 = $8,824. The weight of Company 1 is $1,324 / $8,824 = 15%. The portfolio return is calculated by the change in total market value from Day 1 to Day 2: (($7.24 * 200 + $10.54 * 750) - $8,824) / $8,824 = 6%.

Consider a Value-Weighted Market Index That Includes the Following Two