$\begin{array}{|l|r|r|r}
\hline \text { Asset } & \text { Number of shares } & \text { Initial price (\$) } & \text { End price (\$) } \
\hline \text { A } & 2000 & 6.00 & 6.10 \
\hline \text { B } & 5000 & 3.00 & 2.25 \
\hline \text { C } & 3000 & 12.00 & 11.50 \
\hline \text { D } & 12000 & 8.50 & 8.85 \
\hline
\end{array}$
-An investor purchased the investment above.What is the value-weighted return on the portfolio?
A) $-1.2 \%$
B) $1.2 \%$
C)$2.3 \%$
D) $2.5\%$

Question

Quizplus · Accepted Answer

We must first calculate the continuously compounded return for each of the four shares.Using equation 1.5,page 14,the return for asset A is ln(6.10/6.00)= 0.165,for asset B is ln(2.25/3.00)= -0.288,for asset C is ln(11.50/12.00)= -0.043 and for asset D is ln(8.85/8.5)= 0.040.The total value of the portfolio is (2000 F1F1F1S1F1F1F10 6.00 + 5000 F1F1F1S1F1F1F10 3.00 + 3000 F1F1F1S1F1F1F10 12.00 + 12000 F1F1F1S1F1F1F10 8.50)= 165000.The value weights for each of the assets A,B,C and D,respectively,are for asset A (2000 F1F1F1S1F1F1F10 6.00)/165000 = 0.073,for asset B = (5000 F1F1F1S1F1F1F10 3.00)/165000 = 0.091,for asset C = (3000 F1F1F1S1F1F1F10 12.00)/165000 = 0.218 and for asset D = (12000 F1F1F1S1F1F1F10 8.50)/165000 = 0.618.Using equation 1.14,page 22,the value-weighted return is calculated as R = (0.073)(0.165)+ (0.091)(-0.288)+ (0.218)(-0.043)+ (0.618)(0.040)= 0.012 or 1.2%.

-An Investor Purchased the Investment Above −1.2%-1.2 \%−1.2% B) 1.2%1.2 \%1.2%

-An Investor Purchased the Investment Above $-1.2 \%$ B) $1.2 \%$