$\begin{array}{|l|r|r|rr}
\hline& \text { Expected Return } & \begin{array}{r}
\text { Standard Deviation of } \
\text { Return }
\end{array} &{\text { Correlation }} \
& & & \text { Coefficients } \
& & & \text { X }& \text {Y} \
\hline \text { Canadian Stock X } & 6 \% & 9 \% & 1.00 & \
\hline \text { American Stock Y } & 4 \% & 8 \% & 0.80 & 1.00\
\hline
\end{array}$

A Canadian plans to buy 100 shares of this American stock for US $20 per share. The current spot rate is C$1.2977 = US $1. Suppose that this investor can sell the stock for US $30 a share a year later. The spot rate at the time of the sale is C$1.3029 = US $1.
-What is the standard deviation of a portfolio if each stock has a 50% weight?

Question

$\begin{array}{|l|r|r|rr} 
\hline& \text { Expected Return } & \begin{array}{r}
\text { Standard Deviation of } \
\text { Return }
\end{array} &{\text { Correlation }} \
& & & \text { Coefficients } \
& &  & \text { X }& \text {Y} \
\hline \text { Canadian Stock X } & 6 \% & 9 \% & 1.00 & \
\hline \text { American Stock Y } & 4 \% & 8 \% & 0.80 & 1.00\
 \hline
\end{array}$

A Canadian plans to buy 100 shares of this American stock for US $20 per share. The current spot rate is C$1.2977 = US $1. Suppose that this investor can sell the stock for US $30 a share a year later. The spot rate at the time of the sale is C$1.3029 = US $1.
-What is the standard deviation of a portfolio if each stock has a 50% weight?

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio can be calculated using the formula: $\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho_{1,2}}$, where $w_1$ and $w_2$ are the weights of the two assets in the portfolio, $\sigma_1$ and $\sigma_2$ are the standard deviations of the returns of the two assets, and $\rho_{1,2}$ is the correlation coefficient between the returns of the two assets. Given that each stock has a 50% weight, the standard deviation of the portfolio is calculated as $\sqrt{0.5^2 * 0.09^2 + 0.5^2 * 0.08^2 + 2 * 0.5 * 0.5 * 0.09 * 0.08 * 0.8} = 8.00\%$.

A Canadian Plans to Buy 100 Shares of This American