Question One

Suppose you are thinking of investing in two assets, $x$ and $Y.$ You expect a retum of $2\%$ from asset $x$ and $5\%$ from asset $Y.$ The standard deviation of retums is $1\%$ for $x$ and $4\%$ for $Y.$ The correlation coefficient between the two returns $()$ is $-0\mathrm{.}5.$

$($i$)$ Calculate the expected retum and standard deviation of the following portfolios.

$($ii$)$ Plot the portfolio efficiency frontier.

$($iii$)$ Derive the formula for the minimum variance portfolio weights and calculate the optimal weights for the minimum variance portfolio using the information given. Indicate on your graph the location of the minimum variance portfolio. Explain your results.

$($iv$)$ Discuss the intuition of your results.