Suppose that there exist two securities $($X and Y$)$ with an annual expected return equal to rx $=8\%$ and ry $=5\%$ and a standard deviation equal to $\backslash$sigma x $=9\%$ and $\backslash$sigma y$=6\%,$ respectively. The correlation coefficient between the returns of these securities is $\backslash$rho $=-0\mathrm{.}8.$

Suppose that there exist two securities and $Y)$ with an annual expected return equal to $r_x=8\%$ and $r_y=5\%$ and a standard deviation equal to ${}_x=9\%$ and ${}_y=6\%,$ respectively. The correlation coefficient between the returns of these securities is $=-0\mathrm{.}8.$

$2\mathrm{.}1$ What is the expected return, the variance and the standard deviation of an equally weighted portfolio consisting of the securities $x$ and $Y?$ Describe every step of your calculations in detail.

$2\mathrm{.}2$ What is the expected return of a portfolio consisting of the securities $x$ and $Y,$ if the weights of the corresponding securities are chosen to minimize the risk of the portfolio? Describe every step of your calculations in detail.

$2\mathrm{.}3$ Discuss and critically evaluate the role of the correlation coefficient in the determination of the portfolio risk$-$return profile?