Consider two assets for which $\backslash$sigma $1=0\mathrm{.}10$ and $\backslash$sigma $2=0\mathrm{.}20.$ If I allocate $100$w$\%$ of my wealth to the first asset, then the variance of my portfolio return is

$\backslash$sigma $2($w$)=0\mathrm{.}01$w$2+0\mathrm{.}04(1$ w$)2+0\mathrm{.}04$w$(1$ w$)\backslash$rho $,$

where $\backslash$rho is the correlation between the returns. I am not able to take short positions.

$($a$)$ Sketch the graph of $\backslash$sigma $2($w$)$ in the case $\backslash$rho $=0.$ Clearly label any important points. $($b$)$ Sketch the graph of $\backslash$sigma $2($w$)$ in the case $\backslash$rho $=0\mathrm{.}6.$ Clearly label any important points.

$($c$)$ Comment on the important differences between your graphs from $($a$)$ and $($b$).$