Problem $3$: Sets of $($Portfolio$)$ Opportunities

Using the formulas for the expected return and the standard deviation of two$-$stock portfolio, complete the following table if securities A and B are: $($i$)$ perfectly positively correlated, $($ii$)$ uncorrelated

and $($iii$)$ perfectly negatively correlated.$$

Assume that E$($rA$)=20\%,\backslash$sigma A $=20\%,$ E$($rB$)=40\%,\backslash$sigma B $=30\%.$

wA wB E$($rP $)\backslash$sigma p$(\backslash$rho $=1)\backslash$sigma p$(\backslash$rho $=0)\backslash$sigma p$(\backslash$rho $=1)$

$100\%0\%$

$90\%10\%$

$80\%20\%$

$70\%30\%$

$60\%40\%$

$50\%50\%$

$40\%60\%$

$30\%70\%$

$20\%80\%$

$10\%90\%$

$0\%100\%$