The $($annual$)$ expected return and standard deviation of returns for $2$ assets are as follows:

The correlation between the returns is $0\mathrm{.}15.$

a$.$ Calculate the expected returns and standard deviations of the following portfolios:

$($i$)80\%$ in $A,20\%$ in $B$

$($ii$)50\%$ in $A,50\%$ in $B$

$($iii$)20\%$ in $A,80\%$ in $B$

b$.$ Find the weights for a portfolio with an expected return of $25\%?$ What is the

standard deviation of this portfolio?

c$.($Difficult$)$ Find the weights for a portfolio with the same standard deviation as

asset A but a higher expected return? $($Trial and error may be a viable strategy;

however, there is an analytical solution.$)$ What is the expected return of this

portfolio?

d$.($Optional$)$ What is the correlation between the returns on the portfolios in parts

a$($i$)$ and a$($iii$)?($Recall that the correlation is the covariance divided by the product

of the standard deviations.$)$