P$.14$ An investor holding a portfolio consisting of two stocks invests $25\%$ of assets in Stock

A and $75\%$ into Stock B$.$ The return $R_A$ from Stock A has a mean of $4\%$ and a standard

deviation of ${}_A=8\%.$ Stock B has an expected return $E(R_B)=8\%$ with a standard

deviation of ${}_B=12\%.$ The portfolio return is $P=0\mathrm{.}25R_A+0\mathrm{.}75R_B.$

$($a$)$ Compute the expected return on the portfolio.

$($b$)$ Compute the standard deviation of the returns on the portfolio assuming that the

two stocks' returns are perfectly positively correlated.

$($c$)$ Compute the standard deviation of the returns on the portfolio assuming that the

two stocks' returns have a correlation of $0\mathrm{.}5.$

$($d$)$ Compute the standard deviation of the returns on the portfolio assuming that the

two stocks' returns are uncorrelated.