$($a$)$ For each of stock $1$ and stock $2,$ calculate expected return and variance of returns. Calculate the

covariance and correlation between the returns on stock $1$ and stock $2.$ Detail all calculations.

$($b$)$ For each of stock $1$ and stock $2,$ calculate alpha and beta. Detail all calculations.

$($c$)$ Use the single index model to calculate systematic and unsystematic risk for each of stock $1$ and

stock $2.$ Detail all calculations.

$($d$)$ Form an equally$-$weighted portfolio of stocks $1$ and $2.$ Using the single index model, what is the

expected return and standard deviation risk of this portfolio? Detail all calculations.