$(30$ points $-$ Portfolio Construction$)$ You are constructing a portfolio of two stocks. Suppose each stock has

the following characteristics:

As a reminder, Var$(x)=[SD(x){]}^2$;Cov$(x,Y)=$Corr$(x,Y)SD(x)SD(Y)$; and $SD(x)=\sqrt[\phantom{2}]{\text{V}\text{a}\text{r}(x)}$

$($a$)(4$ points$)$ Find the variance of each stock and the covariance of the two stocks.

$($b$)(15$ points$)$ You have six possible choices for weights in mixing the two stocks.

In each of the weight options, compute the expected return and standard deviation.

$($c$)(5$ points$)$ From each portfolio choice, plot the standard deviation on $x-$axis and expected return on $Y-$

axis. Briefly discuss the graph.

$($d$)(6$ points$)$ Should you consider purchasing only Stock A if you want to minimize your risk? Why or why

not? Explain and support your answers with results.