Assume that the data below apply to two efficient portfolios.

Portfolio R$$

i $\backslash$sigma i

A $10\%6\%$

B $8\%4\%$

$\backslash$rho ij $=+5$

$6$

$($a$)$ What is the efficient frontier? Derive it analytically and sketch it in the mean$-$variance

plan.

$($b$)$ Suppose now there is a riskless asset with Rf $=2\%,$ valid for both deposit and borrowing.

What would then be the efficient frontier?

$($c$)$ How would you change your answers to $($a$)-($b$)$ if short$-$selling if forbidden or limited a la

Lintner? Explain and consider both:

$($i$)$ the case when the portfolios A and B are still feasible.

$($ii$)$ the case when at least one of the portfolios, A or B$,$ is no longer feasibl