Here are some characteristics of two securities:

Security $1$ E$[$R$1]=\mathrm{.}10$ $1=\mathrm{.}05$

Security $2$ E$[$R$2]=\mathrm{.}16$ $2=\mathrm{.}08$

Answer the following questions:

$($a$)$ Which security should an investor choose if she wants to $($i$)$ maximize expected

returns, $($ii$)$ minimize risk $($assume the investor cannot form a portfolio$)?$

$($b$)$ Suppose the correlation of returns on the two securities is $+1\mathrm{.}0.$ What is the op$-$

timal portfolio of securities $1$ and $2$ for an investor whose objective is to minimize

risk. Assume that short sales are not allowed?

$($c$)$ Suppose the correlation of returns is $-1\mathrm{.}0.$ What weights should the investor put

on these two securities to get a portfolio that has zero risk?

$($d$)$ What is the expected return on the portfolio in $($c$)?$ Suppose the yield on Treasury

bills, i$.$e$.,$ the riskless rate, is $10\%.$ Describe how you would create an arbitrage?