Problem $1$: Stock Pickers

You evaluate two securities$,$ A & B$,$ as potential investment opportunities. The expected return

of stock A is $9\%,$ its standard deviation $10\%$ and its beta value is $0\mathrm{.}8.$ The expected return of stock

B is $15\%,$ its standard deviation $30\%$ and its beta equal to $1\mathrm{.}5.$ The risk free rate is $5\%.$

$1.$ If you are allowed to pick only one stock, which one will it be$?[$Hint: Use the Sharpe Ratio$]$

$2.$ If you are allowed to pick only one stock to add it to your already well$-$diversified portfolio,

then which one will it be$?[$Hint: Use the Treynor Ratio$]$

$3.$ If your picks in $(1)$ and $(2)$ are different, explain the reason.