$($ Investment Management $)($ Finance$)$

$MRY$ can invest $in$ two financial $securities,$ security A and security $B.$ The table below gives $a$

description $of$ the states $of$ the world, their respective probabilities, and the return $of$ each security

$in$ each state.

$a.$ Compute the expected return and the standard deviation $of$ returns $of$ a portfolio which

places weight $30\%in$ security A and $70\%in$ security $B.$

$b.If$ the risk$-$free interest rate $isRF=2\%,$ estimate the optimal risky portfolio for the investor

when short sales are allowed. Calculate the expected return and standard deviation $of$

the optimal risky portfolio.

$c.$ Suppose that there $is$ a third security, security $C.$ Its return $is-10\%$ when the market $is$

Bear, and $10\%$ when the market $is$ normal. When the market $is$ Bull, security $C$ has $50\%$

chance $to$ give a return $of20\%$ and $50\%to$ give a return $of100\%.$ Find the optimal risky

portfolio for $MRY,$ when $he$ can invest $insecuritiesA,B,$ and $C$ and short sales are

allowed. Calculate the expected return and standard deviation $of$ the optimal risky

portfolio.