Question $1(30$ points$)$

Discuss whether each of following statements is true or false and WHY.

a$.$ Suppose all the assumptions of the Capital Asset Pricing Model hold, we can show that

a well$-$diversified portfolio's return $r_p$ and its ${}_p$ satisfies

$E(r_p)-r_f={}_p(E(r_m)-r_f),$

where $r_m$ is the market portfolio's return and $r_f$ is the risk$-$free rate. $(10$ points$)$

b$.$ Suppose there is no arbitrage in the financial market, we can show that a particular

stock's return $r_i$ and its ${}_i$ satisfies

$E(r_i)-r_f={}_i(E(r_m)-r_f),$

where $r_m$ is the market portfolio's return and $r_f$ is the risk$-$free rate. $(10$ points$)$

c$.$ Consider the equity carve$-$outs example $($i$.$e$.,3$ Com and Palm case$),$ one of the reasons

why the law of one price fails is the difficulty of purchasing the child company Palm's shares.

$(10$ points$)$