e$)$ Should firm B$\text{'}$s shareholders vote against the new project and WHY?

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

$a.$ It is due to the noise trader risk that the stock price of a company goes up when

it drops from Russell $1000$ index to Russell $2000$ index. $(10$ 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.

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 short selling Palm's shares.

d$.$ The Siamese Twin Companies of Royal Dutch and Shell is an example of risk$-$

free arbitrage.