Suppose Einar Aas $($who is that?$)$ buys $200$ shares of Nordic Power Corp. at $$60$ each.

The clearinghouse NASDUCK sets a margin requirement of $30\%$ and charges an interest

rate of $r=5\%$ on the loan for purchasing the shares.

$($a$)$ How much cash does Einar need to invest?

$($b$)$ Calculate the margin call of NASDUCK if the price falls to $$55.$

$($c$)$ What is the return for Einar on the transaction after the price decline?

$($d$)$ How is the return on equity influenced by a change in the interest rate $r?$ Does your

answer depend on the size of the margin requirement? $[$Hint: For this sensitivity

analysis use a derivative with respect to $r$ and, then, $m.]$

Suppose that instead Einar short sells $200$ shares of German Power Weak Inc. at $$60$

each. NASDUCK now sets a margin requirement of $30\%.$

$($e$)$ How much cash does Einar need to invest?

$($f$)$ Calculate the margin call of NASDUCK if the price increases to $$65.$

$($g$)$ Suppose the price falls to $$55.$ How much cash can Einar take out from his margin

account?

$($h$)$ Suppose he takes out $50\%$ of the amount in part $($g$).$ At what price threshold will

Einar face a margin call by NASDUCK?