In this question, we examine the economic implication of a lock$-$up period that prevents a large shareholder from selling his shares in a given time period. We assume that the market expected return rm $=10\%$ with a standard deviation$=15\%.$ The risk$-$free rate is rf $=2\%.$ The correlation between Adora and the market is$=0\mathrm{.}5$ with a standard deviation of $30\%.$ As one of the founders you hold all your wealth, $5$M$,$ in Adora shares. You have committed not to sell your Adora shares during the upcoming year.

$($a$)$ Based on CAPM, what is the expected wealth you will have one year from now and what is the standard deviation?

$($b$)$ Based on CAPM, what is the highest expected return you can achieve for the same risk level as your holdings?

$($c$)$ Based on parts $($a$)$ and $($b$),$ what is the economic cost of the restriction of not selling your Adora shares?

Hint: The economic cost can be calculated based on the amount of money that if

invested efficiently would generate the same outcome.

$($d$)$ Redo part $($c$),$ assuming that in addition to your Adora holdings you have $5$M invested in the market portfolio.

$($e$)$ Provide an intuitive explanation for the finding in part $($c$)$ as compared to part $($b$).$