In January $1$st $2020$ you realise airline travel will be heavily restricted so that the stock of$,$ say, Delta airlines will go down.

$($a$)$ How can you build a short$-$sale to profit fom this? $2$

$($b$)$ Assume your broker agrees to a short$-$sale, she lends you $$50,000$ in Delta stock on January $1$st $2020,$ you need to put up $3\%$ of additional collateral at the broker for a deposit. The yearly risk$-$free rate on this deposit is $0\mathrm{.}2\%.$ Delta Airlines stock price went from about $$59$ to $$40$ during $2020.$ Delta$$s dividend yield in $2020$ is about $4\%($roughly speaking this is the ratio of the dividend paid during the year divided by the initial stock price$).$ How much money did your investment yield if you close the position on January $1$st $2021?$

$($c$)$ Let$$s say that in a parallel world you made the same bet but you got it wrong, in fact covid$-19$ turned out to be just a flu $($as many were saying in early $2020$ in our world$),$ no air travel restrictions happened, and Delta stock went up by $3\%$ same dividend yield in one year. What would be the return of your investment?