The table below shows the daily closing values of the Dow Jones Industrial Average $($DJIA$),$ along with the daily prices for the DJIA futures contract with maturity date November $15$ of the same year. The futures contract size is $$10$ times the DJIA index value.

$\backslash$table$[[,$DJIA Index,DJIA Futures Price$],[$Sep $10,35,500,35,480],[$Sep $11,35,800,35,770],[$Sep $12,35,600,35,580]]$

The initial margin required for the futures contract is $$15,000$ per contract. The maintenance margin is $$12,000$ per contract. The risk$-$free rate is $1\mathrm{.}5\%$ per year $($continuously compounded$).$ Assume this is the rate you earn on your margin account.

$($a$)$ Suppose you take a long position in $5$ futures contracts on Sep $10.$ What is your profit$/$loss on Sep $11$ and Sep $12?$ What is the balance in your margin account at the end of each of these days? Do you face any margin calls?

$($b$)$ Repeat part $($i$)$ for a short position of $2$ futures contracts.

$($c$)$ Using the Sep $12$ index value and futures price, what is the implied dividend yield on the DJIA? $($There are $64$ days in total between Sep $12$ and Nov $15.)$

$1$

$($d$)$ For the three days shown, the index value is larger than the futures price. Why?