Obtain closing price and rate information from Thursday, May $16.$ Please consult the WSJ and$/$or CME website for data.

$1.$ Pricing Stock Index Futures

$($A$)$ Compute the annual dividend yield implied in the pricing of the Sept. $2024$ E$-$mini S&P $500$ stock index futures. Assume the contract expires on the third Friday of the maturity month. $($Use the $3-$month SOFR term rate to proxy the financing rate and use an Actual$/360$ day count.$)$

$($B$)$ Regardless of your answer in $($A$),$ assume that the actual dividend yield is $4\mathrm{.}0\%$ for the S&P $500$ index.

i$)$ Calculate the theoretical equilibrium futures price for the Sept $2024$ E$-$mini S&P $500$ stock index futures contract.

ii$)$ What is the amount of mispricing $($that is$,$ what is the difference between the actual reported and theoretical futures price$)?$

iii$)$ Show in detail the necessary steps to conduct the arbitrage.

$($C$)$ Repeat part $($B$)$ assuming instead a dividend yield of $0\mathrm{.}50\%.$