You manage a $$42$ million portfolio, currently all invested in equities, and believe that the market is on the verge of a big but shortlived downturn. You would move your portfolio temporarily into T$-$bills, but you do not want to incur the transaction costs of liquidating and reestablishing your equity position. Instead, you decide to temporarily hedge your equity holdings with E$-$mini S&P $500$ index futures contracts.

Required:

a$.$ Should you be long or short the contracts?

b$.$ If your equity holdings are invested in a market$-$index fund, into how many contracts should you enter? The S&P $500$ index is now at $3,800$ and the contract multiplier is $$50.$

Note: Round your answer to $1$ decimal place.

c$.$ How does your answer to part $($b$)$ change if the beta of your portfolio is $0\mathrm{.}5?$

Note: Round your intermediate calculations and final answer to $1$ decimal place.

$\backslash$table$[[$a$.$ Should you be long or short the contracts?$],[$b$.$ Number of contracts$],[$c$.$ Number of contracts$]]$