You manage a $$15\mathrm{.}2$ million portfolio, currently all invested in equities, and believe that the market is on the verge of a big but short$-$lived 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.

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

multiple choice

Long

Short

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 $1,126$ and the contract multiplier is $$250.($Round your answer to $1$ decimal place.$)$

c$.$ How does your answer to part $($b$)$ change if the beta of your portfolio is $0\mathrm{.}4?($Round your intermediate calculations and final answer to $1$ decimal place.$)$