You manage a $$20\mathrm{.}5$ 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.

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

Short

Long

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 $$4100$ and the contract multiplier is $50.$

$$ Number of contracts

c$.$ How many contracts should you enter into if the beta of your portfolio is $0\mathrm{.}6?$

Number of contracts