The computer output shows the correlation between the monthly returns of Waterworks stock and the S&P $500$ index. A hedge fund manager has a belief that Waterworks stock is undervalued and expects it to outperform by $2\mathrm{.}4\%$ in the next month. The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P $500$ index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of $2\mathrm{.}4\%$ over the coming month.

a$*1$He has a portfolio of Waterworks stock worth $$2$ million and wants to hedge his market exposure for the next month using $1-$month maturity S&P $500$ futures contracts. He needs to know the number of contracts he should enter. The current value of S&P $500$ is $1,200$ and the contract multiplier is $$250.$

What is the number of contracts?

a$-2.$ Should he buy or sell contracts? already have the answer

b$.$ He possesses Waterworks stock with a valuation of $$2$ million in his portfolio. He intends to mitigate his market exposure for the approaching month by employing S&P $500$ futures contracts with a maturity of $1-$month. He requires assistance in determining the number of contracts to be entered into. The existing value of S&P $500$ stands at $1,200,$ and the contract multiplier is $$250.$ So what is the standard deviation?