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 $2\%$ over the coming month.

Required:

a$-1.$ If he holds a $$8\mathrm{.}0$ million portfollo of Waterworks stock and wishes to hedge market exposure for the next month using one$-$month

maturity S&P $500$ futures contracts, how many contracts should he enter? The S&P $500$ currently is ot $2\mathrm{.}000$ and the contract

multiplier is $$50.$

a$-2.$ Should he buy or sell contracts?

Buy

Sell

$S$

b$.$ Assuming that monthly returns are approximately normally distributed. what is the probability that this market$-$neutral strategy will

lose money over the next month? Assume the risk$-$free rate is $0\mathrm{.}7\%$ per month. $($Do not round intermediate calculations. Round your

percentage answer to $2$ decimal places.$)$