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 $2\mathrm{.}3\%$ over the coming month.

Beta R$-$square Standard Deviation

of Residuals

$0\mathrm{.}50\mathrm{.}650\mathrm{.}09($i$.$e$.,9\%$ monthly$)$

a$-1.$ If he holds a $$3$ million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using $1-$month maturity S&P $500$ futures contracts, how many contracts should he enter? The S&P $500$ currently is at $600$ and the

contract multiplier is $$250.$

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

multiple choice

Buy

Sell

b$.$ What is the standard deviation of the monthly return of the hedged portfolio?

c$.$ 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 $0\mathrm{.}5\%$ per month. $($Enter your answer as percent rounded to $2$ decimal places, e$.$g$.,$ enter $"12\mathrm{.}53\%"$ and not $"0\mathrm{.}1253.")$