The following is part of the computer output from a regresslon of monthly returns on Waterworks stock agalnst the S&P $500$ Index. A hedge fund manager belleves that Waterworks Is underpriced, with an alpha of $24\%$ over the coming month.

$\backslash$table$[[$Beta$,$R$-$square,Standard Deviation$],[0\mathrm{.}7,0\mathrm{.}65,0\mathrm{.}13$ of Residuals$],[,0.,1..13\%$ monthy$),]]$

a$-1.$ If he holds a $$5$ million portfollo of Waterworks stock, and wishes to hedge market exposure for the next month using $1-$month maturity S&P $500$ futures contracts, how many contracts should he enter? The S&P $500$ currently is at $1,000$ and the contract multiplier is $$250.$

$\backslash$table$[[$Number of contracts,$14]]$

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

Buy

Sell

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

Standard deviation

C$.$ Assuming that monthly returns are' approximately normally distributed, what is the probability that thls market$-$neutral strategy will lose money over the next month? Assume the risk$-$free rate is $0\mathrm{.}2\%$ per month. $($Enter your answer as percent rounded to $2$ decimal places, e$\mathrm{.}9.$ enter $"1253\%"$ and not $"0\mathrm{.}1253.")$

Probability