The followng 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 belleves that Waterworks Is underpriced, wth an alpha of $24\%$ over the coming month.

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

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

Number of contracts

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

Buy

Sell

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

Standard deviation

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 $0\mathrm{.}2\%$ per month. $($Enter your answer as percent rounded to $2$ decimal places, e$\mathrm{.}9.$ enter $"1253\%"$ and not $"01253.")$

Probability