Ihe 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 $1\%$ over the coming month.

Required:

a$-1.$ If he holds a $$9\mathrm{.}2$ million portfolio 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 at $2,000$

and the contract multiplier is $$50.$

Number of contracts

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

Buy

Sell

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 $1\mathrm{.}0\%$ per month. $($Do not round intermediate calculations.

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