4.(7 points) The following is part of the computer output from a regression of monthly returns of Waterworks stock against the S&P 500 index monthly returns. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.

Beta

R-square

Standard deviation

0.9

0.5

0.055 (i.e. 5.5% monthly)

(a)(4 points) 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? Should he buy or sell contracts? The S&P 500 currently is at 1,200 and the contract multiplier is $250.

(b)(3 points) What is the annualised standard deviation of the monthly return of the hedged portfolio?