Question

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 1% over the coming month. Standard Deviation Beta R-square of Residuals 0.75 0.65 0.03 (i.e., 3% monthly) a-1.

If he holds a $11.2 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.

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 0.6% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solution :-

(A - 1 )

Number of future contracts that should be shorted to hedge the portfolio =

= ( Portfolio Value * Beta ) / ( Index * Contract Multiplier )

= ( $11,200,000 * 0.75 ) / ( 2,000 * $50 )

= 84 Contracts

(A - 2)

He Should Sell Contracts .

( B )

Expected return of the market = Alpha + Rf = 1% + 0.6% = 1.6% per month

Now the Z Value for a rate of return Zero

Z = - 1.6% / 3.00% = - 0.5333

N ( - 0.5333 ) = 0.2969 = 29.69%

Probability = 29.69%

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