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 2% over the coming month.

		Standard Deviation
Beta	R-square	of Residuals
0.75	0.65	0.06 (i.e., 6% monthly)

a-1. If he holds a $6 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 0.5% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a1. Contract = Value of Portfolio * Beta / (S&P Current Price * Multiplier)

Contract = 6000000 * 0.75 / (2000 * 50)

Contract = 45 Contracts

a2. we already have a portfolio of assets as a manager we might fear that the value of portfolio might get reduced thus we will enter into sell future contracts to protect against value reduction

b. Expected return = Risk free rate + Alpha = 0.50% + 2% = 2.50%

Probability of loss = NormsDist(return in loss - expected Return) / Standard deviation

Probability of loss = NormsDist((0 - 2.50%) / 6)

Probability of loss = 33.83% or 0.33

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