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.)
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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