The S&P index is currently is at 2,024. You manage a $5 million indexed equity p

Question

The S&P index is currently is at 2,024. You manage a $5 million indexed equity portfolio (Therefore, the beta of this portfolio is 1, same as the Market) The S&P 500 futures contract has a multiplier of 250.

a) If you are bearish on the stock market, how many contracts should you sell at 2,150 to fully eliminate your risk over the next 6 months?

b) How would your hedging strategy change if instead of holding an indexed portfolio, you hold a portfolio of socks with a beta of 1.5? How many contracts would now choose to sell? Would your hedged position be riskless?

Explanation / Answer

Part A)

The number of contracts can be calculated as follows:

Number of Contracts = Portfolio Value/(Selling Price*Mulitplier Factor)

Here, Portfolio Value = $5,000,000, Selling Price = $2,150 and Multiplier Factor = 250

Using these values in the above formula, we get,

Number of Contracts = 5,000,000/(2,150*250) = 9.30 or 10 Contracts

_________

Part B)

The number of contracts can be calculated with the use of following formula:

Number of Contracts = (Portfolio Value*Beta)/(Selling Price*Mulitplier Factor)

Here, Portfolio Value = $5,000,000, Beta = 1.50, Selling Price = $2,150 and Multiplier Factor = 250

Using these values in the above formula, we get,

Number of Contracts = (5,000,000*1.50)/(2,150*250) = 13.95 or 14 Contracts

Yes, by selling 14 contracts, the hedged position would be riskless.

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