How many index futures to hedge a stock book?

Question

You manage a \20 million long equity book with a beta of 1.1 to the S&P 500. You hedge its market exposure with E-mini S&P 500 futures. The index is at 5{,}000 and the contract multiplier is \50 (so one contract represents 5{,}000 	imes 50 = \250{,}000 of index notional). How many futures contracts do you short to neutralize the book's market risk?

Accepted Answer

Beta tells you the book behaves like \beta dollars of index per dollar invested. So its market-equivalent exposure is \beta 	imes 	ext{portfolio value} = 1.1 	imes \20	ext{M} = \22	ext{M of index exposure}. Each contract offsets \250{,}000 of index notional, so the number to short is N = \frac{\beta 	imes 	ext{portfolio value}}{	ext{index} 	imes 	ext{multiplier}} = \frac{22{,}000{,}000}{250{,}000} = 88 	ext{ contracts.} Short 88 E-mini contracts. This zeroes the market (beta) component of the book's risk. What remains is the portfolio's idiosyncratic, stock-specific risk, which the…

How many index futures to hedge a stock book?

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