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Hedging with Futures

A hedge replaces price risk with basis risk. That trade is usually worth making, and understanding what remains is as important as the hedge itself.

Computing the number of contracts

For an exposure of value VV hedged with a contract of notional NN:

n=β×VNn = \beta \times \frac{V}{N}

The β\beta term adjusts for the fact that your exposure and the hedge instrument do not move one-for-one. Omit it and you are assuming they do.

Worked example: hedging a $5m book with E-minis

A $5m equity portfolio with β=1.2\beta = 1.2 to the S&P 500. The E-mini contract is $50 times the index, so at 5,000 index points one contract is $250,000 notional.

n=1.2×5,000,000250,000=24 contracts, soldn = 1.2 \times \frac{5{,}000{,}000}{250{,}000} = 24 \text{ contracts, sold}

Drop beta to 1.0 and the hedge falls to 20 contracts, leaving a fifth of the market exposure unhedged on a book that moves 20% more than the index. That gap is the entire reason the beta term is there.

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