You own a portfolio which is valued at $12.0 million and which has a beta of 1.35. You would like to create a riskless portfolio by hedging with S&P 500 futures
contracts. The contract size is $250 times the index level. How many futures
contracts are needed if the current S&P 500 index is 3983?

16 S&P 500 futures contracts

Explanation:

The number of contracts can be calculated by:

= (1 * beta) × Stock value/(Contract size * Index level)

= 1.35 × 12,000,000 / ( 250 * 3,983)

= 1.35 × 12,000,000 / ‭995,750‬

= 16 S&P 500 futures contracts

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